In this paper, Imperialist Competitive Algorithm (ICA) and Genetic Algorithm (GA) are used to find the optimal form for torispherical dome ends under internal pressure load. According to fabrication and strength of material requirements, a group of compromised counters are studied. According to ASME Section VIII and BS5500 pressure vessel codes, a reasonable buckling pressure limit is proposed. Four-centered ellipse method is used to describe the geometry of the torispherical dome end that this method is commonly used in engineering drawing. A minimum weight optimization problem based on buckling pressure is studied. Two different size torispherical dome end examples are selected and studied. Imperialist Competitive Algorithm is found to be very efficient and easy to use for the applications, such as torispherical dome end and subjected to internally pressurized loading.
This document summarizes a study on modeling carbon fiber reinforced polymer (CFRP) cruciform specimens under biaxial fatigue loading. It describes the development of a biaxial loading mechanism that subjects cruciform specimens to tension-tension or compression-compression loading at ratios of 1:1 to 1:4. Finite element models of cruciform specimens with different layer configurations were created in ANSYS and fatigue analyzed in nCode DesignLife. Results showed that modeling the CFRP as orthotropic rather than isotropic reduced the predicted fatigue life, with the orthotropic material exhibiting greater sensitivity to load duration. Increasing layer numbers from 6 to 10 also increased fatigue life.
Probabilistic design and random optimization of hollow rectangular composite ...IAEME Publication
This document describes a probabilistic design and random optimization of a hollow rectangular composite beam structure using finite element analysis. A Monte Carlo simulation was conducted by randomly varying design parameters like beam length, ply angles, elastic modulus, and force within defined ranges. Scatter plots of maximum bending stress were obtained for different parameter combinations. Random optimization was then performed to minimize bending stress, obtaining 1000 feasible sets. The best set that reduced bending stress the most is proposed as the optimized design.
This document summarizes a study that uses finite element analysis and Monte Carlo simulation to analyze the bending stress of hollow circular composite beams under random loading conditions. The study varies design parameters like beam length, radius, ply angles, elastic modulus, and force randomly within defined ranges. It analyzes the relationship between maximum bending stress and each parameter. Random optimization is then performed to determine a set of parameters that minimize bending stress. The best optimized set is proposed to reduce bending stress under different loading conditions.
Probabilistic Design Hollow of Airfoil Wing by Using Finite Element MethodIJERA Editor
This document presents a probabilistic finite element analysis of the bending stress in a hollow NACA0012 airfoil composite wing. The analysis varies key geometric parameters, material properties, composite layer properties, and applied load within realistic ranges using Monte Carlo simulation. Scatter plots show the effects of each input parameter on the bending stress output. The results identify that chord length, ply thickness, orientation angle, Young's modulus in the XX direction, and shear modulus in XY have the most significant effects on bending stress, while other inputs have less influence. This probabilistic analysis can help determine robust input parameters and limits for optimization of the airfoil wing design.
This document summarizes a study that used finite element analysis to analyze stress concentrations at bolt hole locations in lap joints. A 3D finite element model of a lap joint was developed using Abaqus software. Non-linear analysis considered the stress-strain behavior of materials and interactions between bolt and plate surfaces. Parametric studies varied the end distance and compared results to failure criteria in design codes. Stress patterns were compared to bearing capacity equations to determine the optimum end distance that prevents premature failure.
Stress Analysis of Automotive Chassis with Various ThicknessesIOSR Journals
Abstract : This paper presents, stress analysis of a ladder type low loader truck chassis structure consisting of
C-beams design for application of 7.5 tonne was performed by using FEM. The commercial finite element
package CATIA version 5 was used for the solution of the problem. To reduce the expenses of the chassis of the
trucks, the chassis structure design should be changed or the thickness should be decreased. Also determination
of the stresses of a truck chassis before manufacturing is important due to the design improvement. In order to
achieve a reduction in the magnitude of stress at critical point of the chassis frame, side member thickness,
cross member thickness and position of cross member from rear end were varied. Numerical results showed that
if the thickness change is not possible, changing the position of cross member may be a good alternative.
Computed results are then compared to analytical calculation, where it is found that the maximum deflection
agrees well with theoretical approximation but varies on the magnitude aspect.
Keywords - Stress analysis, fatigue life prediction and finite element method etc.
Experimental Investigations to Study the Air Flow Patterns on the Headlight D...IJERA Editor
This paper presents some experimental investigations to study the air flow patterns on the headlight domes of different two wheelers (HERO HONDA PASSION PLUS and BAJAJ PULSAR) which influence the stability of the vehicle. The pressure distribution over the surface of the profile and the drag force are to be determined for various headlight dome orientations. This study helps in suggesting the suitable headlight dome profile that may reduce the drag force and effect of turbulence which in turn leads to the increase of vehicle stability. The results obtained during the simulation are to be validated by conducting the experiments on the scale down model of the headlight dome of HERO HONDA PASSION PLUS using Wind Tunnel test rig. The Computational Fluid Dynamics (CFD) tool was used to simulate the air flow pattern on the headlight dome in which boundary layer separation doesn’t exist. The results obtained from the simulation are to be compared with the experimental results from the wind tunnel and the variation is to be found and that should be in the acceptable limit.
Deformation Analysis of a Triangular Mild Steel Plate Using CST as Finite Ele...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
This document summarizes a study on modeling carbon fiber reinforced polymer (CFRP) cruciform specimens under biaxial fatigue loading. It describes the development of a biaxial loading mechanism that subjects cruciform specimens to tension-tension or compression-compression loading at ratios of 1:1 to 1:4. Finite element models of cruciform specimens with different layer configurations were created in ANSYS and fatigue analyzed in nCode DesignLife. Results showed that modeling the CFRP as orthotropic rather than isotropic reduced the predicted fatigue life, with the orthotropic material exhibiting greater sensitivity to load duration. Increasing layer numbers from 6 to 10 also increased fatigue life.
Probabilistic design and random optimization of hollow rectangular composite ...IAEME Publication
This document describes a probabilistic design and random optimization of a hollow rectangular composite beam structure using finite element analysis. A Monte Carlo simulation was conducted by randomly varying design parameters like beam length, ply angles, elastic modulus, and force within defined ranges. Scatter plots of maximum bending stress were obtained for different parameter combinations. Random optimization was then performed to minimize bending stress, obtaining 1000 feasible sets. The best set that reduced bending stress the most is proposed as the optimized design.
This document summarizes a study that uses finite element analysis and Monte Carlo simulation to analyze the bending stress of hollow circular composite beams under random loading conditions. The study varies design parameters like beam length, radius, ply angles, elastic modulus, and force randomly within defined ranges. It analyzes the relationship between maximum bending stress and each parameter. Random optimization is then performed to determine a set of parameters that minimize bending stress. The best optimized set is proposed to reduce bending stress under different loading conditions.
