This document contains a collection of practice problems related to finite element analysis of two-dimensional vector variable problems, including axisymmetric problems. The problems cover derivation of element stiffness matrices and strain-displacement matrices for various element types under different conditions, calculation of element stresses and displacements, modeling of cylinders under pressure, and determination of global stiffness matrices for structures. The elements and conditions include constant strain triangles, linear strain triangles, axisymmetric triangles, plane stress, plane strain, and shells.
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
One of the most Simple and Interesting topics in Engineering is FEA. My work will guide average students to score good marks. I have given you full package which includes 2 Marks and Question Banks of previous year. All the Best
For Guidance : Comment Below Happy to Teach and Learn along with you guys
General steps of the finite element methodmahesh gaikwad
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
Study of Different Structural Elements Used For Thin Composite PlateIOSR Journals
Composites are extensively used in aerospace and automotive industry. The requirement usually is to
create holes in composite members to facilitate mounting of various members. These holes act as stress
concentration regions and the causes of failure. At present, the analytical treatments developed are very
restrictive to particular cases. Thus to analyze complex hole patterns subjected to tensile loadings there is
necessity of FEA software. FEA tool offers different structural elements for analysis, each with different number
of nodes. Engineer has to shortlist the elements and need to carryout permutations for selecting suitable element
for analysis. Thus study of these different elements is carried out as part of this paper. Different Structural
Finite elements are thus studied and applied to a model under study for tensile loading condition. The results of
FE Analysis are validated against analytical solution and best fit Structural element is suggested at the end if
paper. Scope of this study is limited to graphite/epoxy composites and can be extended further.
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
One of the most Simple and Interesting topics in Engineering is FEA. My work will guide average students to score good marks. I have given you full package which includes 2 Marks and Question Banks of previous year. All the Best
For Guidance : Comment Below Happy to Teach and Learn along with you guys
General steps of the finite element methodmahesh gaikwad
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
Study of Different Structural Elements Used For Thin Composite PlateIOSR Journals
Composites are extensively used in aerospace and automotive industry. The requirement usually is to
create holes in composite members to facilitate mounting of various members. These holes act as stress
concentration regions and the causes of failure. At present, the analytical treatments developed are very
restrictive to particular cases. Thus to analyze complex hole patterns subjected to tensile loadings there is
necessity of FEA software. FEA tool offers different structural elements for analysis, each with different number
of nodes. Engineer has to shortlist the elements and need to carryout permutations for selecting suitable element
for analysis. Thus study of these different elements is carried out as part of this paper. Different Structural
Finite elements are thus studied and applied to a model under study for tensile loading condition. The results of
FE Analysis are validated against analytical solution and best fit Structural element is suggested at the end if
paper. Scope of this study is limited to graphite/epoxy composites and can be extended further.
Design and Analysis Nose Landing Gear SupportIJSRD
Nose landing gear support bracket is one of the main parts in the nose landing gear assembly, whose function is to maintain the stability of the landing gear during the movements. This work is focused on the FEA analysis of support bracket by varying the stress concentration area, The objective of this work is to determine the static and modal analysis of support bracket with different stress concentration areas, then analysis is done using ANSYS WORKBENCH, These results could provide some useful suggestions for design and improvement for the better component
ELASTO-PLASTIC ANALYSIS OF A HEAVY DUTY PRESS USING F.E.M AND NEUBER’S APPR...IAEME Publication
Heavy duty presses are subjected to extreme load conditions especially during operations like bending, shearing, drawing etc. It generates very high stresses in the punch and die of the press tool. As a sequel to this, failure of the press tool occurs, sometimes prematurely. Hence estimation of the stresses under severe load conditions is of paramount importance.
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
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.
Analysis and Estimation of Stiffness of Outer Race of Aircraft Bearingspaperpublications3
Abstract: The prime objective of the project is to determine the stiffness of the outer race of the aircraft bearing used in auxiliary gearbox. The main need of the project reflects in the conclusion derived from the data after calculation and analysis that it gives the minimum necessary value and maximum limits of the dimensions, and stiffness for the given material required for the outer race of the bearing which was designed and analyzed based on the data. Other data such as Bulk modulus, Rigidity modulus etc., could be calculated from the Stiffness found out for the bearing. Here the changes are made to the dimensions of the outer race in the design stage and the results are simulated in software solution, based on which we can reach a conclusion. Respective data for designing the outer race such as dimension, material of the outer race, standard procedures for design and analysis were followed by reference from standard books, papers and under guidance and discretion of respondents at CVRDE.
