Functionally gradient materials (FGM) are one of the most widely used materials in various
applications because of their adaptability to different situations by changing the material constituents as per the
requirement. Most structural components used in the field of engineering can be classified as beams, plates, or
shells for analysis purposes. In the present study the power law, sigmoid and exponential distribution is
considered for the volume fraction distributions of the functionally graded plates. The work includes parametric
studies performed by varying volume fraction distributions and boundary conditions. Also static analysis of
functionally gradient material plate is carried out by sigmoid law and verified with the published results. The
convergence study of the results is optimized by changing the mesh size and layer size. Power law and
exponential law are applied for the same material and set of conditions.
Analysis of buckling behaviour of functionally graded platesByju Vijayan
1. The document discusses the buckling behavior of functionally graded plates through two case studies.
2. The first case study analyzes the buckling of simply supported functionally graded rectangular plates under non-uniform in-plane compressive loading using classical plate theory. It finds that the critical buckling coefficient increases with the power law index and aspect ratio.
3. The second case study examines the buckling of imperfect functionally graded plates under in-plane compressive loading. It determines that the critical buckling load depends on factors like the load ratio, power law index, and amplitude of imperfection.
This document outlines a student's workplan to study the fracture of functionally graded materials. The plan includes conducting a literature review to identify gaps and objectives, modeling the material and analyzing it using software, performing parametric studies on properties like reinforcement size and volume fractions, and submitting a final report. Experimental results are also presented on a photoelastic model that show stress distributions and crack propagation under loading. Numerical finite element modeling is found to match the experimental photoelastic results to within 5-8 percent.
Material Parameter and Effect of Thermal Load on Functionally Graded CylindersIJMER
The present study investigates the creep in a thick-walled composite cylinders made
up of aluminum/aluminum alloy matrix and reinforced with silicon carbide particles. The distribution
of SiCp is assumed to be either uniform or decreasing linearly from the inner to the outer radius of
the cylinder. The creep behavior of the cylinder has been described by threshold stress based creep
law with a stress exponent of 5. The composite cylinders are subjected to internal pressure which is
applied gradually and steady state condition of stress is assumed. The creep parameters required to
be used in creep law, are extracted by conducting regression analysis on the available experimental
results. The mathematical models have been developed to describe steady state creep in the composite
cylinder by using von-Mises criterion. Regression analysis is used to obtain the creep parameters
required in the study. The basic equilibrium equation of the cylinder and other constitutive equations
have been solved to obtain creep stresses in the cylinder. The effect of varying particle size, particle
content and temperature on the stresses in the composite cylinder has been analyzed. The study
revealed that the stress distributions in the cylinder do not vary significantly for various combinations
of particle size, particle content and operating temperature except for slight variation observed for
varying particle content. Functionally Graded Materials (FGMs) emerged and led to the development
of superior heat resistant materials.
Thermal analysis of FGM plates using FEM methodRajani Dalal
The document describes an M. Tech dissertation presentation on using finite element analysis to model the thermal behavior of functionally graded material plates. It discusses the objectives of analyzing FGM plates through literature review, developing a finite element computer code, and determining temperature profiles to compare with conventional materials. The introduction defines FGMs as composites with continuously varying material properties through the thickness to reduce stresses and improve bonding between dissimilar materials like ceramics and metals.
Stress Analysis of Functionally Graded Disc Brake Subjected To Mechanical Loa...IJMER
This document analyzes the stress on functionally graded disc brakes subjected to mechanical loading. It models disc brakes with 40, 50, and 60 holes made of cast iron, FGM 1 (Al2O3-Al), and FGM 2 (Zr-Al). It finds that FGMs experience lower stress than cast iron. FGM 2 experiences lower stress than FGM 1. Stress increases with more holes and higher material variation parameter k. Displacement is highest for cast iron and increases with k for FGM 1 more than FGM 2. Thermal flux also increases with k and is highest for FGM 2 due to its higher conductivity. In conclusion, FGM 2 performs better than FGM 1 and
Thermal Resistance Approach to Analyze Temperature Distribution in Hollow Cyl...S M Shayak Ibna Faruqui
Thermal Resistance Approach to Analyze Temperature Distribution in Hollow Cylinders Made of Functionally Graded Material (FGM): Under Dirichlet Boundary Condition
The document proposes a thermal resistance approach (TRA) to analyze the temperature distribution in hollow cylinders made of functionally graded materials (FGMs) under Dirichlet boundary conditions. The TRA models the FGM cylinder as a thermal resistance network to bypass the non-linearity introduced by the power-law variation of thermal conductivity. Results from the TRA are found to match previous analytical and numerical solutions with less than 0.000012% average error. The TRA can determine temperature profiles for any material gradient distribution and provides insights into tailoring material gradients for desired temperature or stress fields.
This research article analyzes the static response of functionally graded material (FGM) plates under transverse loads for varying aspect ratios. FGM plates are modeled with power law, sigmoid law, and exponential distributions for the volume fraction. Finite element analysis is performed in ANSYS to model FGM plates with 16 layers. Parameters such as volume fraction distribution and aspect ratio are varied. The FGM plate is subjected to uniform and point loads, and the response is analyzed. Results provide insight into how the varying material properties of FGMs impact their structural response under different loading and geometric conditions.
Static and Transient Vibrational Analysis of Functionally Graded MaterialIRJET Journal
This document discusses static and transient vibrational analyses of functionally graded materials (FGMs) using finite element modeling. FGMs are composite materials with continuous variation of material properties, such as a ceramic-metal mixture. The analyses examine deflection, vibration frequencies, and transient response of FGM plates and shells under mechanical and thermal loads. Results show the material gradient and volume fractions significantly impact structural response. Finite element modeling using first-order shear deformation theory is employed to efficiently analyze the functionally graded structures.
Analysis of buckling behaviour of functionally graded platesByju Vijayan
1. The document discusses the buckling behavior of functionally graded plates through two case studies.
2. The first case study analyzes the buckling of simply supported functionally graded rectangular plates under non-uniform in-plane compressive loading using classical plate theory. It finds that the critical buckling coefficient increases with the power law index and aspect ratio.
3. The second case study examines the buckling of imperfect functionally graded plates under in-plane compressive loading. It determines that the critical buckling load depends on factors like the load ratio, power law index, and amplitude of imperfection.
This document outlines a student's workplan to study the fracture of functionally graded materials. The plan includes conducting a literature review to identify gaps and objectives, modeling the material and analyzing it using software, performing parametric studies on properties like reinforcement size and volume fractions, and submitting a final report. Experimental results are also presented on a photoelastic model that show stress distributions and crack propagation under loading. Numerical finite element modeling is found to match the experimental photoelastic results to within 5-8 percent.
Material Parameter and Effect of Thermal Load on Functionally Graded CylindersIJMER
The present study investigates the creep in a thick-walled composite cylinders made
up of aluminum/aluminum alloy matrix and reinforced with silicon carbide particles. The distribution
of SiCp is assumed to be either uniform or decreasing linearly from the inner to the outer radius of
the cylinder. The creep behavior of the cylinder has been described by threshold stress based creep
law with a stress exponent of 5. The composite cylinders are subjected to internal pressure which is
applied gradually and steady state condition of stress is assumed. The creep parameters required to
be used in creep law, are extracted by conducting regression analysis on the available experimental
results. The mathematical models have been developed to describe steady state creep in the composite
cylinder by using von-Mises criterion. Regression analysis is used to obtain the creep parameters
required in the study. The basic equilibrium equation of the cylinder and other constitutive equations
have been solved to obtain creep stresses in the cylinder. The effect of varying particle size, particle
content and temperature on the stresses in the composite cylinder has been analyzed. The study
revealed that the stress distributions in the cylinder do not vary significantly for various combinations
of particle size, particle content and operating temperature except for slight variation observed for
varying particle content. Functionally Graded Materials (FGMs) emerged and led to the development
of superior heat resistant materials.
Thermal analysis of FGM plates using FEM methodRajani Dalal
The document describes an M. Tech dissertation presentation on using finite element analysis to model the thermal behavior of functionally graded material plates. It discusses the objectives of analyzing FGM plates through literature review, developing a finite element computer code, and determining temperature profiles to compare with conventional materials. The introduction defines FGMs as composites with continuously varying material properties through the thickness to reduce stresses and improve bonding between dissimilar materials like ceramics and metals.
Stress Analysis of Functionally Graded Disc Brake Subjected To Mechanical Loa...IJMER
This document analyzes the stress on functionally graded disc brakes subjected to mechanical loading. It models disc brakes with 40, 50, and 60 holes made of cast iron, FGM 1 (Al2O3-Al), and FGM 2 (Zr-Al). It finds that FGMs experience lower stress than cast iron. FGM 2 experiences lower stress than FGM 1. Stress increases with more holes and higher material variation parameter k. Displacement is highest for cast iron and increases with k for FGM 1 more than FGM 2. Thermal flux also increases with k and is highest for FGM 2 due to its higher conductivity. In conclusion, FGM 2 performs better than FGM 1 and
Thermal Resistance Approach to Analyze Temperature Distribution in Hollow Cyl...S M Shayak Ibna Faruqui
Thermal Resistance Approach to Analyze Temperature Distribution in Hollow Cylinders Made of Functionally Graded Material (FGM): Under Dirichlet Boundary Condition
The document proposes a thermal resistance approach (TRA) to analyze the temperature distribution in hollow cylinders made of functionally graded materials (FGMs) under Dirichlet boundary conditions. The TRA models the FGM cylinder as a thermal resistance network to bypass the non-linearity introduced by the power-law variation of thermal conductivity. Results from the TRA are found to match previous analytical and numerical solutions with less than 0.000012% average error. The TRA can determine temperature profiles for any material gradient distribution and provides insights into tailoring material gradients for desired temperature or stress fields.
This research article analyzes the static response of functionally graded material (FGM) plates under transverse loads for varying aspect ratios. FGM plates are modeled with power law, sigmoid law, and exponential distributions for the volume fraction. Finite element analysis is performed in ANSYS to model FGM plates with 16 layers. Parameters such as volume fraction distribution and aspect ratio are varied. The FGM plate is subjected to uniform and point loads, and the response is analyzed. Results provide insight into how the varying material properties of FGMs impact their structural response under different loading and geometric conditions.
Static and Transient Vibrational Analysis of Functionally Graded MaterialIRJET Journal
This document discusses static and transient vibrational analyses of functionally graded materials (FGMs) using finite element modeling. FGMs are composite materials with continuous variation of material properties, such as a ceramic-metal mixture. The analyses examine deflection, vibration frequencies, and transient response of FGM plates and shells under mechanical and thermal loads. Results show the material gradient and volume fractions significantly impact structural response. Finite element modeling using first-order shear deformation theory is employed to efficiently analyze the functionally graded structures.