Probabilistic Design Hollow of Airfoil Wing by Using Finite Element MethodIJERA Editor
This document presents a probabilistic finite element analysis of the bending stress in a hollow NACA0012 airfoil composite wing. The analysis varies key geometric parameters, material properties, composite layer properties, and applied load within realistic ranges using Monte Carlo simulation. Scatter plots show the effects of each input parameter on the bending stress output. The results identify that chord length, ply thickness, orientation angle, Young's modulus in the XX direction, and shear modulus in XY have the most significant effects on bending stress, while other inputs have less influence. This probabilistic analysis can help determine robust input parameters and limits for optimization of the airfoil wing design.
This document summarizes a study that used finite element analysis to analyze stress concentrations at bolt hole locations in lap joints. A 3D finite element model of a lap joint was developed using Abaqus software. Non-linear analysis considered the stress-strain behavior of materials and interactions between bolt and plate surfaces. Parametric studies varied the end distance and compared results to failure criteria in design codes. Stress patterns were compared to bearing capacity equations to determine the optimum end distance that prevents premature failure.
Stress Analysis of Automotive Chassis with Various ThicknessesIOSR Journals
Abstract : This paper presents, stress analysis of a ladder type low loader truck chassis structure consisting of
C-beams design for application of 7.5 tonne was performed by using FEM. The commercial finite element
package CATIA version 5 was used for the solution of the problem. To reduce the expenses of the chassis of the
trucks, the chassis structure design should be changed or the thickness should be decreased. Also determination
of the stresses of a truck chassis before manufacturing is important due to the design improvement. In order to
achieve a reduction in the magnitude of stress at critical point of the chassis frame, side member thickness,
cross member thickness and position of cross member from rear end were varied. Numerical results showed that
if the thickness change is not possible, changing the position of cross member may be a good alternative.
Computed results are then compared to analytical calculation, where it is found that the maximum deflection
agrees well with theoretical approximation but varies on the magnitude aspect.
Keywords - Stress analysis, fatigue life prediction and finite element method etc.
Experimental Investigations to Study the Air Flow Patterns on the Headlight D...IJERA Editor
This paper presents some experimental investigations to study the air flow patterns on the headlight domes of different two wheelers (HERO HONDA PASSION PLUS and BAJAJ PULSAR) which influence the stability of the vehicle. The pressure distribution over the surface of the profile and the drag force are to be determined for various headlight dome orientations. This study helps in suggesting the suitable headlight dome profile that may reduce the drag force and effect of turbulence which in turn leads to the increase of vehicle stability. The results obtained during the simulation are to be validated by conducting the experiments on the scale down model of the headlight dome of HERO HONDA PASSION PLUS using Wind Tunnel test rig. The Computational Fluid Dynamics (CFD) tool was used to simulate the air flow pattern on the headlight dome in which boundary layer separation doesn’t exist. The results obtained from the simulation are to be compared with the experimental results from the wind tunnel and the variation is to be found and that should be in the acceptable limit.
Deformation Analysis of a Triangular Mild Steel Plate Using CST as Finite Ele...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Composite dome Shape and Pressure Vessels Optimizationalilimam2
This document presents a multi-level optimization strategy for composite pressure vessels with nonmetallic liners. In the first level, different head shapes (geodesic and ellipsoidal) and winding angles are compared based on maximizing a "modified shape factor" objective function calculated using finite element analysis. In the second level, the stacking sequence and number of layers are further optimized for the best head shape and winding angle selected in level 1. The goal is to optimize design variables like head shape, winding angle, layer thickness, number of layers, and stacking sequence to improve burst pressure, internal volume, and reduce vessel weight.
This paper presents an algorithm for shape optimization of composite pressure
vessels head. The shape factor which is defined as the ratio of internal volume to weight of
the vessel is used as an objective function. Design constrains consist of the geometrical
limitations, winding conditions, and Tsai-Wu failure criterion. The geometry of dome shape
is defined by a B-spline rational curve. By altering the weights of control points, depth of
dome, and winding angle, the dome shape is changed. The proposed algorithm uses genetic
algorithm and finite element analysis to optimize the design parameters. The algorithm is
applied on a CNG pressure vessel and the results show that the proposed algorithm can
efficiently define the optimal dome shape. This algorithm is general and can be used for
general shape optimization
Studies on geometrical featured metallic shell structures for inward inversionIAEME Publication
This document summarizes research on the inward inversion of metallic shell structures with various geometric features for energy absorption applications. Experiments were conducted using an Instron testing machine to apply loads and measure force-displacement responses for aluminum shell samples with different shapes, wall thicknesses, steps, and curvatures. Finite element simulations of the inversion process matched well with experimental force-displacement graphs and stress distributions. Key findings include frusta with 6-7 degree angles absorbed the most energy, while steps and uneven curvatures reduced energy absorption and caused unstable force responses. Thicker shells and straighter top portions also improved energy absorption performance during inversion.
Gas foil bearing analysis and the effect of bump foil thickness on its perfor...ijmech
Gas foil bearings (GFBs) satisfy many of the requirements noted for novel oil-free turbomachinery.However, GFBs have a limited load carrying capacity. This paper presents a numerical model in order to assess the performance characteristics of gas foil bearings. The finite difference scheme has been used to discretize the governing Reynolds equation and the pressure is calculated by solving non-linear matrix equation using Newton-Raphson technique. The static performance analysis has been carried out. The computational analysis have been compared with the experimental and theoretical results available in the literature and the effects of bump foil thickness, number of bumps and bump compliance coefficient on the load carrying capacity at different rotor speed have been investigated. The results of the study show that too thin bump foil thickness may lead to a significant decrease in the load capacity. However for accurate predictions of the foil bearing performances, more details foil structure of 1D and 2D finite element model
should be considered.
The Effect of Direct- and Cross-Rolling on Mechanical Properties and Microstr...Kaveh Rahimi Mamaghani
Severely deformed commercial pure aluminum sheets by constrained groove pressing are direct and crossrolled.
The grain size evolution and dislocation density during rolling are studied using Williamson-Hall
analysis on x-ray diffraction patterns of the deformed samples. These results and optical microscopy
observations show that subsequent direct or cross-rolling of constrained groove pressed aluminum can
produce elongated fine grains. The minimum crystallite size is achieved after cross-rolling of constrained
groove pressed samples. By direct-rolling or cross-rolling of annealed sheet, the maximum intensity in x-ray
diffraction patterns remains on (200) like annealed aluminum but direct-rolling or cross-rolling of constrained
groove pressed sheets changes the maximum intensity from (111) for constrained groove pressed
sheets to (220). Also, mechanical properties are studied using tensile test and hardness measurement. The
results show that cross-rolling on constrained groove pressed samples is more effective than direct-rolling in
mechanical properties improvement.
