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FEA Exam for Engineering Students

This document contains two practice tests for a finite element analysis exam. It includes questions about deriving the stiffness of a 1D bar element, the differences between FDM and BEM, discretization in FEA, assembling global stiffness matrices, applying boundary conditions, and calculating displacements, strains, stresses, and error for 1D and 2D problems. It also asks students to plot displacement and strain values as functions of distance for a given system.

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270 views2 pages

FEA Exam for Engineering Students

This document contains two practice tests for a finite element analysis exam. It includes questions about deriving the stiffness of a 1D bar element, the differences between FDM and BEM, discretization in FEA, assembling global stiffness matrices, applying boundary conditions, and calculating displacements, strains, stresses, and error for 1D and 2D problems. It also asks students to plot displacement and strain values as functions of distance for a given system.

Uploaded by

hayaaaa
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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FEA (FINITE ELEMENT ANALYSIS) IM-405

Test no 01 (A) Roll No:------------------

1. For 1-D bar element show that k=AE/L.


2. What is the difference between FDM and BEM.
3. There are many engg. problems for which we cannot obtain exact solution.why?

4.For the one-dimensional problem shown, calculate:


a. The global stiffness matrix before the application of boundary conditions.
b. The reduced stiffness matrix after the application of boundary conditions.
K1 = 10,000 N/mm
K2 = 5,000 N/mm
K3 = 10,000 N/mm
F = 500 N

c.Plot the stress elements as a function of the distance.

d.In the above questions, will the answers be the exact answers? If your answer is no,
what aspect of the problem makes it so the FEA answer is not fully correct?

5.A simply supported beam under UDL as shown. The governing differential equation is

EI/2 (d2y/dx2)-F=0

B.C’s i) u(0)=0

ii) u(L)=0

Convert the given differential equation into difference equation using central divided difference approximation, if
F=20 lb/in, l=100 in, E=30x106 lb/ in2 , I=100 in4

F
FEA (FINITE ELEMENT ANALYSIS) IM-405
Test no 01 (B) Roll No:------------------

1. Write down the assumptions on which the formulation of an elastic bar is based.
2. What are the advantages of FEM over FDM?
3. FEA is based on the concept of Discritization, what is discritization?

4.For the given system

(i) Solve for the two elemental stiffness matrices.


(ii) Assemble the global stiffness matrix.
(iii) Compute the global applied force vector (R) considering
only the gravitational force acting on the rod elements.
(iv) After applying the appropriate restraint condition(s), solve
for the nodal displacements.
(v) Solve for the reaction force(s) at the restraint(s).
(vi) Solve for the element strains.
(vii) Solve for the element stresses.

Plot the displacement of both elements as a function of the distance from the top.

Plot the strain of both elements as a function of the distance from the top.

5. Find the relative true error if the exact value is y(x) =0.5320” and the approximated value is y(x)
=0.5998”.

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