Keywords: Aircraft Bearings, Loading, Deflection, Moment of inertia, Stiffness.
Title: Analysis and Estimation of Stiffness of Outer Race of Aircraft Bearings
Author: Adithiyan. E. S, Arvind. B, Balaji. C, Elango. M, Mr. Ramaniraj. A
ISSN 2393-8471
International Journal of Recent Research in Civil and Mechanical Engineering (IJRRCME)
Paper Publications
Determination of Stress Concentration factor in Linearly Elastic Structures w...IJERA Editor
Stress concentration is the localization of stress around stress raisers. Sudden changes in the geometry of
structures give rise to stress values that are higher than those obtained by elementary equations of solid
mechanics. Therefore the evaluation of stress state at such locations needs specialized techniques such as Finite
Element Method (FEM).The finite element method is a numerical procedure that can be used to obtain solution
to a large variety of engineering problems such as structural, thermal, heat transfer, electromagnetism and fluid
flow.
In the present investigation, focus has been kept on the finite element modeling and determination of stress
concentration factor (SCF) in linearly elastic structures with different stress-raisers such as circular and elliptical
holes and double semicircular notch at different locations in a finite plate. The results obtained from FEM are
compared with those obtained by analytical relations as given in literature. A commercially available finite
element solver ANSYS has been used for the modeling and analysis in the investigation. Throughout the
investigation, plane82, which is an eight node two-dimensional element is used for the discretization.
Material Optimization of Leaf Spring of Tractor Trolley by FEAIJMER
Leaf Spring (LS) is an indispensable machine element of the automobile sector. In this
particular work we are analyzed a LS with the help of Finite Element Method when subjected to static
loads and appropriate boundary conditions. The LS taken into consideration is that of a Tractor Trolley
having a Gross Vehicle Weight of 20 ton. According to the existing dimension of simple leaf spring it
has modeled in solid works 2013.after that cad model has used to discretized in to small no of element
and nodes to perform the required finite element analysis. Initially analysis has done for three different
materials and taken the most economic and suitable material for leaf spring in the optimization stages.
Comparision of material was perform on the basis of result obtained from the analysis of leaf spring like
von mises stress, strain and deflection.
Probabilistic Design of Hollow Circular Composite Structure by using Finite E...IJERA Editor
This study represents simulation of hollow circular composite beam by using Monte Carlo method .A three
dimensional static analysis of large displacement type has been carried out. Finite element analysis of hollow
circular composite structure has been carried out and uncertainty in bending stress is analyzed. Bending stress
was objective function. Beam length, beam radius, elastic modulus, shear modulus and Poisson ratio of epoxy
graphite, ply angles of hollow circular section, radius and force are randomly varied within effective range and
their effect on bending stress has been analyzed. In order to validate the results, one loop of simulation is
benchmarked from results in literature. Ultimately, best set of probabilistic design variable is proposed to reduce
bending stress under static loading condition.
Probabilistic Design Hollow of Airfoil Wing by Using Finite Element MethodIJERA Editor
This study represents simulation of Airfoil composite beam by using Monte Carlomethod. A three dimensional static analysis of large displacement type has been carried out. Finite element analysis of NACA0012 airfoil composite structure has been carried out and uncertainty in bending stress is analyzed. Bending stress was objective function. Chord length , beam length ,elastic modulus in XY,YZ,XZ,shear modulus of epoxy graphite in in XY,YZ,XZ, ply angle and ply thickness of airfoil section, force are varied within effective range and their effect on bending stress has been analyzed. In order to validate the results, one loop of simulation is benchmarked from results in literature. Ultimately, best set of probabilistic design variable is proposed to reduce bending stress under static loading condition.
DETAILED STUDIES ON STRESS CONCENTRATION BY CLASSICAL AND FINITE ELEMENT ANAL...IAEME Publication
Stress concentration is very important aspect in all aspects of mechanical design, it arises due to geometric discontinuities in the structure common examples are openings in pressure vessels and piping it is observed that the maximum stress is much more than the nominal stress .The conventional methods for determining the stress concentration factors are the empirical formulae mentioned in design handbooks such as Roark’s formulae for stress and strain this formulas can also be expressed in terms of graphs the finite element method a regarded as the third dimension in engineering plays very important role in the overall design process, this is mainly because it reduces the dependence on standard available geometries, experimentation and most importantly the time and cost associated with it however it has been observed that the finite element analysis results are depended on mesh quality parameters and this fact has not been studied thoroughly the main aim of the present study is to consider a standard configuration that is a plate with a circular hole in it subjected to axial tension
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
ME6603 - FINITE ELEMENT ANALYSIS UNIT - IV NOTES AND QUESTION BANK
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44. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 79
UNIT – IV – TWO DIMENSIONAL VECTOR VARIABLE PROBLEMS
PART – A
4.1) Write a displacement function equation for CST element. [AU, May / June – 2016]
4.2) Give the stiffness matrix equation for an axisymmetric triangular element.