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.
This document reviews research on magneto-rheological (MR) and electro-rheological (ER) fluids. It discusses the properties of MR fluids and their behavior with and without an external magnetic field. It also describes common models used to characterize MR fluids, including the Bingham plastic and Herschel-Bulkley models. The document then summarizes several research papers on topics like modeling MR fluid behavior, optimizing MR damper design using computational fluid dynamics, developing control systems for MR dampers in artillery gun recoils, and performing experiments to validate theoretical MR damper models. It concludes that damping force in MR dampers depends non-linearly on fluid properties and applied magnetic fields, and is influenced by parameters
Stress Analysis of FRP Composite Cylinder with Closed EndsIOSR Journals
Composite cylinders made of a polymer matrix such as epoxy reinforced with glass or carbon fibers possess extremely high strength. Proper modeling of FRP composite cylinder is very essential for many applications. FRP composite cylinders are commonly used in the aerospace, automotive, marine and construction industries. The present work is to study the variation of stressesat the top end, middle and bottom end portions of a composite cylinder by varying the diameter to thickness ratio(S) and fiber angle (θ).The four layered angle ply (θ0/-θ0/-θ0/θ0) composite cylinder is considered forthe present work and behavior of each portion (Top end, middle and Bottom end) is studied.For the present work composite cylinder is modeled in ANSYS and analysis was carried out using numerical software. It isfound thatthe increment of stress takes place linearly with respect to D/t ratio due to reduction in thickness of the layer.The critical fiber angle is 45⁰ to 60⁰ as it offers high resistance against axial and circumferential deformation in middle and end portions.
Assessment of Flow Control using Passive Devices around Bluff BodiesAnuragSingh1049
This article presents a review study on the experimental investigation of aerodynamic force on a car like bluff bodies along with the simulations using different turbulence models used in CFD (Computational Fluid Dynamics). The aim of the study is to find a useful method for the better design of a car body. It was observed that combination of wind tunnel experiments and CFD computation can lead to better aerodynamic design. Significant reduction in coefficient of the lift and drag for a car model were found when a more streamlined body design was adopted. Appropriate change in the slant angle for the car body can significantly reduce the fuel consumption. Also, the use of simulations in combination with the experimental observations helps in predicting the flow behavior more accurately.
CFD and EXPERIMENTAL ANALYSIS of VORTEX SHEDDING BEHIND D-SHAPED CYLINDERAM Publications
The flow around bluff bodies is an area of great research of scientists for several years. Vortex shedding is
one of the most challenging phenomenon in turbulent flows. This phenomenon was first studied by Strouhal. Many
researchers have modeled the various objects as cylinders with different cross-sections among which square and
circular cylinders were the most interested sections to study the vortex shedding phenomenon. The Vortex Shedding
frequency depends on different aspects of the flow field such as the end conditions, blockage ratio of the flow passage,
and width to height ratio. This case studies the wave development behind a D-Shaped cylinder, at different Reynolds
numbers, for which we expect a vortex street in the wake of the D-Shaped cylinder, the well known as von Kármán
Street. This body typically serves some vital operational function in aerodynamic. In circular cylinder flow separation
point changes with Reynolds number but in D-Shaped cylinder there is fix flow separation point. So there is more
wake steadiness in D-Shaped cylinder as compared to Circular cylinder and drag reduction because of wake
steadiness.In the present work CFD simulation is carried out for flow past a D-Shaped cylinder to see the wake
behavior. The Reynolds number regime currently studied corresponds to low Reynolds number, laminar and
nominally two-dimensional wake. The fluid domain is a two-dimensional plane with a D-Shaped cylinder of
dimensions B=90mm, H=80mm and L=200mm. CFD calculations of the 2-D flow past the D-Shaped cylinder are
presented and results are validated by comparing with Experimental results of pressure distribution on cylinder
surface. The experimentation is carried out using small open type wind tunnel. The flow visualization is done by
smoke visualization technique. Results are presented for various B/H ratios and Reynolds numbers. The variation of
Strouhal number with Reynolds number is found from the analysis. The focus of the present research is on reducing
the wake unsteadiness.
EXPERIMENTAL and ANALYTICAL ANALYSIS of FLOW PAST D-SHAPED CYLINDERAM Publications
The study of flow past the bluff body is very important in aerodynamics. The D-Shaped cylinder is one of the
bluff bodies which serve some vital operational function in aerodynamic. So it is necessary to study the flow past the DShaped
cylinder. In this paper the flow past D-Shaped cylinder of dimensions B=90mm, H=80mm, and L=200mm is
studied experimentally and analytically. The analytical results are validated with experimental results. The flow
parameter drag co-efficient is calculated for different Reynolds number using Drag co-efficient relation and results of
drag co-efficient are validated with experimental results. Based on the experimental and analytical results, the drag coefficient
of circular cylinder and D-Shaped cylinder are compared. The Strouhal number is calculated using Strouhal
number co-relation for different Reynolds number and results of Strouhal number are validated with previous results
from literature. The experimentation is carried in small open type wind tunnel. The Reynolds number regime currently
studied corresponds to low Reynolds number. The present research involves the calculation of drag co-efficient for DShaped
cylinder. This experiment is based on existing wind tunnel that is already developed. The focus of the present
research is on finding the drag co-efficient both by experimentally and analytically.
h
m
Seg-
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Segment
Length
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X2
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1. The document presents an analysis of optimizing the cost of reinforced concrete chimneys through the use of interior point methods in MATLAB.
2. The objective is to minimize total construction cost subject to constraints related to stresses, reinforcement percentages, and bearing capacity. Design variables include segment thicknesses, vertical and horizontal reinforcement amounts.
3. The optimization was run for a 66m chim
Theoretical study for r.c. columns strengthened with gfrp with different main...Ahmed Ebid
DOI: 10.13140/2.1.3631.9041
It becomes a common practice to strength and repair reinforced concrete columns by wrapping them with GFRP sheets. The aim of this research is to develop a formula to describe the relation between the gain of strength of reinforced concrete square columns, their longitudinal reinforcement and number of warped layers of GFRP sheets. The research is based on simulating loading tests of a set of 12 reinforced concrete columns with different reinforcement ratios and different number of warped layers of GFRP sheets using ANSYS software. The outputs of the ANSYS models are verified using experimental tests results carried out by the author in earlier research. The results of the study are used to develop a proposed formula to correlate the axial capacity of the warped square RC column with its reinforcement ratio and the confining stress caused by the sheets. Values from both proposed formula design and formula of Egyptian Code of Practice (ECP) are compared with ANSYS outputs and experimental results. The final conclusion is that gained strength due to confining equals to (confining stress / Fcu)
This study developed mathematical models to optimize weld bead geometry for TIG welding of aluminum hybrid composites. Response surface methodology was used to establish relationships between welding parameters (arc voltage, current, speed) and bead characteristics (height, width, penetration). Experiments were conducted using a Box-Behnken design. Quadratic models relating the parameters to characteristics had correlation coefficients over 75% and were found to accurately represent the welding process. Optimization identified the optimal parameter combination for achieving desirable bead geometry.