The present investigation deals with the static analysis of adhesively bonded inner tapered double lap joint in laminated FRP composites subjected to transverse loading using three-dimensional theory of elasticity based finite element method. Many researchers studied the influences of various parameters on the failure behaviour on the composites. In those studies, the typical bonding parameters are surface conditions, fillet, bond line thickness, and environmental conditions. In the present study the stresses and deformation characteristics of adhesively bonded inner tapered double lap joint made of generally and especially orthotropic laminates (FRP) subjected to transverse loading for the three different adhesive angles, three different adhesive thicknesses with different fibre angle orientations, i.e. the adhesive angles from 350 to 450 increased in steps of 50. The variation in stresses and deflection are studied when the fibre angle orientation is varied from 00 to 900 in steps of 150. The adhesive thickness varies from 0.05 to 0.15 insteps of 0.05mm. In all the above cases stresses and displacements at various locations are evaluated for the static boundary conditions
1. The document analyzes the stress distribution over a hybrid composite material with carbon and glass fibers and epoxy, with a central circular hole, under tensile loading.
2. Three specimens were experimentally tested according to ASTM standards and found to have a maximum stress concentration near the central hole.
3. Finite element analysis was also conducted and found the results to match the experimental values, with maximum stress occurring near the central hole.
Higher Order Normal Shear Deformation Theory for Static FG Rectangular PlatesIRJET Journal
The document discusses static analysis of functionally graded rectangular plates using higher order normal shear deformation theory (HONST). Functionally graded materials have properties that vary continuously through the thickness, modeled by a power law relationship. HONST is used to derive governing equations for the functionally graded plate based on equilibrium and strain-displacement relationships. Material properties are calculated according to the power law and volume fractions. Numerical results are obtained for plates under different loads and boundary conditions and compared to validate the model.
Effect of lamination angle on maximum deflection of simply supported composit...RAVI KUMAR
In this project a composite laminated beam is studied with glass-epoxy and graphite-epoxy combination. The beam is composed of four layers of different combination of composite material (glass epoxy and graphite epoxy composite). The beam is simply supported at both the ends and is subjected to uniformly distributed load along the length. Transverse deflection is computed for different lamination angle (0^0-〖90〗^0) by using Euler- Bernoulli’s theory (or CLPT). Maximum transverse deflection analysis is carried out using derived analytical expressions. The research carried out in this project will enable to determine the beam strength due to bending loads. The importance of fibre reinforcement in the manufacturing of the beam is studied in terms of bending strength of the beam. MATLAB codes are generated to implement analytical expiations of the composite beam.
The main objective of the paper is to find out the lamination angle at which minimum deflection is obtained & to find out the effect of lamination angle on maximum transverse deflection of the beam.
This document discusses the development and characterization of polymer-ceramic composite materials with continuous fiber reinforcement and functionally graded properties for aerospace applications. Specifically, it examines quartz fabric-reinforced composites with a silicone resin and fused silica powder matrix that is compositionally graded across the thickness. The composites demonstrated improved mechanical and thermal properties over non-graded materials, including high flexural strength, low thermal expansion, and the ability to withstand high heating rates without delamination or charring. The results suggest these functionally graded composites are promising candidates for reusable high-temperature aerospace structures.
The document summarizes a study that analyzed the structural properties of composite T-joints with different cut-out shapes using finite element analysis and Tsai-Hill failure criteria. A composite T-joint model was created and subjected to pulling, shear, and bending loads. Models with different cut-out shapes but the same total cut-out area were also analyzed under the same loads. Results found that for transverse pulling loads, a vertical ellipse cut-out shape performed best with no failure, while other shapes showed failure. For shear and bending loads, different cut-out shapes performed best. The best overall shape was selected based on composite performance under all three loading conditions.
ANALYSIS OF TEMPERATURE FIELD IN A COMPOSITE FUNCTIONALLY GRADED MATERIAL PLA...IJAMSE Journal
A finite element model is constructed to analyze the effects of steady state temperature field on FGM layer
thickness. The first-order shear deformation model is exploited to investigate the uncoupled thermal
behavior of functionally graded plates in Abacus environment. The continuum is divided into 540 elements
and 541 nodes using two node linear elements. The results show that the temperature distribution in the
composite plate is more reasonable with increase in the thickness of FGM layer. The comparison with the
non-graded two layered composite plate, the temperature field of the Zirconia/FGM/Aluminum three
layered composite plate is in the form of a curve but in case of non-graded two layered composite plate the
temperature field is in the form of inclined straight line with sharp bend at the interface of metal and
ceramic phase.
1) The document describes a finite element analysis of the superplastic blow-forming of Ti-6Al-4V titanium alloy sheet into a closed ellip-cylindrical die.
2) The simulations investigate the effects of shear friction factor, die entry radius, die height, and die short-axis length on thickness distribution, stress, strain, and damage within the formed product.
3) The results confirm the suitability of using the DEFORMTM 3D finite element software to model superplastic blow-forming of Ti-6Al-4V titanium alloy.
In the present work, static and free vibration response of functionally graded beam
is investigated under thermal environment using Finite Element method (FEM). The
functionally graded (FG) material beam is considered to be composed of various
material combinations like metal/metal, metal/ceramic and ceramic/ceramic. The
material properties of the beam are assumed to be graded in the thickness direction
according to a simple power law distribution. The deflection and mode shapes of the
FG beams are obtained for Clamped-Free, Clamped-Clamped and Simply Supported
boundary conditions under both mechanical and thermal load. Numerical results are
obtained for the model in ANSYS software to show the influence of grading of materials,
material constituents, boundary conditions, volume fraction and temperature
conditions on the response of the FG beams
Identification of Material Parameters of Pultruded FRP Composite Plates using...Subhajit Mondal
This document summarizes research that used finite element model updating to identify material parameters of pultruded fiber reinforced plastic (FRP) composite plates. Researchers conducted experimental modal testing on an FRP plate to measure its vibration responses. They then used an inverse eigensensitivity method to update a finite element model of the plate, adjusting the model's in-plane elastic parameters until its responses matched experimental data. This allowed them to estimate the plate's actual elastic properties nondestructively. The technique was validated using independent quasi-static tests, demonstrating its potential for structural health monitoring of pultruded FRP infrastructure.
Analysis of Isotropic Perforated Stiffened Plate Using FEMIJERA Editor
In this paper, studied the structural instability caused by circular and square perforated plate having all round simply supported and clamped plate boundary conditions subjected to inplane uniaxial compression loading and also the strengthening effect of the stiffeners when they are reinforced to the unperforated and perforated plate in longitudinal and transverse directions. The area ratios, aspect ratios and types of stiffeners are the parameters considered. A general purpose finite element analysis software ANSYS is used to carry out the study. Results show that the presence of a central circular and square perforations causes reduction in buckling strength of plate and stiffeners can be used to compensate this reduction before it can be used to its best advantage. It is also observed that the plate strengthening effect of longitudinal stiffener is more than that of transverse stiffener for both unperforated and perforated plate. An economical design is possible by introducing stiffeners of optimum size.
“Investigation of Structural Analysis of Composite Beam Having I- Cross Secti...IOSR Journals
Abstract: - In structural applications, beam is one of the most common structural members that have been
considered in design. This paper is intended to provide tools that ensure better designing options for composite
laminates of I -beam. In this Paper an analytical method & FEM approach calculating axial stiffness , Axial
stress ,Axial strain of flange and web laminates. The results show the stacking sequence and fiber angle
orientation strongly affects strength of composite I-beam.
This document discusses the additive manufacturing of optimized inserts for sandwich composite structures. It begins with background on traditional hot bonded inserts and their limitations. Topology optimization is then used to reduce the weight of the insert design while maintaining strength. Various optimized shapes are analyzed and a butterfly shape is found to improve thermal and structural performance. Additive manufacturing constraints are considered in the final design. Lattice structures are also analyzed and added to further reduce weight and improve thermal behavior for additive manufacturing of the optimized insert.
This paper addresses the fracture toughness ( ), or also known as critical stress intensity Factor, according to
conditions of Lineal Elastic Fracture Mechanics (LEFM). The characterization of the mechanical properties in
tensile and fracture toughness of structural steel pipes API-5L used in hydrocarbons transportation was
performed. For fracture toughness, the material was tested through fatigue crack propagation on standardized
compact specimen (CT) according to ASTM E-399 norm. A thickness (B) equal to and a crack size (a) equal
to 0.5w were used. With the porpoise of establishing the adequate conditions at the crack tip, the specimens were
subjected to fatigue pre-cracking by application of repeated cycles of load in tensile-tensile and constant load
amplitude with a load ratio of R = 0.1. The experimental Compliance method was used based on data obtained
from load vs. Crack Mouth Opening Displacement (CMOD). The results show a Stress Intensity factor of 35.88
MPa√m for a 25 mm crack size specimen. The device used for testing is a MTS-810 machine with capacity of
100KN and 6 kHz sampling rate, which meets the conditions of the ASTM E-399 standard. The cracking
susceptibility of steel is influenced by the size, morphology and distribution of non-metallic inclusions,
thermochemical interaction with the environment and microstructure.
Idealized solid propellant is models is analysed for thick sphere subjected to internal
pressure, whose casing is made of composite materials,. Results obtained from present
elements are compared with analytical results and 8 noded counterpart of MARC. Solid
Rocket Motor (SRM) is developed based on casting method where solid propellant grains
are cast into a composite or metallic casing. Generally, SRMs are exposed to extreme
loading scenarios during storage, transportation, and firing, leading to cracks in the solid
propellants. In this paper, Computational Finite Element Analysis is performed with
developed 8 node quadrilateral, 9 node quadrilateral and 6 node triangular elements
using Herrmann formulation to analyze stress and strain variations in the mid segments
of the typical SRM subjected to pressure loading. The obtained results are compared with
commercially available Finite element software
Fabrication and Analysis of Single Lap Joint Glass Fiber Reinforced Polymer C...IRJET Journal
This document summarizes research on analyzing the tensile strength of single lap joints in glass fiber reinforced polymer (GFRP) composite materials. Specifically, it looks at uni-directional and bi-directional ply composites with 10% silicon carbide additions. The composites were fabricated using hand layup and tested experimentally, numerically via finite element analysis, and analytically. Results showed that the bi-directional ply composite had a higher tensile strength than the uni-directional ply composite, making it more suitable for aircraft and automotive applications.
Analysis of Thermal Buckling of Ceramic-Metal Functionally Graded Plates Usin...IJERA Editor
This document analyzes the thermal buckling of ceramic-metal functionally graded plates using an improved third order shear deformation theory. It presents the governing equations and solution method using the Ritz method. Results are given for aluminum oxide-steel plates with simply supported and clamped boundary conditions. Increasing the plate thickness ratio and decreasing the power law index are found to decrease the critical buckling temperature. The improved theory provides more accurate predictions for thicker functionally graded plates compared to other plate theories.