4.3) What is axisymmetric element?
4.4) Give examples of axisymmetric problems. [AU, May / June – 2012]
4.5) What is an axisymmetric problem? [AU, April / May – 2011]
4.6) Write short notes on axisymmetric problems.
[AU, Nov / Dec – 2007, April / May – 2009]
4.7) What is meant by axi-symetric field problem? Given an example.
[AU, Nov / Dec – 2009]
4.8) When are axisymmetric elements preferred? [AU, Nov / Dec – 2013]
4.9) State the situations where the axisymmetric formulation can be applied.
[AU, April / May – 2011]
4.10) Give four applications where axisymmetric elements can be used.
[AU, April / May – 2011]
4.11) List the applications of axisymmetric elements. [AU, May / June – 2016]
4.12) State the applications of axisymmetric elements. [AU, Nov / Dec – 2010]
4.13) Write down the stress-strain relationship matrix for an axisymmetric triangular
element. [AU, May / June – 2016]
4.14) Write down the constitutive relationship for axisymmetric problem.
[AU, April / May – 2009]
4.15) Write down the constitutive relationship for the plane stress problem.
[AU, Nov / Dec – 2010]
4.16) What do you mean by constitutive law and give the constitutive law for axi-
symmetric problems? [AU, April / May, Nov / Dec – 2008]
45. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 80
4.17) Specify the body force term and the body force vector for axisymmetric triangular
element. [AU, Nov / Dec – 2013]
4.18) Give one example each for plane stress and plane strain problems.
[AU, April / May - 2008]
4.19) Explain plane strain problem with an example. [AU, May / June – 2012]
4.20) Give a brief note on static condensation.
4.21) Prove that 2 0 for plane strain condition.
4.22) Differentiate axi – symmetric and cyclic –symmetric structures.
4.23) Differentiate axi-symmetric load and asymmetric load with examples.
4.24) State the condition for axi-symmetric problem.
4.25) List the required conditions for a problem assumed to be axisymmetric.
[AU, April / May – 2010]
4.26) What are the four basic sets of elasticity equations? [AU, May / June – 2012]
4.27) Give examples for the following cases.
4.28) a) plane stress problem b) plane strain problem c) axi-symmetric problem
4.29) Define the following terms with suitable examples [AU, April / May – 2010]
i) Plane stress, plane strain ii) Node, element and shape functions
iii) Axisymmetric analysis iv) Iso – parametric element
4.30) Define the term initial strain.
4.31) State the effect of Poisson’s ratio in plane strain problem.
4.32) How will the stress field vary linearly?
4.33) Compare the changes in the D matrix evolved out of plane strain, plane stress and axi-
symmetric problem.
4.34) What are the types of shell element? [AU, May / June – 2016]
46. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 81
PART – B
4.35) Derive the element strain displacement matrix and element stiffness matrix of a CST
element. [AU, April / May – 2011]
4.36) Explain the terms plane stress and plane strain problems. Give the constitutive laws
for these cases. [AU, Nov / Dec – 2007, April / May – 2009]
4.37) Derive the equations of equilibrium in the case of a three dimensional system.
[AU, Nov / Dec – 2007, 2008, April / May – 2009]
4.38) Derive the expression for constitutive stress-strain relationship and also reduce it to
the problem of plane stress and plane strain. [AU, Nov / Dec - 2008]
4.39) Derive the constant-strain triangular element’s stiffness matrix and equations.
[AU, April / May - 2008]
4.40) Derive the linear – strain triangular element’s stiffness matrix and equations.
[AU, April / May – 2008]
4.41) Derive the stiffness matrix and equations for a LST element.