A novel dual point clamper for low-rigidity plate milling with deformation co...eSAT Journals
Abstract
The surface profile accuracy plays a significant role in achieving the overall product’s functional performance, which is seriously impacted by the cutting forces, clamping forces, and residual stresses. Conventionally, many researches about deformation compensation focus on cutting forces and fixture layout and do not consider clamping forces. Actually, clamping forces, which would dynamically change along with the movements of cutting tools, are essential in precision machining process. In this paper, a novel dual-point clamper method with adaptive deformation compensation is proposed to improve the workpieces milling precision. Based on the Generalized Principle of Superposition Method, a mathematical model considering the deflection from both cutting forces and clamping forces has been estimated and compared with the traditional clamping scheme. Both 3D finite element model (FEM) based simulation experiments and experimental case studies are carried out, and their results show good agreement with each other. The deflection computation and prediction from numerical studies indicates the efficiency and correctness of the proposed approach.
Keywords: Compensation; Deformation; Fixture; Milling
Optimization for stiffeners of rectangular surface condenser operating under ...eSAT Journals
Abstract Surface condenser operates under differential external pressure during its service life which causes deformation of equipment. Stiffening arrangements are provided in condenser to restrict deformation of equipment within allowable limit. Condenser is the equipment having lot of internals like heater tube, protruded nozzles, baffles, inside piping etc. So, it is essential to optimize location and size of stiffeners. In the present study sub-assembly of rectangular surface condenser is analysed for optimization of stiffener size. Response surface optimization along with design of experiment methodology is used for stiffener optimization. Design of experiment is carried out with the help of central composite design method. Optimization of stiffener size and location of the stiffener helps to reduce obstruction to steam flow in condenser. Key Words: Response surface optimization, Design of experiment, Central Composite design, Screening optimization, Finite Element Method.
Forming Limit Prediction of High Tensile Strength Steel using FEA SimulationIJERD Editor
Forming limit prediction of High Tensile Strength Steel (HTSS) sheet was carried out by using finite element analysis. JSTAMP/NV was used in the finite element analysis. Thickness of HTSS specimen was 1.0mm, and the length was 120mm.And the width was varied from 20mm to 80mm. Stretching test was operated by Erichsen test. In this study, the forming limit prediction method for predicting the localized necking before the fracture was proposed.FLD of HTSS was compared between experimental results and analytical results. Forming limit diagrams (FLD) obtained by FEAagreed well with the FLD obtained by experiment.
IRJET- Optimal Riser Design for Sand Casting of Drop Ball using Constraint Op...IRJET Journal
This document presents an optimization of the riser design for sand casting of a drop ball weighing 11370 kg and made of steel. The objective is to minimize the riser volume through constrained optimization in MATLAB to increase casting yield. A mathematical model of a cylindrical riser with insulating sleeve and neck is developed. The optimized riser dimensions of 1.03 m3 volume, 1.05 m diameter and height are found to provide a 16.6% reduction from the industry riser volume of 1.236 m3, meeting shrinkage requirements. Validation with modulus method calculations supports the optimized design.
Contact Pressure Validation of Steam Turbine Casing for Static Loading ConditionIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Static Structural, Fatigue and Buckling Analysis of Jet Pipe Liner by Inducin...IRJET Journal
This document analyzes the static structural, fatigue, and buckling behavior of conventional and corrugated jet pipe liners through finite element analysis. A conventional liner model and optimized corrugated liner model were created and meshed. Static structural analysis found that the corrugated liner had lower deformation and similar von-Mises stresses to the conventional liner. Fatigue analysis determined the corrugated liner had a slightly lower fatigue life but still above the design target of 1 million cycles. Buckling analysis revealed the corrugated liner had a higher buckling load multiplier, indicating it is stiffer than the conventional liner against buckling. In conclusion, introducing corrugation improved the liner's buckling strength without negatively impacting other
Composite dome Shape and Pressure Vessels Optimizationalilimam2
This document presents a multi-level optimization strategy for composite pressure vessels with nonmetallic liners. In the first level, different head shapes (geodesic and ellipsoidal) and winding angles are compared based on maximizing a "modified shape factor" objective function calculated using finite element analysis. In the second level, the stacking sequence and number of layers are further optimized for the best head shape and winding angle selected in level 1. The goal is to optimize design variables like head shape, winding angle, layer thickness, number of layers, and stacking sequence to improve burst pressure, internal volume, and reduce vessel weight.
This paper presents an algorithm for shape optimization of composite pressure
vessels head. The shape factor which is defined as the ratio of internal volume to weight of
the vessel is used as an objective function. Design constrains consist of the geometrical
limitations, winding conditions, and Tsai-Wu failure criterion. The geometry of dome shape
is defined by a B-spline rational curve. By altering the weights of control points, depth of
dome, and winding angle, the dome shape is changed. The proposed algorithm uses genetic
algorithm and finite element analysis to optimize the design parameters. The algorithm is
applied on a CNG pressure vessel and the results show that the proposed algorithm can
efficiently define the optimal dome shape. This algorithm is general and can be used for
general shape optimization
Studies on geometrical featured metallic shell structures for inward inversionIAEME Publication
This document summarizes research on the inward inversion of metallic shell structures with various geometric features for energy absorption applications. Experiments were conducted using an Instron testing machine to apply loads and measure force-displacement responses for aluminum shell samples with different shapes, wall thicknesses, steps, and curvatures. Finite element simulations of the inversion process matched well with experimental force-displacement graphs and stress distributions. Key findings include frusta with 6-7 degree angles absorbed the most energy, while steps and uneven curvatures reduced energy absorption and caused unstable force responses. Thicker shells and straighter top portions also improved energy absorption performance during inversion.