Study on Transverse Displacement in Composite Laminated Plates across Thickne...IOSRJMCE
: In this paper main focus is given on alternative ways of thermal load applied through the thickness of laminated composite plate. Research has assumed gradient or constant thermal profile along the thickness of the plate. Laminated composite is a complex material therefore assumed loading profiles may not obey the gradient or constant thermal profile path therefore, as a research in all total 10 thermal profiles are studied. The results in tabular and graphical forms are presented along with discussion. First Order Shear Deformation Theory (FOST) is used for analysis. Various quantities, namely in plane as well as transverse displacements and stresses are obtained when thermal load is applied in various orientations along the thickness of the plate. Main focus in this article is analysis of transverse shear displacement and results are presented in tabular and graphical form.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...MSEJjournal1
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
The use of functional nano-metric easy-clean layers on material surfaces can reduce the dirt adsorption, facilitate dirt removal by rain, avoid dirt concentration /stripes and reduce cleaning efforts (longer intervals between cleaning and easier cleaning). OCAS, a Flemish steel research center has developed cost-competitive easy-clean coating layers that can be applied to a whole range of materials (painted metal, painted wood, plastics, glass, stone, and textile).
The document provides an overview of buckling analysis in ANSYS. It discusses buckling of columns with well-defined end conditions, buckling of a special column, and second order analysis of a simple beam. The preprocessing, solution, and postprocessing phases of ANSYS are outlined. Step-by-step instructions are given for modeling each example and obtaining the buckling load using eigenvalue buckling analysis. Manual calculations are also shown for comparison.
The document discusses using the differential quadrature method to analyze buckling in thin plates. It provides an overview of buckling and introduces the differential quadrature method as an efficient numerical technique. The method transforms differential equations into algebraic equations using sampling points. The document applies the method to analyze buckling in isotropic rectangular plates with different boundary conditions and aspect ratios. Results show the differential quadrature method provides accurate results using fewer grid points compared to other methods like finite element analysis.
The present investigation deals with the static analysis of adhesively bonded inner tapered double lap joint in laminated FRP composites subjected to transverse loading using three-dimensional theory of elasticity based finite element method. Many researchers studied the influences of various parameters on the failure behaviour on the composites. In those studies, the typical bonding parameters are surface conditions, fillet, bond line thickness, and environmental conditions. In the present study the stresses and deformation characteristics of adhesively bonded inner tapered double lap joint made of generally and especially orthotropic laminates (FRP) subjected to transverse loading for the three different adhesive angles, three different adhesive thicknesses with different fibre angle orientations, i.e. the adhesive angles from 350 to 450 increased in steps of 50. The variation in stresses and deflection are studied when the fibre angle orientation is varied from 00 to 900 in steps of 150. The adhesive thickness varies from 0.05 to 0.15 insteps of 0.05mm. In all the above cases stresses and displacements at various locations are evaluated for the static boundary conditions
1. The document analyzes the stress distribution over a hybrid composite material with carbon and glass fibers and epoxy, with a central circular hole, under tensile loading.
2. Three specimens were experimentally tested according to ASTM standards and found to have a maximum stress concentration near the central hole.
3. Finite element analysis was also conducted and found the results to match the experimental values, with maximum stress occurring near the central hole.
Higher Order Normal Shear Deformation Theory for Static FG Rectangular PlatesIRJET Journal
The document discusses static analysis of functionally graded rectangular plates using higher order normal shear deformation theory (HONST). Functionally graded materials have properties that vary continuously through the thickness, modeled by a power law relationship. HONST is used to derive governing equations for the functionally graded plate based on equilibrium and strain-displacement relationships. Material properties are calculated according to the power law and volume fractions. Numerical results are obtained for plates under different loads and boundary conditions and compared to validate the model.
Effect of lamination angle on maximum deflection of simply supported composit...RAVI KUMAR
In this project a composite laminated beam is studied with glass-epoxy and graphite-epoxy combination. The beam is composed of four layers of different combination of composite material (glass epoxy and graphite epoxy composite). The beam is simply supported at both the ends and is subjected to uniformly distributed load along the length. Transverse deflection is computed for different lamination angle (0^0-〖90〗^0) by using Euler- Bernoulli’s theory (or CLPT). Maximum transverse deflection analysis is carried out using derived analytical expressions. The research carried out in this project will enable to determine the beam strength due to bending loads. The importance of fibre reinforcement in the manufacturing of the beam is studied in terms of bending strength of the beam. MATLAB codes are generated to implement analytical expiations of the composite beam.
The main objective of the paper is to find out the lamination angle at which minimum deflection is obtained & to find out the effect of lamination angle on maximum transverse deflection of the beam.
This document discusses the development and characterization of polymer-ceramic composite materials with continuous fiber reinforcement and functionally graded properties for aerospace applications. Specifically, it examines quartz fabric-reinforced composites with a silicone resin and fused silica powder matrix that is compositionally graded across the thickness. The composites demonstrated improved mechanical and thermal properties over non-graded materials, including high flexural strength, low thermal expansion, and the ability to withstand high heating rates without delamination or charring. The results suggest these functionally graded composites are promising candidates for reusable high-temperature aerospace structures.
The document summarizes a study that analyzed the structural properties of composite T-joints with different cut-out shapes using finite element analysis and Tsai-Hill failure criteria. A composite T-joint model was created and subjected to pulling, shear, and bending loads. Models with different cut-out shapes but the same total cut-out area were also analyzed under the same loads. Results found that for transverse pulling loads, a vertical ellipse cut-out shape performed best with no failure, while other shapes showed failure. For shear and bending loads, different cut-out shapes performed best. The best overall shape was selected based on composite performance under all three loading conditions.
ANALYSIS OF TEMPERATURE FIELD IN A COMPOSITE FUNCTIONALLY GRADED MATERIAL PLA...IJAMSE Journal
A finite element model is constructed to analyze the effects of steady state temperature field on FGM layer
thickness. The first-order shear deformation model is exploited to investigate the uncoupled thermal
behavior of functionally graded plates in Abacus environment. The continuum is divided into 540 elements
and 541 nodes using two node linear elements. The results show that the temperature distribution in the
composite plate is more reasonable with increase in the thickness of FGM layer. The comparison with the
non-graded two layered composite plate, the temperature field of the Zirconia/FGM/Aluminum three
layered composite plate is in the form of a curve but in case of non-graded two layered composite plate the
temperature field is in the form of inclined straight line with sharp bend at the interface of metal and
ceramic phase.
1) The document describes a finite element analysis of the superplastic blow-forming of Ti-6Al-4V titanium alloy sheet into a closed ellip-cylindrical die.
2) The simulations investigate the effects of shear friction factor, die entry radius, die height, and die short-axis length on thickness distribution, stress, strain, and damage within the formed product.
3) The results confirm the suitability of using the DEFORMTM 3D finite element software to model superplastic blow-forming of Ti-6Al-4V titanium alloy.
In the present work, static and free vibration response of functionally graded beam
is investigated under thermal environment using Finite Element method (FEM). The
functionally graded (FG) material beam is considered to be composed of various
material combinations like metal/metal, metal/ceramic and ceramic/ceramic. The
material properties of the beam are assumed to be graded in the thickness direction
according to a simple power law distribution. The deflection and mode shapes of the
FG beams are obtained for Clamped-Free, Clamped-Clamped and Simply Supported
boundary conditions under both mechanical and thermal load. Numerical results are
obtained for the model in ANSYS software to show the influence of grading of materials,
material constituents, boundary conditions, volume fraction and temperature
conditions on the response of the FG beams
Identification of Material Parameters of Pultruded FRP Composite Plates using...Subhajit Mondal
This document summarizes research that used finite element model updating to identify material parameters of pultruded fiber reinforced plastic (FRP) composite plates. Researchers conducted experimental modal testing on an FRP plate to measure its vibration responses. They then used an inverse eigensensitivity method to update a finite element model of the plate, adjusting the model's in-plane elastic parameters until its responses matched experimental data. This allowed them to estimate the plate's actual elastic properties nondestructively. The technique was validated using independent quasi-static tests, demonstrating its potential for structural health monitoring of pultruded FRP infrastructure.
Analysis of Isotropic Perforated Stiffened Plate Using FEMIJERA Editor
In this paper, studied the structural instability caused by circular and square perforated plate having all round simply supported and clamped plate boundary conditions subjected to inplane uniaxial compression loading and also the strengthening effect of the stiffeners when they are reinforced to the unperforated and perforated plate in longitudinal and transverse directions. The area ratios, aspect ratios and types of stiffeners are the parameters considered. A general purpose finite element analysis software ANSYS is used to carry out the study. Results show that the presence of a central circular and square perforations causes reduction in buckling strength of plate and stiffeners can be used to compensate this reduction before it can be used to its best advantage. It is also observed that the plate strengthening effect of longitudinal stiffener is more than that of transverse stiffener for both unperforated and perforated plate. An economical design is possible by introducing stiffeners of optimum size.
“Investigation of Structural Analysis of Composite Beam Having I- Cross Secti...IOSR Journals
Abstract: - In structural applications, beam is one of the most common structural members that have been
considered in design. This paper is intended to provide tools that ensure better designing options for composite
laminates of I -beam. In this Paper an analytical method & FEM approach calculating axial stiffness , Axial
stress ,Axial strain of flange and web laminates. The results show the stacking sequence and fiber angle
orientation strongly affects strength of composite I-beam.
This document discusses the additive manufacturing of optimized inserts for sandwich composite structures. It begins with background on traditional hot bonded inserts and their limitations. Topology optimization is then used to reduce the weight of the insert design while maintaining strength. Various optimized shapes are analyzed and a butterfly shape is found to improve thermal and structural performance. Additive manufacturing constraints are considered in the final design. Lattice structures are also analyzed and added to further reduce weight and improve thermal behavior for additive manufacturing of the optimized insert.
This paper addresses the fracture toughness ( ), or also known as critical stress intensity Factor, according to
conditions of Lineal Elastic Fracture Mechanics (LEFM). The characterization of the mechanical properties in
tensile and fracture toughness of structural steel pipes API-5L used in hydrocarbons transportation was
performed. For fracture toughness, the material was tested through fatigue crack propagation on standardized
compact specimen (CT) according to ASTM E-399 norm. A thickness (B) equal to and a crack size (a) equal
to 0.5w were used. With the porpoise of establishing the adequate conditions at the crack tip, the specimens were
subjected to fatigue pre-cracking by application of repeated cycles of load in tensile-tensile and constant load
amplitude with a load ratio of R = 0.1. The experimental Compliance method was used based on data obtained
from load vs. Crack Mouth Opening Displacement (CMOD). The results show a Stress Intensity factor of 35.88
MPa√m for a 25 mm crack size specimen. The device used for testing is a MTS-810 machine with capacity of
100KN and 6 kHz sampling rate, which meets the conditions of the ASTM E-399 standard. The cracking
susceptibility of steel is influenced by the size, morphology and distribution of non-metallic inclusions,
thermochemical interaction with the environment and microstructure.