[AU, Nov / Dec – 2012]
4.42) Derive the element strain displacement matrix and element stiffness matrix of a
triangular element. [AU, May / June – 2012]
4.43) Derive the expression for the element stiffness matrix for an axisymmetric shell
element. [AU, Nov / Dec – 2007, April / May – 2009]
4.44) Describe the step by step procedure of solving axisymmetric problem by finite
element formulation. [AU, May / June – 2012]
4.45) Derive an expression for the stiffness matrix of an axisymmetric element.
[AU, April / May – 2011]
4.46) For an axisymmetric triangular element. Obtain the [B] matrix and constitutive matrix
[AU, Nov / Dec – 2010]
4.47) Derive the stress-strain relationship matrix (D) for the axisymmetric triangular
element. [AU, Nov / Dec – 2012]
4.48) Explain the modeling of cylinders subjected to internal and external pressure using
axisymmetric. [AU, Nov / Dec – 2011]
47. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 82
4.49) For a thick cylinder subjected to internal and external pressure, indicate the steps of
finding the radial stress. [AU, Nov / Dec – 2010]
4.50) Derive the material property matrix for axisymmetric elasticity.
[AU, Nov / Dec – 2011]
4.51) Explain Galerkin’s method of formulation for determining the stiffness matrix for an
axisymmetric triangular element. [AU, Nov / Dec – 2013]
4.52) The (x, y) co- ordinates of nodes i, j and k of an axisymmetric triangular element are
given by (3, 4), (6, 5), and (5, 8) cm respectively. The element displacement (in cm)
vector is given as q = [0.002, 0.001, 0.001, 0.004, -0.003, 0.007]T
. Determine the element
strains. [AU, Nov / Dec – 2009]
4.53) Calculate the element stresses 21 and,,, xyyx and the principle angle p for
the element shown below.
4.54) For the triangular element shown below, obtain the strain – displacement relation
matrix B and determine the strains x ,y and xy.
48. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 83
4.55) Consider the triangular element show in Figure. The element is extracted from a thin
plate of thickness 0.5 cm. The material is hot rolled low carbon steel. The Nodal co-
ordinates are xi =0, yi = 0, xj =0, yj = -1, xk =0, yk = -1 cm,. Determine the elemental
stiffness matrix. Assuming plane stress analysis. Take µ = 0.3 and E = 2.1*107
N/cm2
[AU, May / June – 2012]
4.56) For the CST element given below, assemble stain displacement matrix. Take t = 20
mm and E = 2*105
N/mm2
[AU, Nov / Dec - 2008]
4.57) For the triangular element as shown in figure. Determine the strain – displacement
matrix [B] and constitutive matrix [D]. Assume plane stress conditions. Take μ = 0.3, E =
30*106
N/m2
and thickness t = 0.1m. Also calculate the element stiffness matrix for the
triangular element. [AU, Nov / Dec – 2016]
49. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 84
4.58) A plate of dimensions 15cm * 6cm * 1cm is subjected to an axial pull of 5kN.
Assuming a typical element is of dimensions as shown in figure. Determine the strain
displacement matrix and constitutive matrix. E = 200GPa, µ = 0.3 and t = 10mm.
[AU, April / May – 2015]
4.59) Obtain the global stiffness matrix for the plate shown in figure. Taking two triangular
elements. Assume plane stress condition. [AU, May / June – 2012]
50. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 85
4.60) For the constant strain triangular element shown in figure below, assemble the strain –
displacement matrix. Take t = 20 mm and E = 2 x 105
N/mm2
.
[AU, Nov / Dec – 2007, 2013, 2015, April / May – 2009]
4.61) For the plane strain element shown in the figure, the nodal displacements are given as
: u1= 0.005 mm, u2 = 0.002 mm, u3=0.0mm, u4 = 0.0 mm, u5 = 0.004 mm, u6 = 0.0
mm. Determine the element stresses. Take E = 200 Gpa and = 0.3. Use unit thickness
for plane strain. [AU, April / May - 2010]
4.62) For the plane strain elements shown in figure, the nodal displacements are given as u1
= 0.005 mm, v1 = 0.002 mm, u2 = 0.0, v2 = 0.0, u3 = 0.005 mm, v3 = 0.30 mm. Determine
the element stresses and the principle angle. Take E = 70 GPa and Poision's ratio = 0.3
and use unit thickness for plane strain. All coordinates are in mm.
[AU, May / June – 2016]
51. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 86
4.63) For the two-dimensional loaded plate as shown in Figure. Determine the nodal
displacements and element stress using plane strain condition considering body force.
Take Young’s modulus as 200 GPa, Poisson’s ratio as 0.3 and density as 7800 kg/m3
.