Gas foil bearing analysis and the effect of bump foil thickness on its perfor...ijmech
Gas foil bearings (GFBs) satisfy many of the requirements noted for novel oil-free turbomachinery.However, GFBs have a limited load carrying capacity. This paper presents a numerical model in order to assess the performance characteristics of gas foil bearings. The finite difference scheme has been used to discretize the governing Reynolds equation and the pressure is calculated by solving non-linear matrix equation using Newton-Raphson technique. The static performance analysis has been carried out. The computational analysis have been compared with the experimental and theoretical results available in the literature and the effects of bump foil thickness, number of bumps and bump compliance coefficient on the load carrying capacity at different rotor speed have been investigated. The results of the study show that too thin bump foil thickness may lead to a significant decrease in the load capacity. However for accurate predictions of the foil bearing performances, more details foil structure of 1D and 2D finite element model
should be considered.
The Effect of Direct- and Cross-Rolling on Mechanical Properties and Microstr...Kaveh Rahimi Mamaghani
Severely deformed commercial pure aluminum sheets by constrained groove pressing are direct and crossrolled.
The grain size evolution and dislocation density during rolling are studied using Williamson-Hall
analysis on x-ray diffraction patterns of the deformed samples. These results and optical microscopy
observations show that subsequent direct or cross-rolling of constrained groove pressed aluminum can
produce elongated fine grains. The minimum crystallite size is achieved after cross-rolling of constrained
groove pressed samples. By direct-rolling or cross-rolling of annealed sheet, the maximum intensity in x-ray
diffraction patterns remains on (200) like annealed aluminum but direct-rolling or cross-rolling of constrained
groove pressed sheets changes the maximum intensity from (111) for constrained groove pressed
sheets to (220). Also, mechanical properties are studied using tensile test and hardness measurement. The
results show that cross-rolling on constrained groove pressed samples is more effective than direct-rolling in
mechanical properties improvement.
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.
This document reviews research on magneto-rheological (MR) and electro-rheological (ER) fluids. It discusses the properties of MR fluids and their behavior with and without an external magnetic field. It also describes common models used to characterize MR fluids, including the Bingham plastic and Herschel-Bulkley models. The document then summarizes several research papers on topics like modeling MR fluid behavior, optimizing MR damper design using computational fluid dynamics, developing control systems for MR dampers in artillery gun recoils, and performing experiments to validate theoretical MR damper models. It concludes that damping force in MR dampers depends non-linearly on fluid properties and applied magnetic fields, and is influenced by parameters
Stress Analysis of FRP Composite Cylinder with Closed EndsIOSR Journals
Composite cylinders made of a polymer matrix such as epoxy reinforced with glass or carbon fibers possess extremely high strength. Proper modeling of FRP composite cylinder is very essential for many applications. FRP composite cylinders are commonly used in the aerospace, automotive, marine and construction industries. The present work is to study the variation of stressesat the top end, middle and bottom end portions of a composite cylinder by varying the diameter to thickness ratio(S) and fiber angle (θ).The four layered angle ply (θ0/-θ0/-θ0/θ0) composite cylinder is considered forthe present work and behavior of each portion (Top end, middle and Bottom end) is studied.For the present work composite cylinder is modeled in ANSYS and analysis was carried out using numerical software. It isfound thatthe increment of stress takes place linearly with respect to D/t ratio due to reduction in thickness of the layer.The critical fiber angle is 45⁰ to 60⁰ as it offers high resistance against axial and circumferential deformation in middle and end portions.
Assessment of Flow Control using Passive Devices around Bluff BodiesAnuragSingh1049
This article presents a review study on the experimental investigation of aerodynamic force on a car like bluff bodies along with the simulations using different turbulence models used in CFD (Computational Fluid Dynamics). The aim of the study is to find a useful method for the better design of a car body. It was observed that combination of wind tunnel experiments and CFD computation can lead to better aerodynamic design. Significant reduction in coefficient of the lift and drag for a car model were found when a more streamlined body design was adopted. Appropriate change in the slant angle for the car body can significantly reduce the fuel consumption. Also, the use of simulations in combination with the experimental observations helps in predicting the flow behavior more accurately.
CFD and EXPERIMENTAL ANALYSIS of VORTEX SHEDDING BEHIND D-SHAPED CYLINDERAM Publications
The flow around bluff bodies is an area of great research of scientists for several years. Vortex shedding is
one of the most challenging phenomenon in turbulent flows. This phenomenon was first studied by Strouhal. Many
researchers have modeled the various objects as cylinders with different cross-sections among which square and
circular cylinders were the most interested sections to study the vortex shedding phenomenon. The Vortex Shedding
frequency depends on different aspects of the flow field such as the end conditions, blockage ratio of the flow passage,
and width to height ratio. This case studies the wave development behind a D-Shaped cylinder, at different Reynolds
numbers, for which we expect a vortex street in the wake of the D-Shaped cylinder, the well known as von Kármán
Street. This body typically serves some vital operational function in aerodynamic. In circular cylinder flow separation
point changes with Reynolds number but in D-Shaped cylinder there is fix flow separation point. So there is more
wake steadiness in D-Shaped cylinder as compared to Circular cylinder and drag reduction because of wake
steadiness.In the present work CFD simulation is carried out for flow past a D-Shaped cylinder to see the wake
behavior. The Reynolds number regime currently studied corresponds to low Reynolds number, laminar and
nominally two-dimensional wake. The fluid domain is a two-dimensional plane with a D-Shaped cylinder of
dimensions B=90mm, H=80mm and L=200mm. CFD calculations of the 2-D flow past the D-Shaped cylinder are
presented and results are validated by comparing with Experimental results of pressure distribution on cylinder
surface. The experimentation is carried out using small open type wind tunnel. The flow visualization is done by
smoke visualization technique. Results are presented for various B/H ratios and Reynolds numbers. The variation of
Strouhal number with Reynolds number is found from the analysis. The focus of the present research is on reducing
the wake unsteadiness.
EXPERIMENTAL and ANALYTICAL ANALYSIS of FLOW PAST D-SHAPED CYLINDERAM Publications
The study of flow past the bluff body is very important in aerodynamics. The D-Shaped cylinder is one of the
bluff bodies which serve some vital operational function in aerodynamic. So it is necessary to study the flow past the DShaped
cylinder. In this paper the flow past D-Shaped cylinder of dimensions B=90mm, H=80mm, and L=200mm is
studied experimentally and analytically. The analytical results are validated with experimental results. The flow
parameter drag co-efficient is calculated for different Reynolds number using Drag co-efficient relation and results of
drag co-efficient are validated with experimental results. Based on the experimental and analytical results, the drag coefficient
of circular cylinder and D-Shaped cylinder are compared. The Strouhal number is calculated using Strouhal
number co-relation for different Reynolds number and results of Strouhal number are validated with previous results
from literature. The experimentation is carried in small open type wind tunnel. The Reynolds number regime currently
studied corresponds to low Reynolds number. The present research involves the calculation of drag co-efficient for DShaped
cylinder. This experiment is based on existing wind tunnel that is already developed. The focus of the present
research is on finding the drag co-efficient both by experimentally and analytically.
h
m
Seg-
ment
Segment
Length
m
X1
mm
X2
mm2
Total
X2
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Avg.