Idealized solid propellant is models is analysed for thick sphere subjected to internal
pressure, whose casing is made of composite materials,. Results obtained from present
elements are compared with analytical results and 8 noded counterpart of MARC. Solid
Rocket Motor (SRM) is developed based on casting method where solid propellant grains
are cast into a composite or metallic casing. Generally, SRMs are exposed to extreme
loading scenarios during storage, transportation, and firing, leading to cracks in the solid
propellants. In this paper, Computational Finite Element Analysis is performed with
developed 8 node quadrilateral, 9 node quadrilateral and 6 node triangular elements
using Herrmann formulation to analyze stress and strain variations in the mid segments
of the typical SRM subjected to pressure loading. The obtained results are compared with
commercially available Finite element software
Fabrication and Analysis of Single Lap Joint Glass Fiber Reinforced Polymer C...IRJET Journal
This document summarizes research on analyzing the tensile strength of single lap joints in glass fiber reinforced polymer (GFRP) composite materials. Specifically, it looks at uni-directional and bi-directional ply composites with 10% silicon carbide additions. The composites were fabricated using hand layup and tested experimentally, numerically via finite element analysis, and analytically. Results showed that the bi-directional ply composite had a higher tensile strength than the uni-directional ply composite, making it more suitable for aircraft and automotive applications.
Analysis of Thermal Buckling of Ceramic-Metal Functionally Graded Plates Usin...IJERA Editor
This document analyzes the thermal buckling of ceramic-metal functionally graded plates using an improved third order shear deformation theory. It presents the governing equations and solution method using the Ritz method. Results are given for aluminum oxide-steel plates with simply supported and clamped boundary conditions. Increasing the plate thickness ratio and decreasing the power law index are found to decrease the critical buckling temperature. The improved theory provides more accurate predictions for thicker functionally graded plates compared to other plate theories.
Study on Transverse Displacement in Composite Laminated Plates across Thickne...IOSRJMCE
: In this paper main focus is given on alternative ways of thermal load applied through the thickness of laminated composite plate. Research has assumed gradient or constant thermal profile along the thickness of the plate. Laminated composite is a complex material therefore assumed loading profiles may not obey the gradient or constant thermal profile path therefore, as a research in all total 10 thermal profiles are studied. The results in tabular and graphical forms are presented along with discussion. First Order Shear Deformation Theory (FOST) is used for analysis. Various quantities, namely in plane as well as transverse displacements and stresses are obtained when thermal load is applied in various orientations along the thickness of the plate. Main focus in this article is analysis of transverse shear displacement and results are presented in tabular and graphical form.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...MSEJjournal1
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
The use of functional nano-metric easy-clean layers on material surfaces can reduce the dirt adsorption, facilitate dirt removal by rain, avoid dirt concentration /stripes and reduce cleaning efforts (longer intervals between cleaning and easier cleaning). OCAS, a Flemish steel research center has developed cost-competitive easy-clean coating layers that can be applied to a whole range of materials (painted metal, painted wood, plastics, glass, stone, and textile).
The document provides an overview of buckling analysis in ANSYS. It discusses buckling of columns with well-defined end conditions, buckling of a special column, and second order analysis of a simple beam. The preprocessing, solution, and postprocessing phases of ANSYS are outlined. Step-by-step instructions are given for modeling each example and obtaining the buckling load using eigenvalue buckling analysis. Manual calculations are also shown for comparison.
The document discusses using the differential quadrature method to analyze buckling in thin plates. It provides an overview of buckling and introduces the differential quadrature method as an efficient numerical technique. The method transforms differential equations into algebraic equations using sampling points. The document applies the method to analyze buckling in isotropic rectangular plates with different boundary conditions and aspect ratios. Results show the differential quadrature method provides accurate results using fewer grid points compared to other methods like finite element analysis.
2014 bamboo a functionally graded composite material dr. pannipa chaowanaTheerawat Thananthaisong
1. Bamboo is a natural composite material made of long cellulose fibers embedded in a lignin matrix. Bamboo's microstructure and properties vary along its length and thickness, making it a functionally graded composite.
2. The study characterized the microstructure of Dendrocalamus asper bamboo through image analysis. Fiber volume fraction and vascular bundle concentration increased from bottom to top and inner to outer parts of the culm.
3. Specific gravity, bending strength and elasticity also increased from bottom to top due to higher fiber content and density. These properties correlated with fiber volume fraction, making bamboo grading useful for design.
Neha Gupta is a materials scientist and engineer with a PhD from IIT Kanpur. She has worked as a faculty member and research fellow. Her research focuses on developing ceramic composites for applications like armor using techniques such as spark plasma sintering. She has published papers in her field and reviewed articles for materials science journals.
This presentation discusses functionally graded materials (FGMs). FGMs are composites with a gradual, continuous transition in composition and structure. They are classified as thin FGMs consisting of thin surface coatings, or bulk FGMs consisting of larger volumes. Common processing techniques for thin FGMs include vapor deposition and plasma spraying, while bulk FGMs can be made using powder metallurgy or centrifugal casting. FGMs have a variety of applications due to properties like resistance to delamination and high impact/abrasion resistance, and are used in industries such as aerospace, defense, energy and medicine.
This Haiku Deck presentation contains photos from various sources including NASA's Marshall Space Flight Center, Defence Images, and individuals like sobolevnrm and woodleywonderworks. The presentation encourages the viewer to be inspired by the images and create their own Haiku Deck presentation on SlideShare.
This document discusses nonlinear thermal analysis of functionally graded plates using higher order theory. It provides background on functionally graded materials and reviews previous research on analyzing the behavior of functionally graded plates under various conditions. The present work aims to determine the nonlinear behavior and static characteristics of functionally graded material plates using a higher order displacement model, taking into account the material variation parameter, boundary conditions, aspect ratios, and thickness ratios. Equations of motion for the higher order displacement model are derived using the principle of virtual work.
This document analyzes the stresses in thick-walled truncated conical pressure vessels made of functionally graded materials (FGM) using finite element analysis in ANSYS. It first provides background on FGMs and discusses previous analytical research on stresses in cylindrical and spherical pressure vessels with exponentially varying material properties. It then outlines the problem formulation, modeling of material properties, geometry, and finite elements in ANSYS. Validation of the finite element model is discussed. The goal is to determine how non-homogeneous, exponentially varying material properties in FGM pressure vessels impact induced stresses compared to homogeneous materials.
Finite Element Analysis of Two Dimensional Functionally Graded Thick Rotating...IJERA Editor
The present study deals with the stress and deformation analysis of thick rotating disks made up of two dimensional functionally graded materials (FGMs) by finite element method. Material properties are distributed according to power law distribution and the disks are subjected to clamped-free boundary condition. Material modeling and finite element modeling for the disk is presented and the resulting deformation and stresses are evaluated. The effect of grading index on the deformation and stresses is investigated and presented. The results obtained show that there is a significant reduction of stresses in two dimensional FGM disks as compared to homogeneous and one dimensional FGM disks.
Verification of The Thermal Buckling Load in Plates Made of Functional Graded...CSCJournals
In this research, thermal buckling of thin plate made of Functionally Graded Materials (FGM) with linear varying thickness is considered. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The supporting condition of all edges of such a plate is simply supported the equilibrium and stability equations of a FGM plate under thermal loads derived based on higher order plate theories via variation formulation, and are used to determine the pre-buckling forces and the governing deferential equation of the plate the buckling analysis of a functionally graded plate is conducted using; the uniform temperature rise, having temperature gradient through the thickness, and linear temperature variation in the thickness and closed–form solutions are obtained. The buckling load is defined in a weighted residual approach. In a special case the obtained results are compared by the results of functionally graded plates with uniform thickness. The influences of the plate thickness variation and the edge ratio on the critical loads are investigated. Finally, different plots indicating the variation of buckling loads. Different gradient exponent k, different geometries and loading conditions were obtained.
The document summarizes research on the thermal buckling of laminate composite spheroidal spherical shells. Finite element analysis was used to analyze the effect of various parameters on the critical buckling temperature of the shells. The parameters investigated included spherical angle, fiber orientation, number of layers, radius to thickness ratio, and shell thickness. The results showed that the critical buckling temperature increased with increasing spherical angle, number of layers, radius to thickness ratio, and shell thickness. Certain fiber orientations like (0,45) exhibited higher critical buckling temperatures compared to others like (0,90). The research provides information to help design composite spherical shells that can withstand higher thermal loads.
TRANSIENT ANALYSIS OF PIEZOLAMINATED COMPOSITE PLATES USING HSDTP singh
Piezoelectric materials have excellent sensing and actuating capabilities have made them the most practical smart materials to integrate with laminated structures. Integrated structure system can be called a smart structure because of its ability to perform self-diagnosis and quick adaption to environment changes. An analytical procedure has been developed in the work based on higher order shear deformation theory subjected to electromechanical loading for investigating transient characteristics of smart material plates. For analysis two displacement models are to be considered i.e., model-1 accounts for strain in thickness direction is zero whereas in model-2 in-plane displacements are expanded as cubic functions of the thickness coordinate. Navier’s technique has been adopted for obtaining solutions of anti-symmetric cross–ply and angle-ply laminates of both model-1 and model-2 with simply supported boundary conditions. For obtaining transient response of a laminated composite plate attached with piezoelectric layer Newmark’s method has been used. Effect of thickness coordinate of composite laminated plates attached with piezoelectric layer subjected to electromechanical loadings is studied.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Exact solution of thermoelectroelastic behavior of a fluid filled fgpmAnubhav Kumar
This document presents an analytical study of the thermoelectroelastic behavior of a fluid-filled functionally graded piezoelectric material (FGPM) cylindrical thin-shell. The FGPM cylindrical shell is composed of piezoceramic and metal components with properties varying through the thickness according to a power law distribution. Governing differential equations are derived based on cylindrical shell theory. An exact solution is obtained using analytical methods. Numerical examples are used to analyze the influence of various factors on the thermoelectroelastic behavior of the fluid-filled FGPM cylindrical thin-shell.
