Download AKTU B-Tech 8th Sem 2016-17 EME061 Finit Element Method Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 8th Semester (Eight Semester) 2016-17 EME061 Finit Element Method Question Paper

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B.TECH.
THEORY EXAMINATION (SEM?VIII) 2016-17
FINIT ELEMENT METHOD
T ime : 3 Hours Max. Marks : 100
Note .' Be precise in your answer. In case ofnumericalproblem assume data wherever not provided.
SECTION ? A
1. Explain the following: 10 x 2 = 20
(a) What is the stiffness matrix?
(b) What is finite element analysis?
(c) Write the advantage of Finite element method.
(d) Write the limitation of FEM.
(e) Explain Galerkin method in short.
(1) What is the convergence?
(g) What is the Global matrix?
(h) Write the stiffness matrix for the beam element.
(i) Write the stages in finite element formulation.
(j) Write the stiffness matrix for truss.
SECTION ? B
2. Attempt any ?ve of the following questions: 5 x 10 = 50
(a) Derive the shape function for linear rectangular element in local coordinate system;
give its dimension of side ?r? and?s? respectively.
(b) Discuss the errors involved in finite element solution with the example of a model
second order differential equation in one dimension.
(c) For a square, isotropic elastic body of thickness ?h?, the displacement are approximated
by1 U(X,Y)=(1-X)yui+ X(1 -Y)U2 U(X, Y) = 0.
(d) State Kirchhoff?s theory and Mindlin theory for plate bending problem. Using four
corner nodes plate, explain displacement, rotation, strain force and moments for both
(e) What do you mean by isoparametric formulation of a finite element problem? Give an
example of real field problem where superparameteric elements can be used and why?
(1) Derive the J acobian for a four nodel rectangular element having coordinates (0, 0), (2,
0), (2, 1) and (0, 1).
(g) A steel rod subjected to compression is modeled by two bar element, as shown in
figure. Determine the nodal displacement and the axial stress in each element. What
other concern should be examined?
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13:20? GPa A=S?? mm2
(h) Line one dimensional element to approximate the temperature distribution along a fan.
The nodal temperature and their corresponding position are shown in figure. What is
the temperature at (a) X: 4cm and (b) X: 80m
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SECTION ? C
Attempt any two of the following questions: 2 x 15 = 30
3
The three member truss shown have identical cross?section ?A? an elastic modulus ".E
Derive the global finite element matrix and evaluate the horizontal and vertical
displacement at the joint ?C? and the reactive forces at joint ?A? and ?B? at hinged
support.
If l???'?'
{?L?
A composite plane wall consist of three materials with conduction and convective
coefficient given as (k1, K2, k3) and (hl, h2, h3) with cross sectional area ?A? each.
Find the effective resistance with an analogy to thermal circuit. Develop global matrix
for temperature change from 400?C to 100?C from one side of wall to other side.
Using Rayleigh?Ritz method, compute the axial displacement ?u? and axial stress ? DX?
for an uniform cross section bar loaded with an uniformly distributed axial load
variation as q = cx along length, where ?c? is load per unit cross section.
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