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concrete
m3
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Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
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Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
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Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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Date: May 29, 2024
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Using Imperialist Competitive Algorithm to Find the Optimum Shape Design of Internally Pressurized Torispherical Dome Ends Based on Buckling Pressure
1. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 387
Using Imperialist Competitive Algorithm to Find the Optimum
Shape Design of Internally Pressurized Torispherical Dome Ends
Based on Buckling Pressure
Behzad Abdi behzad.abdi@gmail.com
Faculty of Mechanical Engineering
University Technology Malaysia-UTM
81310 UTM, Skudai, Johor, Malaysia
Hamid Mozafari mozafari.h@gmail.com
Faculty of Mechanical Engineering
University Technology Malaysia-UTM
81310 UTM, Skudai, Johor, Malaysia
Amran Ayob amran@fkm.utm.my
Faculty of Mechanical Engineering
University Technology Malaysia-UTM
81310 UTM, Skudai, Johor, Malaysia
Abstract
In this paper, Imperialist Competitive Algorithm (ICA) and Genetic Algorithm (GA)
are used to find the optimal form for torispherical dome ends under internal
pressure load. According to fabrication and strength of material requirements, a
group of compromised counters are studied. According to ASME Section VIII and
BS5500 pressure vessel codes, a reasonable buckling pressure limit is
proposed. Four-centered ellipse method is used to describe the geometry of the
torispherical dome end that this method is commonly used in engineering
drawing. A minimum weight optimization problem based on buckling pressure is
studied. Two different size torispherical dome end examples are selected and
studied. Imperialist Competitive Algorithm is found to be very efficient and easy
to use for the applications, such as torispherical dome end and subjected to
internally pressurized loading.
Keywords: Imperialist Competitive Algorithm, Genetic Algorithm, Four-Centered Ellipse Method,
Torispherical, Buckling Pressure, Internal Pressure
1. INTRODUCTION
Pressure vessels are very important in shell structures and a majority of them are axisymmetric.
Torispherical dome ends are frequently used as end closures on pressure vessels and different
types of cylindrical containers which can be found in various fields, such as aerospace, food
processing, chemical, nuclear, oil industries, and so on. In this paper, we are only concerned with
the structural honesty of the dome ends of the pressure hull.
Designers are seeking for maximum strength of structure with minimum weight. Minimum weight
design of cylindrical and conical shells have been studied in details [1-3]. It seems that, for
external pressurized cased, the optimization of torispherical dome ends under buckling
2. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 388
constraints was attempted in [4-6]. But studies concerned with the optimal shape design of
torispherical dome end which under internal pressure loading are still limit. In this paper, we
looked for an optimal deign of torispherical dome end according to elastic – plastic buckling
pressure.
The British pressure vessel code BS5500 gives the design pressure w
P of internally pressurized
dome ends which is not allowed to exceed 1/8.33 of the elastic plastic buckling pressure b
P while
for the ASME section VIII it is 1/19.4. Therefore, in this paper, reasonable buckling pressure
range is proposed between 8.33 w
P and19.4 w
P .
By using four-centered ellipse, three commonly used dome geometries that namely hemispherical
dome, ellipsoidal dome, and torispherical dome can be described [7]. This method is commonly
used in engineering drawing and it is very useful in the design and construction of the dome
structure.
Imperialist Competitive Algorithm (ICA) is a new socio – politically motivated global search
strategy that has recently been introduced for dealing with different optimization task [8]. This
evolutionary optimization strategy has shown great performance in both convergence rate and
better global optima achievement [9-11]. In this paper, we used imperialist Competitive Algorithm
in optimizing torispherical dome ends and compared it with the genetic algorithm results.
2. GEOMETRY OF TORISPHERICAL DOME ENDS
At first, consider an elastic torispherical dome end with constant thickness t (Figure 1) under
static internal pressure. It can be assumed that there is not any flange and the torispherical dome
end is fully clamped at the edge.
The geometry of torispherical dome end can be constructed by using the four-centered ellipse
method (Figure 1).
If we know the ratio
b
K
a
= , then the other parameter , ,rθ φ , and R can be determined from the
following equation:
FIGURE 1: Geometry of torispherical dome end
1 1
tan tan
b
K
a
θ − −
= =
(1)
/ 2a D=
b
OA
B
φθ
r
R
t
3. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 389
2
π
φ θ= − (2)
2
1 sin cos
2 cos
a
r
θ θ
θ
+ −
=
(3)
1 sin
1
2sin cos
a
R
θ
θ θ
−
= +
(4)
Finally, the total weight of torispherical dome end with constant thickness is [5, 6]
( )2 2
2 cos 1 cos
2
W t r r R
π
πγ ω= − Φ + Φ + − Φ
(5)
Where
2
D
r a rω = − = − (6)
1
sin
R r
ω−
Φ =
−
(7)
And γ is the specific gravity.
In the [5, 6] Thickness t and the ratios / , /r D R D were selected for the design variables of the
optimum shape design of torispherical dome end. However, in this article, when the four-centered
ellipse method is used, the radius of spherical cap R and the radius of toroidal knuckle r have
certain relations which can be expressed as function of the angle of spherical cap θ and the
ratio K . Therefore the thickness t and the ratio K are selected for design variables.
The choice of boundary values for the thickness t and the ratio K depends on practical
application. From Harvey’s study [14] in order to minimize the hoop stresses, the torispherical
dome end must should a large knuckle radius. Must of pressure vessel contraction codes
recognize this fact and therefore specify a minimum permissible knuckle radius. For instance, the
British pressure vessel codes BS5500 and the ASME version VIII specify the minimum value of
the knuckle radius as 6% of the crown radius. Therefore, the lower limit on the knuckle
shallowness ( / 0.06r D = ) is chosen in this article. Blachut [5] showed that an unexpected drop in
the buckling strength with the range 0.45 / 0.5r D≤ ≤ . Therefore, the range of /r D is selected to
be 0.06 / 0.45r D≤ ≤ in this paper.
3. MATHEMATICAL FORMULATION
An internally pressurized torispherical dome end is designed for the minimum weight objective
satisfying specified design requirement. The manufacturing limitations on the geometric
parameters and the mechanical properties of the shell material are the preassigned parameters
for this design problem. The following optimization problem can then be formulated.
3.1 Cost function
Accompanying engineering demands for high pressure vessels with and without large sizes are
often the economic ones of weight reduction to save materials, to enhance shipping and erection
procedures and reduce fabrication costs. Therefore, cost function ( )F x% for weight is considered
to be minimized in this paper
Minimize ( ) /d s
F x W W=%
4. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 390
Where s
W is the weight of hemispherical dome end (
21
2
s
W D tπγ= ) and d
W is the weight of
torispherical dome end.