Micromechanical Modeling of the Macroscopic Behavior of Soft Ferromagnetic Co...IJMERJOURNAL
ABSTRACT: Soft ferromagnetic composites consist of ferromagnetic particles embedded within nonmagnetic electrically insulating matrix. The aims of this article are twofold. In the first one, multiaxial nonlinear isothermal constitutive equations that govern the behavior of soft ferromagnetic materials are generalized to include the temperature and hysteretic effects. The second aim consists of developing a micromechanical analysis which takes into account the detailed interaction between the phases, and establishes the instantaneous concentration tensors which relate between the local magneto-thermo-elastic field and the externally applied loading. The ferromagnetic particles constituents employed in the micromechanical analysis are governed by the developed magneto-thermo-elastic coupled hysteretic constitutive relations. With the established concentration tensors, the macroscopic (global) re- sponse of the composite can be readily determined at any instant of loading. The offered micromechanical modeling is capable of predicting the response of soft ferromagnetic composites that are subjected to various types of magneto-thermo-elastic loadings, and it can be employed by the designerto easily determine the composite response for a particular desired application.
Numerical Analysis of Hygrothermal Effect on Laminated Composite PlatesIRJET Journal
This document presents a numerical analysis of the hygrothermal effects on laminated composite plates. It summarizes previous research on modeling the behavior of composite laminates under temperature and moisture gradients. The analysis uses the finite element tool ABAQUS to model simply supported cross-ply laminates and compare the displacement and stress results to analytical solutions. The numerical model considers shear deformation and transverse thermal strains and predicts the hygrothermal response of symmetric and antisymmetric angle-ply plates with different layer orientations and material properties.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Design and fabrication of corrugated sandwich panel using taguchi method 2IAEME Publication
The document discusses the design and fabrication of corrugated sandwich panels using the Taguchi method to optimize panel dimensions for maximum flexural modulus. Key parameters analyzed included sheet thickness, core height, shape and material. An orthogonal array experiment was conducted using ANSYS to evaluate flexural modulus under 3-point bending. The results identified optimal dimensions that provided both high strength and robust design.
Recent Development In Modelling and Analysis of Functionally Graded MaterialsIRJET Journal
This document summarizes recent developments in modeling and analyzing functionally graded materials (FGMs). FGMs are advanced composite materials with properties that vary continuously based on location. Various modeling techniques are discussed, including higher-order shear deformation theories and homogenization methods to determine effective material properties. Applications of FGMs mentioned include aerospace, defense, energy, and biomedical due to advantages like reducing stresses at interfaces and increasing fracture toughness.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
IRJET- Structural Analysis of Viscoelastic Materials: Review PaperIRJET Journal
This document reviews research on analyzing the structural behavior of viscoelastic materials from 1964 to the present. Viscoelastic materials exhibit both elastic and viscous properties, resulting in time-dependent stress and strain under static loads. Finite element methods have been developed using mixed formulations and Herrmann elements to better model the nearly incompressible and time-dependent behavior of materials like solid rocket propellants. The document surveys various studies applying these methods to problems like propellant grain analysis and pavement modeling to account for the viscoelastic nature of materials.
Three dimensional static analysis of two dimensional functionally graded platesrtme
In this paper, static analysis of two dimensional functionally graded plates based on three dimensional
theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The
effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated.
The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it
shows very good agreement
Three dimensional static analysis of two dimensional functionally graded platesijmech
In this paper, static analysis of two dimensional functionally graded plates based on three dimensional theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated. The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it shows very good agreement.
This document summarizes a study that used finite element modeling to simulate the hot rolling process and investigate the effects of various process parameters. The study developed a 3D finite element model of the hot rolling process using Abaqus software. It then analyzed how changes in parameters like slab thickness, rolling speed, roll diameter, thickness reduction, and temperature affect outcomes like temperature distribution, stress, strain, and roll force. The model was validated by comparing its predictions to theoretical results from previous studies. The results showed that increasing rolling speed, roll diameter, or thickness reduction increased roll force, while increasing temperature decreased roll force. Higher speeds also decreased minimum slab surface temperature.
This document reviews different methods for analyzing thick orthotropic plates, including their strengths and weaknesses. It discusses classical plate theory, Mindlin plate theory, the method of initial functions, state space method, and exact 3D solutions. The document focuses on elastic solutions that account for plate thickness and consider effects like shear deformation that are neglected in classical plate theory. It analyzes Ambartsumyan's and Kirchhoff-Love theories in particular and how later methods tried to improve on their limitations regarding thickness effects.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Similar to Analysis of Functionally Graded Material Plate under Transverse Load for Various Boundary Conditions (20)
This document provides a technical review of secure banking using RSA and AES encryption methodologies. It discusses how RSA and AES are commonly used encryption standards for secure data transmission between ATMs and bank servers. The document first provides background on ATM security measures and risks of attacks. It then reviews related work analyzing encryption techniques. The document proposes using a one-time password in addition to a PIN for ATM authentication. It concludes that implementing encryption standards like RSA and AES can make transactions more secure and build trust in online banking.
This document analyzes the performance of various modulation schemes for achieving energy efficient communication over fading channels in wireless sensor networks. It finds that for long transmission distances, low-order modulations like BPSK are optimal due to their lower SNR requirements. However, as transmission distance decreases, higher-order modulations like 16-QAM and 64-QAM become more optimal since they can transmit more bits per symbol, outweighing their higher SNR needs. Simulations show lifetime extensions up to 550% are possible in short-range networks by using higher-order modulations instead of just BPSK. The optimal modulation depends on transmission distance and balancing the energy used by electronic components versus power amplifiers.
This document provides a review of mobility management techniques in vehicular ad hoc networks (VANETs). It discusses three modes of communication in VANETs: vehicle-to-infrastructure (V2I), vehicle-to-vehicle (V2V), and hybrid vehicle (HV) communication. For each communication mode, different mobility management schemes are required due to their unique characteristics. The document also discusses mobility management challenges in VANETs and outlines some open research issues in improving mobility management for seamless communication in these dynamic networks.
This document provides a review of different techniques for segmenting brain MRI images to detect tumors. It compares the K-means and Fuzzy C-means clustering algorithms. K-means is an exclusive clustering algorithm that groups data points into distinct clusters, while Fuzzy C-means is an overlapping clustering algorithm that allows data points to belong to multiple clusters. The document finds that Fuzzy C-means requires more time for brain tumor detection compared to other methods like hierarchical clustering or K-means. It also reviews related work applying these clustering algorithms to segment brain MRI images.
1) The document simulates and compares the performance of AODV and DSDV routing protocols in a mobile ad hoc network under three conditions: when users are fixed, when users move towards the base station, and when users move away from the base station.
2) The results show that both protocols have higher packet delivery and lower packet loss when users are either fixed or moving towards the base station, since signal strength is better in those scenarios. Performance degrades when users move away from the base station due to weaker signals.
3) AODV generally has better performance than DSDV, with higher throughput and packet delivery rates observed across the different user mobility conditions.
This document describes the design and implementation of 4-bit QPSK and 256-bit QAM modulation techniques using MATLAB. It compares the two techniques based on SNR, BER, and efficiency. The key steps of implementing each technique in MATLAB are outlined, including generating random bits, modulation, adding noise, and measuring BER. Simulation results show scatter plots and eye diagrams of the modulated signals. A table compares the results, showing that 256-bit QAM provides better performance than 4-bit QPSK. The document concludes that QAM modulation is more effective for digital transmission systems.
The document proposes a hybrid technique using Anisotropic Scale Invariant Feature Transform (A-SIFT) and Robust Ensemble Support Vector Machine (RESVM) to accurately identify faces in images. A-SIFT improves upon traditional SIFT by applying anisotropic scaling to extract richer directional keypoints. Keypoints are processed with RESVM and hypothesis testing to increase accuracy above 95% by repeatedly reprocessing images until the threshold is met. The technique was tested on similar and different facial images and achieved better results than SIFT in retrieval time and reduced keypoints.
This document studies the effects of dielectric superstrate thickness on microstrip patch antenna parameters. Three types of probes-fed patch antennas (rectangular, circular, and square) were designed to operate at 2.4 GHz using Arlondiclad 880 substrate. The antennas were tested with and without an Arlondiclad 880 superstrate of varying thicknesses. It was found that adding a superstrate slightly degraded performance by lowering the resonant frequency and increasing return loss and VSWR, while decreasing bandwidth and gain. Specifically, increasing the superstrate thickness or dielectric constant resulted in greater changes to the antenna parameters.
This document describes a wireless environment monitoring system that utilizes soil energy as a sustainable power source for wireless sensors. The system uses a microbial fuel cell to generate electricity from the microbial activity in soil. Two microbial fuel cells were created using different soil types and various additives to produce different current and voltage outputs. An electronic circuit was designed on a printed circuit board with components like a microcontroller and ZigBee transceiver. Sensors for temperature and humidity were connected to the circuit to monitor the environment wirelessly. The system provides a low-cost way to power remote sensors without needing battery replacement and avoids the high costs of wiring a power source.
1) The document proposes a model for a frequency tunable inverted-F antenna that uses ferrite material.
2) The resonant frequency of the antenna can be significantly shifted from 2.41GHz to 3.15GHz, a 31% shift, by increasing the static magnetic field placed on the ferrite material.
3) Altering the permeability of the ferrite allows tuning of the antenna's resonant frequency without changing the physical dimensions, providing flexibility to operate over a wide frequency range.
This document summarizes a research paper that presents a speech enhancement method using stationary wavelet transform. The method first classifies speech into voiced, unvoiced, and silence regions based on short-time energy. It then applies different thresholding techniques to the wavelet coefficients of each region - modified hard thresholding for voiced speech, semi-soft thresholding for unvoiced speech, and setting coefficients to zero for silence. Experimental results using speech from the TIMIT database corrupted with white Gaussian noise at various SNR levels show improved performance over other popular denoising methods.
This document reviews the design of an energy-optimized wireless sensor node that encrypts data for transmission. It discusses how sensing schemes that group nodes into clusters and transmit aggregated data can reduce energy consumption compared to individual node transmissions. The proposed node design calculates the minimum transmission power needed based on received signal strength and uses a periodic sleep/wake cycle to optimize energy when not sensing or transmitting. It aims to encrypt data at both the node and network level to further optimize energy usage for wireless communication.
This document discusses group consumption modes. It analyzes factors that impact group consumption, including external environmental factors like technological developments enabling new forms of online and offline interactions, as well as internal motivational factors at both the group and individual level. The document then proposes that group consumption modes can be divided into four types based on two dimensions: vertical (group relationship intensity) and horizontal (consumption action period). These four types are instrument-oriented, information-oriented, enjoyment-oriented, and relationship-oriented consumption modes. Finally, the document notes that consumption modes are dynamic and can evolve over time.