[AU, April / May – 2011]
4.64) Determine the stiffness matrix for the triangular elements with the (x, y) coordinates
of the nodes are (0,-4), (8,0) and (0,4) at nodes i, j, k. Assume plane stress condition. E =
200 GPa, Poisson's ratio = 0.35. [AU, Nov / Dec – 2014]
4.65) A thin plate a subjected to surface fraction as shown in Figure. Calculate the global
stiffness matrix. Table t = 25 mm, E = 2 *105
N/mm2
and γ = 0.30. Assume plane stress
condition. [AU, Nov / Dec – 2011]
52. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 87
4.66) Determine the deflection of a thin plate subjected to extensional load as shown.
4.67) Determine the nodal displacements and the element stresses for the two dimensional
loaded plate as shown in figure. Assume plane stress condition. Body force may be
neglected in comparison to the external forces. Take E = 210GPa, µ = 0.25, Thickness t =
10mm. [AU, May / June – 2011]
4.68) Calculate nodal displacement and elemental stresses for the truss shown in Figure. E
= 70 GPa cross-sectional area A = 2 cm2
for all truss members. [AU, Nov / Dec – 2012]
53. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 88
4.69) A thin elastic plate subjected to uniformly distributed edge load as shown below.
Find the stiffness and force matrix of the element.
4.70) For the configuration as shown in figure determine the deflection at the point load
applications. Use one model method. Assume plane stress condition.
[AU, April / May – 2011]
4.71) A long cylinder of inside diameter 80 mm and outside diameter 120 mm snugly fits in
a hole over its full length. The cylinder is then subjected to an internal pressure of 2
54. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 89
MPa. Using two elements on the 10 mm length shown, find the displacement at the inner
radius.
4.72) The nodal co-ordinates for an axisymmetric triangular element are given in figure.
Evaluate strain-Displacement matrix for that element. [AU, May / June – 2016]
4.73) Determine the stiffness matrix for the axisymmetric element shown in fig, Take E as
2.1* 105
N/mm2
and Poisson's ratio as 0.3. [AU, Nov / Dec – 2012, 2016]
4.74) Determine the element stresses for the axisymmetric element as shown below. Take
E = 2.1 x 105
N/mm2
and = 0.25.
55. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 90
Use the nodal displacements as
u1 = 0.05 mm w1 = 0.03 mm
u2 = 0.02 mm w2 = 0.02 mm
u3 = 0 mm w3 = 0 mm
4.75) Compute the strain displacement matrix for the following axisymmetric element.
Also calculate the element stress vectors. If [AU, April / May – 2011]
[q] = [ 3.484 0 3.321 0 0 0]T
* 10-3
cm
[D] = [
27 12 12 0
12 27 12 0
12 12 27 0
0 0 0 8
]
4.76) Calculate the element stiffness matrix and the thermal force vector for the
axisymmetric triangular element as shown below. The element experiences a 150º C
increase in temperature. Take = 10 x 10-6
/ ºC, E = 2 x 105
N/mm2
and µ= 0.25
All dimensions are mm
(9,10)
(6,7) (8,7)
X
Y
1 2
3
56. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 91
4.77) Calculate the element stiffness matrix for the axisymmetric triangular element shown
in Fig. The element experiences a 15 °C increase in temperature. The coordinates are in
mm. Take α= 10 x 10-6
/ °C, E = 2 x 105
N/mm2
, v = 0.25. [AU, May / June – 2016]
4.78) An open ended steel cylinder has a length of 200mm and the inner and outer
diameters as 68mm and 100mm respectively. The cylinder is subjected to an internal
pressure of 2MPa. Determine the deformed shape and distribution of principle stresses.
Take E = 200GPa and Poisson’s ratio = 0.3 [AU, April / May – 2011]
4.79) The steel flywheel as shown below rotates at 3000 rpm. Find the deformed shape of
the fly wheel and give the stress distribution.
4 in
12 in
2 in
1 in
1 in
E = 30 x 10
0.3
6
Psi
v =
4.80) Solve the axi-symmetric field problem as shown below, for the mesh shown there. T0
= 1000ºC R0= 0.02 m, g0 = 107
x 2 W/ m3
= internal heat generation, K = 20
W/mºC
57. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 92
L
4.81) The open –ended steel cylinder as shown below is subjected to an internal pressure of
1MPa. Find the deformed shape and the distribution of principal stresses.