3.2 Design variables
The dimensions of the torispherical dome end are selected as the independent design variables.
These variables are:
(a) The thickness of torispherical dome end, 1
x t=
(b) The ratio of minor axis to the major axis, 2
/ tanx K b a θ= = =
(c) The major axis of the torispherical dome end, 3
x a=
According to engineering design consideration, the length of major radius a is specified which
must coincide with cylindrical shell at the junction. Therefore, there are two independent design
variables taken for this problem. Therefore the vector x% will be given as
( ),opt
x t K=%
3.3 Constraints
The lower and upper bounds are imposed on all the design variables. Based on the standard of
practical design, a reasonable buckling pressure range is proposed. The BS5500 design pressure
is not allowed to exceed / 8.33b
P , and the corresponding ratio for ASME is /19.4b
P .
The constraints i
g are represented by the following:
(a) The lower bound on buckling pressure
1
( )
0L b
b
P P
g
P
−
= ≤
Where b
P is the critical buckling pressure and L
P is the lower bound of critical buckling pressure,
( 8.33L w
P P= where w
P is the maximum work pressure).
(b) The upper bound on buckling pressure
2
( )
0b U
U
P P
g
P
−
= ≤
Where U
P is the lower bound of critical buckling pressure. ( 19.4U w
P P= )
(c) The lower bound on design variables
3
( )
0
( )
Li
i
Ui Li
x x
g
x x
−
= ≤
−
Where i
x are design variables ( 1, 2)i = ,
Ui
x is the upper bound value of design variable i
x and
Li
x is the lower bound value of design variables i
x
(d) The upper bound on design variables
4
( )
0
( )
Ui
i
Ui Li
x x
g
x x
−
= ≤
−
5. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 391
4. IMPERIALIST COMPETITIVE ALGORITHM
Imperialist competitive algorithm (ICA) is a new evolutionary algorithm for optimization. This
algorithm starts with an initial population. Each population in ICA is called country. Some of the
best countries in the population selected to be the imperialists and the rest form the colonies of
these imperialists. In this algorithm the more powerful imperialist, have the more colonies. When
the competition starts, imperialists attempt to achieve more colonies and the colonies start to
move toward their imperialists. So during the competition the powerful imperialists will be
improved and the weak ones will be collapsed. At the end just one imperialist will remain. In this
stage the position of imperialist and its colonies will be the same. The flowchart of this algorithm
is shown in Figure 2 [11]. More details about this algorithm are presented in [8-13].
FIGURE 2: Flowchart of the imperialist competitive algorithm (ICA) [11].
5. MODEL DESCRIPTION
In this paper, two reference models of the torispherical dome end were considered. Both Models
have the same poisson’s ratio of 0.3 and the same elastic modulus of
7 2
3.0 10 /lbf in× . The fixed
major axis a for model 1 is 63.98in and 91.73in for model 2. The principal dimensions for two
references models are showed in table 1. The range of the ratio K is selected as
0.21 0.95K≤ ≤ , and the range of thickness t as 50 / 150D t≤ ≤ . The preassigned lower and
upper bound of design variables which were used in this paper are listed in table 2.
Torispherical dome Model 1 Model 2
Length of major axis. a 63.98 in 91.73 in
Ratio of minor to major axis, /K b a= 0.61 0.53
Thickness, t 1.26 in 1.77 in
Radius of toroidal knuckle, r 29.28 in 34.35 in
Angle of toroidal knuckle, φ 58.62
o
61.99
o
Radius of spherical cap, R 95.91 in 156.83 in
Angle of spherical cap, θ 32.38
o
28.01
o
TABLE 1: The Principle Design Data of Reference Dome
6. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 392
Torispherical dome Side constraint Model 1 Model 2
Major axis. a Fixed 63.98 in 91.73 in
Ratio of minor to major
axis, /K b a=
Lower bound 0.21 0.21
Upper bound 0.95 0.95
Thickness, t
Lower bound 0.85 in 1.22 in
Upper bound 2.56 in 3.66 in
TABLE 2: The Upper and Lower Bounds of Design Variables
6. NUMERICAL RESULTS AND DISCUSSION
The numerical comparison between the results of the two optimal torispherical dome ends
and two reference dome ends models are listed in table 3 and 4. Table3. The results in table
3 are optimized by using Genetic Algorithm (GA) and in table 4 we use Imperialist
competitive algorithm (ICA) for optimization. Also, the comparisons between optimal dome
ends and referenced dome ends are displayed in Figure 3 and Figure 4. For a hemispherical
dome end, the thickness effects of the dome end to weight and the effect of ratio K to
weight are showed in Figure 5 and Figure 6. In additional, for a hemispherical dome end, the
thickness effects of the dome end to the buckling pressure is studied and showed in Figure 7
and table 5. Also, if thickness is kept constant, the effect of ratio K to the buckling pressure
of torispherical dome end is also studied and the results are showed in Figure 8 and table 6.
If the ratio K is kept constant, the effect of thickness to the buckling pressure is also studied
and the results are showed in Figure 9 and table 7.