The document summarizes a study of different microstrip patch antenna configurations with slotted ground planes. Three antenna designs were proposed and their performance evaluated through simulation: a conventional square patch, an elliptical patch, and a star-shaped patch. All antennas were mounted on an FR4 substrate. The effects of adding different slot patterns to the ground plane on resonance frequency, bandwidth, gain and efficiency were analyzed parametrically. Key findings were that reshaping the patch and adding slots increased bandwidth and shifted resonance frequency. The elliptical and star patches in particular performed better than the conventional design. Three antenna configurations were selected for fabrication and measurement based on the simulations: a conventional patch with a slot under the patch, an elliptical patch with slots
1) The document describes a study conducted to improve call drop rates in a GSM network through RF optimization.
2) Drive testing was performed before and after optimization using TEMS software to record network parameters like RxLevel, RxQuality, and events.
3) Analysis found call drops were occurring due to issues like handover failures between sectors, interference from adjacent channels, and overshooting due to antenna tilt.
4) Corrective actions taken included defining neighbors between sectors, adjusting frequencies to reduce interference, and lowering the mechanical tilt of an antenna.
5) Post-optimization drive testing showed improvements in RxLevel, RxQuality, and a reduction in dropped calls.
This document describes the design of an intelligent autonomous wheeled robot that uses RF transmission for communication. The robot has two modes - automatic mode where it can make its own decisions, and user control mode where a user can control it remotely. It is designed using a microcontroller and can perform tasks like object recognition using computer vision and color detection in MATLAB, as well as wall painting using pneumatic systems. The robot's movement is controlled by DC motors and it uses sensors like ultrasonic sensors and gas sensors to navigate autonomously. RF transmission allows communication between the robot and a remote control unit. The overall aim is to develop a low-cost robotic system for industrial applications like material handling.
This document reviews cryptography techniques to secure the Ad-hoc On-Demand Distance Vector (AODV) routing protocol in mobile ad-hoc networks. It discusses various types of attacks on AODV like impersonation, denial of service, eavesdropping, black hole attacks, wormhole attacks, and Sybil attacks. It then proposes using the RC6 cryptography algorithm to secure AODV by encrypting data packets and detecting and removing malicious nodes launching black hole attacks. Simulation results show that after applying RC6, the packet delivery ratio and throughput of AODV increase while delay decreases, improving the security and performance of the network under attack.
The document describes a proposed modification to the conventional Booth multiplier that aims to increase its speed by applying concepts from Vedic mathematics. Specifically, it utilizes the Urdhva Tiryakbhyam formula to generate all partial products concurrently rather than sequentially. The proposed 8x8 bit multiplier was coded in VHDL, simulated, and found to have a path delay 44.35% lower than a conventional Booth multiplier, demonstrating its potential for higher speed.
This document discusses image deblurring techniques. It begins by introducing image restoration and focusing on image deblurring. It then discusses challenges with image deblurring being an ill-posed problem. It reviews existing approaches to screen image deconvolution including estimating point spread functions and iteratively estimating blur kernels and sharp images. The document also discusses handling spatially variant blur and summarizes the relationship between the proposed method and previous work for different blur types. It proposes using color filters in the aperture to exploit parallax cues for segmentation and blur estimation. Finally, it proposes moving the image sensor circularly during exposure to prevent high frequency attenuation from motion blur.
This document describes modeling an adaptive controller for an aircraft roll control system using PID, fuzzy-PID, and genetic algorithm. It begins by introducing the aircraft roll control system and motivation for developing an adaptive controller to minimize errors from noisy analog sensor signals. It then provides the mathematical model of aircraft roll dynamics and describes modeling the real-time flight control system in MATLAB/Simulink. The document evaluates PID, fuzzy-PID, and PID-GA (genetic algorithm) controllers for aircraft roll control and finds that the PID-GA controller delivers the best performance.
We have designed & manufacture the Lubi Valves LBF series type of Butterfly Valves for General Utility Water applications as well as for HVAC applications.
Accident detection system project report.pdfKamal Acharya
The Rapid growth of technology and infrastructure has made our lives easier. The
advent of technology has also increased the traffic hazards and the road accidents take place
frequently which causes huge loss of life and property because of the poor emergency facilities.
Many lives could have been saved if emergency service could get accident information and
reach in time. Our project will provide an optimum solution to this draw back. A piezo electric
sensor can be used as a crash or rollover detector of the vehicle during and after a crash. With
signals from a piezo electric sensor, a severe accident can be recognized. According to this
project when a vehicle meets with an accident immediately piezo electric sensor will detect the
signal or if a car rolls over. Then with the help of GSM module and GPS module, the location
will be sent to the emergency contact. Then after conforming the location necessary action will
be taken. If the person meets with a small accident or if there is no serious threat to anyone’s
life, then the alert message can be terminated by the driver by a switch provided in order to
avoid wasting the valuable time of the medical rescue team.
Build the Next Generation of Apps with the Einstein 1 Platform.
Rejoignez Philippe Ozil pour une session de workshops qui vous guidera à travers les détails de la plateforme Einstein 1, l'importance des données pour la création d'applications d'intelligence artificielle et les différents outils et technologies que Salesforce propose pour vous apporter tous les bénéfices de l'IA.
Applications of artificial Intelligence in Mechanical Engineering.pdfAtif Razi
Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...PriyankaKilaniya
Energy efficiency has been important since the latter part of the last century. The main object of this survey is to determine the energy efficiency knowledge among consumers. Two separate districts in Bangladesh are selected to conduct the survey on households and showrooms about the energy and seller also. The survey uses the data to find some regression equations from which it is easy to predict energy efficiency knowledge. The data is analyzed and calculated based on five important criteria. The initial target was to find some factors that help predict a person's energy efficiency knowledge. From the survey, it is found that the energy efficiency awareness among the people of our country is very low. Relationships between household energy use behaviors are estimated using a unique dataset of about 40 households and 20 showrooms in Bangladesh's Chapainawabganj and Bagerhat districts. Knowledge of energy consumption and energy efficiency technology options is found to be associated with household use of energy conservation practices. Household characteristics also influence household energy use behavior. Younger household cohorts are more likely to adopt energy-efficient technologies and energy conservation practices and place primary importance on energy saving for environmental reasons. Education also influences attitudes toward energy conservation in Bangladesh. Low-education households indicate they primarily save electricity for the environment while high-education households indicate they are motivated by environmental concerns.
Digital Twins Computer Networking Paper Presentation.pptxaryanpankaj78
A Digital Twin in computer networking is a virtual representation of a physical network, used to simulate, analyze, and optimize network performance and reliability. It leverages real-time data to enhance network management, predict issues, and improve decision-making processes.
A high-Speed Communication System is based on the Design of a Bi-NoC Router, ...DharmaBanothu
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Determination of Equivalent Circuit parameters and performance characteristic...pvpriya2
Includes the testing of induction motor to draw the circle diagram of induction motor with step wise procedure and calculation for the same. Also explains the working and application of Induction generator
Analysis of Functionally Graded Material Plate under Transverse Load for Various Boundary Conditions
1. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 10, Issue 5 (Jan. 2014), PP 46-55
www.iosrjournals.org
www.iosrjournals.org 46 | Page
Analysis of Functionally Graded Material Plate under Transverse
Load for Various Boundary Conditions
Manish Bhandari1
Dr. Kamlesh Purohit 2
Associate Professor1
Jodhpur Institute of Technology, Jodhpur, Rajasthan
Professor2
& HOD, Jai Narain Vyas University, Jodhpur, Rajasthan
Abstract: Functionally gradient materials (FGM) are one of the most widely used materials in various
applications because of their adaptability to different situations by changing the material constituents as per the
requirement. Most structural components used in the field of engineering can be classified as beams, plates, or
shells for analysis purposes. In the present study the power law, sigmoid and exponential distribution is
considered for the volume fraction distributions of the functionally graded plates. The work includes parametric
studies performed by varying volume fraction distributions and boundary conditions. Also static analysis of
functionally gradient material plate is carried out by sigmoid law and verified with the published results. The
convergence study of the results is optimized by changing the mesh size and layer size. Power law and
exponential law are applied for the same material and set of conditions.
Keyword: A. Functional composites C. Elastic properties C. Finite element analysis (FEA)
I. Introduction
The material property of the FGM can be tailored to accomplish the specific demands in various engineering
utilizations to achieve the advantage of the properties of individual material. This is possible due to the material
composition of the FGM changes sequentially in a preferred direction. The thermo-mechanical deformation of
FGM structures have attracted the attention of many researchers in the past few years in different engineering
applications which include design of aerospace structures, heat engine components and nuclear power plants
etc. A huge amount of published literature observed for evaluation of thermomechanical behavior of
functionally gradient material plate using finite element techniques. It includes both linearity and non linearity
in various areas. A few of published literature highlights the importance of topic. A number of approaches have
been employed to study the static bending problems of FGM plates. The assessment of thermo-mechanical
deformation behavior of functionally graded plate structures considerably depends on the plate model
kinematics. G. N. Praveen and J. N. Reddy (1997) reported that the response of the plates with material
properties between those of the ceramic and metal is not intermediate to the responses of the ceramic and metal
plates [1]. J. N. Reddy (1998) reported theoretical formulations and finite element analysis of the
thermomechanical, transient response of functionally graded cylinders and plates with nonlinearity [2]. Z.-Q.
Cheng, R.C. Batra (1999), developed a new solution in closed form for the functionally graded elliptic plate
rigidly clamped at the edges.It was found that thein-plane displacements and transverse shear stresses in a
functionally graded plate do not agree with those assumed in classical and shear deformation plate theories [3].
J. N. Reddy (2000) formulated Navier's solutions in conjunction with Finite element models of rectangular
plates based on the third-order shear deformation plate theory for functionally graded plates [4]. Bhavani V.
Sankar (2002) solved the thermoelastic equilibrium equations for a functionally graded beam in closed-form to
obtain the axial stress distribution [5]. L.F. Qian, R.C. Batra, L.M. Chen (2004) analyzed static deformations,
free and forced vibrations of a thick rectangular functionally graded elastic plate by using a higher order shear
and normal deformable plate theory and a meshless local Petrov–Galerkin (MLPG) method [6].A.J.M.
Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, P.A.L.S. Martins (2005), presented the use of the
collocation method with the radial basis functions to analyze several plate and beam problems with a third-order
shear deformation plate theory (TSDT) [7]. M. Tahani1, M. A. Torabizadeh and A. Fereidoon (2006),
developedanalytical method to analyze analytically displacements and stresses in a functionally graded
composite beam subjected to transverse load and the results obtained from this method were compared with the
finite element solution done by ANSYS [8]. Shyang-Ho Chi, Yen-Ling Chung (2006) evaluated the numerical
solutions directly from theoretical formulations and calculated by finite element method using MARC
program.Besides, they compared the results of P-FGM, S-FGM and E-FGM [9] [10]. Hui Wang, Qing-Hua
Qin (2007) developed a meshless algorithm to simulate the static thermal stress distribution in two-dimensional
(2D) functionally graded materials (FGMs). The analog equation method (AEM) was used to obtain the
equivalent homogeneous system to the original nonhomogeneous equation [11]. Yasser M. Shabana, Naotake
Noda (2008) used the homogenization method (HM) based on the finite element method (FEM) to determine
the full set of the macroscopic effective properties which lead to the same thermomechanical behavior as the one
2. Analysis of Functionally graded material plate under transverse load for various boundary
www.iosrjournals.org 47 | Page
of the material with the periodic microstructure [12]. M. Mahdavian (2009), derived equilibrium and stability
equations of a FGM rectangular plate under uniform in-plane compression [13]. Ashraf M. Zenkour and
Daoud S. Mashat (2010) determined the thermal buckling response of functionally graded plates using
sinusoidal shear deformation plate theory (SPT) [14]. S.S. Alieldin, A.E. Alshorbagy, M. Shaat (2011),
proposed three transformation procedures of a laminated composite plate to an equivalent single-layer FG plate.
The first approach is a curve fitting approach which is used to obtain an equivalent function of the FG material
property, the second approach is the effective material property approach and the third approach is the volume
fraction approach in which the FG material property varies through the plate thickness with the power law [15].
Kyung-Su Na, and Ji-Hwan Kim (2011) reported stress analysis of functionally graded composite plates
composed of ceramic, functionally graded material and metal layers using finite element method. Numerical
results were compared for three types of materials. The 18-node solid element was selected for more accurate
modeling of material properties in the thickness direction [16]. Vanam B. C. L., Rajyalakshmi M. and Inala
R. (2012) analyzed the static analysis of an isotropic rectangular plate with various boundary conditions and
various types of load applications. Numerical analysis (finite element analysis, FEA) has been carried out by
developing programming in mathematical software MATLAB and they compared results with that were
obtained by finite element analysis software ANSYS [17]. MostaphaRaki, Reza Alipour and
AmirabbasKamanbedast (2012), derived equilibrium and stability equations of a rectangular plate made of
functionally graded material (FGM) under thermal loads based on the higher order shear deformation plate
theory [18]. Mohammad Talha and B N Singh (2012) reported formulations based on higher order shear
deformation theory with a considerable amendment in the transverse displacement using finite element method
(FEM) [19].Srinivas.G and Shiva Prasad.U (2012) focused on analysis of FGM flat plates under mechanical
loading in order to understand the effect variation of material properties on structural response using ANSYS
software [20]. Srinivas.G and Shiva Prasad.U (2013) focused on analysis of FGM flat plates under thermal
loading in order to understand the effect variation of material properties has on structural response. Results are
compared to published results in order to show the accuracy of modeling FGMs using ANSYS software [21].
In the present study the power law, sigmoid and exponential distribution is considered for the volume fraction
distributions of the functionally graded plates. The studies include analysis of the response of structural element
specifically plates made of functionally graded materials. The work includes parametric studies performed by
varying volume fraction distributions and boundary conditions. The finite element software ANSYS APDL-13
is used for the modeling and analysis purpose.
II. Material gradient of FGMplates
The effective material properties like Young‘s modulus, Poisson‘s ratio, coefficient of thermal expansion,
thermal conductivity etc. on the upper and lower surfaces are different but are preassigned. However, the
Young‘s modulus and Poisson‘s ratio of the plates vary continuously only in the thickness direction (z-axis)
i.e.E = E(z), ν = ν (z). However, the Young‘s moduli in the thickness direction of the FGM plates vary with
power-law functions (P-FGM), exponential functions (E-FGM), or with sigmoid functions (S-FGM).A mixture
of the two materials composes the through the thickness characteristics. The FGM plate of thickness ‗h‘ is
modeled usually with one side of the material as ceramic and the other side as metal.
2.1 Power Law
The material properties of a P-FGM can be determined by the rule of mixture:
P(z) = (Pt−Pb)Vf +Pb (1)
Material properties are dependent on the volume fraction Vf of P-FGM which obeys power law
Vf=(z/h+1/2)n
(2)
where n is a parameter that dictates the material variation profile through the thickness known as is the volume
fraction exponent. At bottom face, (z/h) = -1/2 and Vf =0, hence P(z) = Pb and At top face, (z/h) =1/2 and so Vf
=1, hence P(z)= Pt where P denotes a generic material property like modulus, Pt and Pb denote the property of
the top and bottom faces of the plate.
3. Analysis of Functionally graded material plate under transverse load for various boundary
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Figure1:Variation of Young‘s modulus in a P-FGM with ‗n‘.
At n = 0 the plate is a fully ceramic plate while at n = ∞ the plate is fully metal. The variation of Young‘s
modulus in the thickness direction of the P-FGM plate is depicted in Figure 1., which shows that the Young‘s
modulus changes rapidly near the lowest surface for n > 1, and increases quickly near the top surface for n < 1.
2.2 Sigmoid Law:
In the case of adding an FGM of a single power-law function to the multi-layered composite, stress
concentrations appear on one of the interfaces where the material is continuous but changes rapidly .Therefore,
Chung and Chi (2001) defined the volume fraction using two power-law functions to ensure smooth
distribution of stresses among all the interfaces. The two power law functions are defined by:
p
h
z
h
zg
2
2
2
1
11 for 0≤z≤h/2,
p
h
z
h
zg
2
2
2
1
2 for -h/2≤z≤0 (3)
By using the rule of mixture, the Young‘s modulus of the S-FGM can be calculated by:
2111 1 EzgEzgzE for 0≤z≤h/2 and 2212 1 EzgEzgzE for -h/2≤z≤0
Figure 2. Variation of Young‘s modulus in a S-FGM with ‗n‘.
50
70
90
110
130
150
170YOUNG'SMODULUS
THICKNESS
P-FGM
n=0, ceremic
n=0.1
n=0.2
n=0.5
n=1
n=2
n=5
n=10
n=100
n= infinity,
metal
50
70
90
110
130
150
170
YOUNG'SMODULUS
THICKNESS
S-FGM n=0
n=0.1
n=0.2
n=0.5
n=1
n=2
n=5
n=10
n=100
n=infinity
4. Analysis of Functionally graded material plate under transverse load for various boundary
www.iosrjournals.org 49 | Page
The variation of Young‘s modulus in the thickness direction of the S-FGM plate is depicted in Figure2., which
shows that the Young‘s modulus changes are gradual because of using two power law functions together as
described above.
2.3 Exponential Law:
Many researchers used the exponential function to describe the material properties of FGMs as follows:
)2/(ln
1
2
2
1
)(
hz
E
E
h
eEzE
(4)
The material distribution in the E-FGM plates is plotted in Figure 3.
Figure 3.Variation of Young‘s modulus in a E-FGM plate.
III. Finite Element Modeling Technique
The material properties of the FGM change throughout the thickness, the numerical model is to be broken up
into various ―layers‖ in order to capture the change in properties. These ―layers‖ capture a finite portion of the
thickness and are treated like isotropic materials. Material properties are calculated from the bottom surface
using the various volume fraction distribution laws. The ―layers‖ and their associated properties are then layered
together to establish the through-the-thickness variation of material properties. Although the layered structure
does not reflect the gradual change in material properties, a sufficient number of ―layers‖ can reasonably
approximate the material gradation. In this paper, the modeling and analysis of FGM plate is carried out using
ANSYS software. ANSYS offers a number of elements to choose from for the modeling of gradient materials.
The FGM characteristics under mechanical and thermal loads studied on a flat plate were modeled in 3-D.
IV. Comparative study
To ascertain the accuracy and proficiency of the present finite element formulation, two examples have
been analyzed for thermo-mechanical deformations of the FGM plates.
Example 1: We first consider the accuracy of the present finite element formulation by comparing the results
with those given by A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian and P.A.L.S. Martins (2005).It
is based on the meshless collocation method and a third-order shear deformation theory. In this example, the
analysis is performed on a square functionally graded plate simply supported at all its edges (SSSS) for side to
thickness ratio a/h = 20, volume fraction index n = 0 (ceramic), 0.5, 1.0, 2, and ∞ (metal) with aspect ratio a/b =
1 where h is the thickness of the plate. The top surface of the plate is ceramic-rich, whereas the bottom surface is
metal-rich. The plate is comprised of metal (Aluminium) and Ceramic (Zirconia). The material properties are
taken as Eb= 70 × 109
N/m2
for Aluminium, and Et= 151 × 109
N/m2
for ceramic. Poisson‘s ratio for both the
materials have been taken as ν = 0.3. The transverse displacement uz has been non-dimensional as follows: ̅̅̅=
uz/h. The comparison of present results with published results is presented in Table 1 which shows the
agreement between the two results is excellent. The difference between the two results is below 3%. The results
show that the performance of the present formulation is very good in terms of solution accuracy.
5. Analysis of Functionally graded material plate under transverse load for various boundary
www.iosrjournals.org 50 | Page
Table 1.Comparison of Present Results With published results
Volume Fraction Exponent (n) Published Results Present Results % Difference
Ceramic (0) 0.0205 0.021 2.43
0.5 0.0262 0.0268 2.29
1 0.0294 0.0302 2.72
2 0.0323 0.0332 2.79
Metal (∞) 0.0443 0.0456 2.93
V. Convergence study
Example 2: The convergence study with respect to varying mesh size and number of layers has been carried
out. The obtained results are compared with those given by Shyang-Ho Chi, Yen-Ling Chung (2006). In this
example, the analysis is performed on a square functionally graded plate simply supported at all its edges
(SSSS) for side to thickness ratio a/h = 50, volume fraction index n = 2with varying aspect ratio (a/h) where h is
the thickness of the plate. The material properties are taken as Ebottom= 210 × 109
N/m2
and Etop= 21 × 109
N/m2
.
Poisson‘s ratio have been taken constant as ν = 0.3. The transverse displacement uz and stress have been non-
dimensional as follows: ̅̅̅= uz/h, and ̅= sy/p. The comparison of present results with published results is
presented in Figure 4 and Figure 5.
Figure 4. The maximum deflection of an S-FGM plate versus the aspect ratio (a/h)
Figure5. The maximum tensile stress of an S-FGM plate versus the aspect ratio (a/h)
Figure 4 and Figure 5 show the variation of maximum deflection and maximum tensile stress for varying aspect
ratio (a/h). An excellent agreement between the present and published results can be observed. The results show
that the performance of the present formulation is very good in terms of solution accuracy.
0.00E+00
5.00E+02
1.00E+03
1.50E+03
2.00E+03
2.50E+03
3.00E+03
3.50E+03
4.00E+03
Nondimensionaltensile
stress(Sy)
Aspect ratio
S-FGM (n 2)PRESENT
PUBLISHED
6. Analysis of Functionally graded material plate under transverse load for various boundary
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Table 2: Convergence study of simply supported FGM plate with respect to mesh size.