Torispherical dome
Model 1 Model 2
Ref. dome
Opt. dome
(GA)
Ref. dome
Opt. dome
(GA)
Length of major axis. a 63.98 in 63.98 in 91.73 in 91.73 in
Ratio of minor to major axis, /K b a= 0.61 0.64 0.53 0.64
Thickness, t 1.26 in 0.87 in 1.77 in 1.24 in
Radius of toroidal knuckle, r 29.28 in 31.42 in 34.35 in 45.04 in
Angle of toroidal knuckle, φ 58.62
o
57.39
o
61.99
o
57.39
o
Radius of spherical cap, R 95.91 in 91.82 in 156.83 in 131.66 in
Angle of spherical cap, θ 32.38
o
32.61
o
28.01
o
32.61
o
Total weight of dome end 913.06 lbf 644.4 lbf 2486.9 lbf 1887.8 lbf
Elastic – Plastic buckling pressure, b
P 8216.6 psi 2741.7 psi 6273.85 psi 2715.9 psi
TABLE 3: The numerical comparison table of torispherical dome ends
7. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 393
Torispherical dome
Model 1 Model 2
Ref. dome
Opt. dome
(ICA)
Ref. dome
Opt. dome
(ICA)
Length of major axis. a 63.98 in 63.98 in 91.73 in 91.73 in
Ratio of minor to major axis, /K b a= 0.61 0.65 0.53 0.65
Thickness, t 1.26 in 0.85 1.77 in 1.22
Radius of toroidal knuckle, r 29.28 in 32.14 in 34.35 in 46.09 in
Angle of toroidal knuckle, φ 58.62o
56.98o
61.99o
56.98o
Radius of spherical cap, R 95.91 in 90.57 in 156.83 in 129.84 in
Angle of spherical cap, θ 32.38o
33.02o
28.01o
33.02o
Total weight of dome end 913.06 lbf 634.1 lbf 2486.9 lbf 1870.9 lbf
Elastic – Plastic buckling pressure, b
P 8216.6 psi 2737.7 psi 6273.85 psi 2742.8 psi
TABLE 4: The numerical comparison table of torispherical dome ends
FIGURE 3: The dome configuration comparison of model 1 for minimum weight design
FIGURE 4: The dome configuration comparison of model 2 for minimum weight design
Optimum Dome
Reference Dome
r R
2D a=
29.28 32.14
95.91 90.57
1.26 0.85
32.38 28.01
58.62 61.99
o o
o o
Reference Dome Optimum Dome
r in r in
R in R in
t in t in
θ θ
φ φ
= =
= =
= =
= =
= =
Optimum Dome
Reference Dome
r R
2D a=
34.35 46.09
156.83 129.84
1.77 1.22
28.01 33.02
61.99 56.98
o o
o o
Reference Dome Optimum Dome
r in r in
R in R in
t in t in
θ θ
φ φ
= =
= =
= =
= =
= =
8. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 394
FIGURE 5: The weight via thickness of hemispherical dome end
FIGURE 6: The weight via the slope K of torispherical dome end
FIGURE 7: The buckling pressure via thickness of hemispherical dome end
9. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 395
Model 1
1 , 63.98K a in= =
Model 2
1 , 91.73K a in= =
( )t in ( )b
P psi ( )t in ( )b
P psi
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
718.7
2257
4193
6519
9173
12124
15349
18828
22546
26490
30648
35013
39574
44325
49260
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
450.4
1301
2419
3756
5285
6986
8845
10850
12992
15265
17661
20176
22804
25542
28386
TABLE 5: The buckling pressure table at some corresponding thickness of hemispherical dome end
FIGURE 8: The Buckling Pressure via the Slope K of Torispherical Dome End
Model 1
1.26 , 63.98t a in= =
Model 2
1.77 , 91.73t a in= =
/K b a= ( )b
P psi /K b a= ( )b
P psi
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
91.97
384.2
910.6
1703
2787
4182
5902
7954
10341
13064
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
89.14
372.3
882.6
1651
2702
4054
5721
7709
10023
12662
TABLE 6: The buckling pressure table at some corresponding thickness of hemispherical dome end
10. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 396
FIGURE 9: The buckling pressure via thickness of torispherical dome end
Model 1
1.61 , 63.98K a in= =
Model 2
0.53 , 91.73K a in= =
( )t in ( )b
P psi ( )t in ( )b
P psi
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
259.7
750.0
1394
2165
3047
4027
5099
6254
7490
8800
10182
11632
13147
14725
16365
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
114.0
329.3
612.4
951.1
1338
1768
2239
2746
3289
3864
4471
5107
5773
6466
7186
TABLE 7: The buckling pressure table at some corresponding thickness of hemispherical dome end
From table 3 and 4 and Figure 3 and 4, the ratio of K is found to be 0.64 for optimal model 1
and mode2 by using Genetic algorithm and it is found to be 0.65 for both of models when we
use imperialist competitive algorithm (ICA), while the ratios of K are chosen as 0.61 and
0.53 for the reference models. The critical buckling pressure are 2741.7 psi for optimum
model 1 and 2715.9 psi for optimum model 2 by using genetic algorithm and 2737.7 psi and
2742.8 psi for imperialist competitive algorithm (ICA) and for reference models being
8216.6 psi and 6273.8 psi .
According to this fact that the ratios of K for the optimum models are bigger than that of
reference models, the shape of the optimum dome ends of two models tend to be bigger
than the reference models, while the buckling pressures are lower than the reference models.
Because of we set the preassigned buckling pressure bound (8.33 10.4w b w
P P P≤ ≤ ) and select
the minimum weight type of cost function, the weight is reduced by 29.4% for model 1 and
11. Behzad Abdi, Hamid Mozafari & Amran Ayob
International Journal of Engineering, (IJE), Volume (4): Issue (5) 397
24.1% for model 2 when we optimized by genetic algorithm and 30% for model 1 and 24.7%
for model 2 while imperialist competitive algorithm is our optimization method.
From table 7 and Figure 9, the critical buckling pressure for a constant ratio K torispherical
dome end is to be raised with the increase of the thickness. Also, the other important factor
of the total weight of the torispherical dome end is thickness. However, the larger the
thickness, the greater the weight and this situation must be taken into account.
7. CONSLUSION & FUTURE WORK
The four-centered ellipse method is a very easy and good method to describing the shape of
the torispherical dome end and it makes the shape optimization problem very easy. This
methodology uses only two design variables: thickness and the ratio of minor axis to major
axis K . Imperialist competitive algorithm is a very efficient and easy to use algorithm for
optimization problems such as the optimization of torispherical dome end subject to internally
pressurized loading and the results of imperialist competitive algorithm are very close to the
results of genetic algorithm.
For future study, the optimum design of composite torispherical dome end may consider such
factor as buckling pressure, strength, space use, manufacturing cost, safety, weight, and so on.
8. REFERENCES
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2. J. Farkas. “Optimum Design of Metal Structures”. John Wiley, New York. 1984
3. J. Middleton and J. Petmska, “Optimal pressure vessel shape design to maximize limit load”.
Engng. Comput. 3, 287-294, 1988
4. E. H. Mansfield, “An optimum surface of revolution for pressurized shell”. Int. J. Mech. Sci.
23, 57-62. 1981
5. J. Blachut, “Search for optimal torispherical end closures under buckling constraints”. Int. J.
Mech. Sci. 31, 623-633. 1989
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optimization inspired by imperialistic competition”, IEEE Congress on Evolutionary
Computation, 4661–4667. 2007
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Algorithm, a novel approach for PID controller design in MIMO distillation column process”,
International Journal of Intelligent Computing and Cybernetics, 1 (3), 337–355. 2008
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Tool for Nash Equilibrium Point Achievement”. Lecture notes in computer science, 5073, 680-
695. 2008
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algorithm to the design of a linear induction motor”, Energy Conversion and Management. 51,
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12. R. Rajabioun, E. Atashpaz-Gargari, C. Lucas., “Colonial Competitive Algorithm as a Tool for
Nash Equilibrium Point Achievement” , Springer LNCS, Book Chapter, 2008
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of Imperialist Competitive Algorithm to Simulation of Energy Demand Based on Economic
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