Parameters 6X6 10X10 20X20 50X50 100X100
Published
Results
% Difference
ux (X10-5
) 7.97 7.95 7.96 7.99 8.01 8.03 0.25
uz (X10-3
) 7.20 7.21 7.22 7.26 7.28 7.38 1.37
Sx (X108
) 1.21 1.26 1.29 1.30 1.31 1.35 2.74
ex (X10-4
) 4.10 4.27 4.35 4.39 4.41 4.44 0.79
In Table 2 the results for transverse deflection, stress and strain are presented for various mesh size. Table 2
shows that as the mesh size increases, the obtained results converge towards the published results. The
difference between the two results for transverse deflection below 1.5% and the difference between the two
results for tensile stress is below 3% which shows the agreement between the two results is excellent. The
results show that the performance of the present formulation is very good in terms of solution accuracy. Hence
finer mesh will help in attaining accurate results. Since higher mesh gives better results, 100X100 mesh is
considered for the present work. The convergence study with respect to varying number of layers is shown in
Table 3. The FGM plate is modeled considering 4, 8 and 16 layers with a mesh size of 100×100. In Table 3 the
results for transverse deflection, stress and strain are presented. The difference between the two results for
transverse deflection is below 2.5% and the difference between the two results for tensile stress is below 2%.
Table 3 shows that as the number of layers increases, the obtained results converge towards the published
results. Since higher number of layers gives better results, 16 layers have been used in the present work.
Therefore, based on the convergence study of mesh size and no. of layers, it is concluded that (100 × 100) mesh
and 16 no. of layers are acceptable for thermoechanical deformation behavior of the FGM plate.
Table 3 : Convergence study of simply supported FGM plate with respect to no. of layers.
Parameters 4 layers 8 layers 16 layers Published Results % Difference
ux (X10-5
) 6.88 7.99 8.30 8.03 3.25
uz (X10-3
) 6.77 7.26 7.40 7.38 2.41
Sx (X108
) 1.20 1.30 1.33 1.35 -1.89
ex (X10-4
) 4.25 4.39 4.43 4.44 -2.26
VI. Results and analysis
The mechanical analysis is conducted for FGM made of combination of metal and ceramic. The metal
and ceramic chosen are Aluminum and Zirconia respectively. The Young's modulus for Aluminum (Em) is 70
GPa and for Zirconia (Ec) 151 GPa. The Poisson's ratio for both the materials is taken as 0.3.A square FGM
plate of simply supported at all of its edges (SSSS) is considered here. The thickness of the plate (h) is taken
0.02m and the aspect ratio (a/b) is taken unity. The value of the udl (po) chosen was equal to 1Xl06
N/m2
.
The mechanical analysis is performed by applying uniformly distributed load (udl) and point load for various
boundary conditions SSSS, CCCC, SCSC, CFCF, CCFF, CCSS, SSFF, SSSC, SSSF and SSCF. The
abbreviation S, C and F stand for simply supported, clamped and free edges respectively. The boundary
conditions imposed at a simply supported (S), a clamped (C) and a free (F) edge are:
Simply supported (S) σxx=0; v=w=0; on x=0 and a; and σyy = 0; u = w = 0; on y = 0 and b;
Clamped (C) : u = v = w = 0; on x = 0, a and y = 0, b;
Free (F) : σxx = σyx = σzx = 0; on x = 0 and a; and σyy = σxy = σzy = 0; on y = 0, b
The analysis is performed for E-FGM and for various values of the volume fraction exponent (n) in P-FGM and
S-FGM. The results are presented in terms of non-dimensional parameters i.e. non-dimensional deflection (̅̅̅ ,
nondimensional tensile stress (̅̅̅̅ and shear strain (exy).
The various non-dimensional parameters used are:
Non-dimensional deflection ̅̅̅ (100 Em h3
uz) / (1-2
) a4
po
And non-dimensional stress̅̅̅̅ h2
/ po a2
where ‗uz‘ is deflection, ‗σ‘ is stress, ‗‘ Poisson‘s ratio (0.3).
6.1 Non-dimensional deflection (̅̅̅
Figure 6, Figure7and Figure 8shows the comparative bar charts of non-dimensional deflection uz for
various boundary conditions of a square plate under uniformly distributed load for P-FGM, S-FGM and E-FGM
7. Analysis of Functionally graded material plate under transverse load for various boundary
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respectively. In case of P-FGM and S-FGM the comparison of various values of volume fraction exponent (n)
have been presented. In case of E-FGM a single graph is obtained.
Figure6: Non-dimensional deflection uz for various boundary conditions (P-FGM)
Figure 7: Non-dimensional deflection uz for various boundary conditions (S-FGM)
Figure8: Non-dimensional deflection uz for various boundary conditions (E-FGM)
It can be observed that the isotropic ceramic plate has the lowest deflection for all the boundary
conditions considered here, and the isotropic metallic has the largest deflection. The deflections become higher
with increasing n. This is due to the fact that the bending stiffness is the maximum for ceramic plate, while
minimum for metallic plate, and degrades continuously as n increases. It is also found that the maximum
deflection occurs for simply supported - free (SSFF) boundary conditions and minimum for clamped (CCCC)
boundary condition for all the cases considered here. The non-dimensional deflection for S-FGM remains closer
for various values of ‗n‘ as compared to that of the P-FGM.
6.2 Non-dimensional tensile stress (̅̅̅̅
Figure 9, Figure 10 and Figure 11 shows the variation of non-dimensional tensile stress (σx) for various
boundary conditions of a square plate under uniformly distributed load for P-FGM, S-FGM and E-FGM
respectively. In case of P-FGM and S-FGM the comparison of various values of volume fraction exponent (n)
have been presented. In case of E-FGM a single graph is obtained.
8. Analysis of Functionally graded material plate under transverse load for various boundary
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Figure9: Non-dimensional tensile stress (σx) for various boundary conditions (P-FGM)
Figure 10: Non-dimensional tensile stress (σx) for various boundary conditions (S-FGM)
Figure 11: Non-dimensional tensile stress (σx) for various boundary conditions (E-FGM)
It can be observed that the isotropic ceramic plate has the lowest tensile stress for all the boundary
conditions considered here, and the isotropic metallic has the largest tensile stress. The tensile stress becomes
higher with increasing n. This is due to the fact that the bending stiffness is the maximum for ceramic plate,
while minimum for metallic plate, and degrades continuously as n increases. It is also found that the maximum
tensile stress occurs for clamped - free (CCFF) boundary conditions and minimum for simply supported –
clamped (SCSC) boundary condition for all the cases considered here. The non-dimensional tensile stress for S-
FGM remains closer for various values of ‗n‘ as compared to that of the P-FGM.
6.3 Shear strain (exy)
Figure 12, Figure 13 and Figure 14 shows the variation of Strain (exy) for various boundary conditions
of a square plate under uniformly distributed load for P-FGM, S-FGM and E-FGM respectively. In case of P-
FGM and S-FGM the comparison of various values of volume fraction exponent (n) have been presented. In
case of E-FGM a single graph is obtained.
9. Analysis of Functionally graded material plate under transverse load for various boundary
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Figure 12: Shear Strain (exy) for various boundary conditions of a square plate (P-FGM)
Figure 13: Shear Strain (exy) for various boundary conditions of a square plate (S-FGM)
Figure 14: Shear Strain (exy) for various boundary conditions of a square plate (E-FGM)
It can be observed that the isotropic ceramic plate has the lowest Strain (exy) for all the boundary
conditions considered here, and the isotropic metallic has the largest Strain (exy). The Strain (exy) becomes
higher with increasing n. This is due to the fact that the bending stiffness is the maximum for ceramic plate,
while minimum for metallic plate, and degrades continuously as n increases. It is also found that the maximum
Strain (exy) occurs for simply supported - free (SSFF) boundary conditions and minimum for clamped (CCCC)
boundary condition for all the cases considered here. The shear strain (exy) for S-FGM remains closer for various
values of ‗n‘ as compared to that of the P-FGM
VII. Conclusions and future scope
Mechanical deformation of functionally graded ceramic-metal plates under various boundary
conditions is analyzed. Convergence and validation studies have been carried out to inculcate the accuracy of
the present formulation. The results show a good agreement with those available in the literature. It is observed
that
(a) The bending response of the functionally graded plate is intermediate to those of the metal and the
ceramic plate. This behavior is found to be true irrespective of boundary conditions.
(b) The bending response for S-FGM remains closer for various values of ‗n‘ as compared to that of the P-
FGM.
(c) The bending response of E-FGM is nearer to the behavior of P-FGM. The work can be extended for
variation in load, loading pattern and other ceramic metal combinations. Also thermal environment may
be imposed in addition to the mechanical loading.
References:
[1] G. N. Praveen and J. N. Reddy, ―Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates‖, Int. J.
Solids Structure, 35, 4457- 4476, 1997.
[2] J. N. Reddy, ―Thermomechanical behavior of functionally graded materials‖, Final Report for AFOSR Grant F49620-95-1-0342,
CML Report 98-01, August 1998.
[3] Z.Q. Cheng and R.C.Batra, ―Three-dimensional thermoelastic deformations of a functionally graded elliptic plate‖, Composites Part
B, 31(1), 97–106, 2000.
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[4] J. N. Reddy, ―Analysis of functionally graded plates‖, Int. J. for numerical methods in engg., Int. J. Numer. Meth. Engg., 47, 663-
684, 2000.
[5] Bhavani V. Sankar and Jerome T. Tzeng, ―Thermal stresses in functionally graded beams‖, AIAA journal, 40, 1228-1232, 2002.
[6] L.FQian, R. C. Batra, and L. M. Chen ―Static and dynamic deformations of thick functionally graded elastic plates by using higher
order shear and normal deformable plate theory and meshless local Petrov-Galerkin method‖ , Composite Part B, 35, 685−697,
2004.
[7] A. J. M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, and P.A.L.S. Martins, ―Static analysis of functionally graded plates using
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[8] M. Tahani1, M. A. Torabizadeh and A. Fereidoon, ―Non-Linear Response of Functionally graded beams under transverse loads‖
14th
Annual (International) Techanical Engineering Conference ,Isfahan University of Technology, Isfahan, Iran, May 2006.
[9] Shyang-Ho Chi and Yen-Ling Chung, ―Mechanical behavior of functionally graded material plates under transverse load—Part I:
Analysis‖, Int. J. of Solids and Structures, 43, 3657–3674, 2006.
[10] Shyang-Ho Chi and Yen-Ling Chung, ―Mechanical behavior of functionally graded material plates under transverse load—Part II:
Numerical results‖, Int. J. of Solids and Structures, 43, 3675–3691, 2006.
[11] Hui Wang and Qing-Hua Qin, ―Meshless approach for thermo-mechanical analysis of functionally graded materials, Engineering
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