Explore topic-wise MCQs in Finite Element Method.

This section includes 13 Mcqs, each offering curated multiple-choice questions to sharpen your Finite Element Method knowledge and support exam preparation. Choose a topic below to get started.

1.

For the following eigenvalue equation to represent a heat transfer problem, a=kA and C= cA. (- frac{d}{dx}(a frac{dU}{dx}) )= CU

A. True
B. False
Answer» B. False
Discussion
2.

The generalized Eigen value problem [K- M]X=0 has a non-zero solution for X. What is the value of if K= ( begin{pmatrix}1&1&1 1&1&1 1&1&1 end{pmatrix} ), M= ( begin{pmatrix}4&4&4 4&4&4 4&4&4 end{pmatrix} )?

A. 1
B. ( frac{1}{2} )
C. 4
D. ( frac{1}{4} )
Answer» E.
Discussion
3.

For the eigenvalue problem of the form A(u) = B(u), which option is not correct about the parameters used in the equation below? (- frac{d^2x}{dx^2}= lambda u )

A. A= ( frac{d^2x}{dx^2} )
B. B=1
C. B=0
D. is called eigenvalue
Answer» D. is called eigenvalue
Discussion
4.

After Finite Element discretization of a structure, which option expresses the free vibrations equation?

A. M +K =F
B. M +K =0
C. M +Kx=F
D. M +Kx=0
Answer» E.
Discussion
5.

Which option is not correct about free vibration analysis problem KX= MX, where X represents the amplitude of displacement x?

A. The displacements are harmonic
B. X represent mode shapes or Eigen vectors
C. represent Eigen value
D. represents Eigen value
Answer» E.
Discussion
6.

The generalized Eigen value problem [K- 2M]X=0 has a non-zero solution for X. What is the value of natural frequency, if K= ( begin{pmatrix}1&1&1 1&1&1 1&1&1 end{pmatrix} ),M= ( begin{pmatrix}9&9&9 9&9&9 9&9&9 end{pmatrix} )?

A. 3
B. 1/9
C. 9
D. 1/3
Answer» E.
Discussion
7.

The free vibrations equation after Finite Element discretization of a structure is expressed as M +Kx=0. Which option is not correct about the free vibration case?

A. Displacements are harmonic
B. x=Xe<sup>i t</sup> where X is amplitude
C. [K- <sup>2</sup>M]X=0
D. KX=M <sup>2</sup>
Answer» E.
Discussion
8.

In FEM, the forced vibrations equation after Finite Element discretization of a structure can be expressed as which option?

A. M +K =F
B. M +K =0
C. M +Kx=F
D. M +Kx=0
Answer» D. M +Kx=0
Discussion
9.

A generalized Eigen value problem [K- 2M]X=0 has a non-zero solution for X. What can be the value of determinant of the matrix [K- 2M]?

A. Any integer
B. 0
C. +1
D. Positive integer
Answer» C. +1
Discussion
10.

In structural mechanics, which option is not correct about linear analysis?

A. Displacements are infinitesimally small
B. Material is linearly elastic
C. Externally applied loads are a function of time
D. Applied loads are not a function of time
Answer» D. Applied loads are not a function of time
Discussion
11.

Which option is not correct about iterative methods for solving system of linear equations?

A. Convergence yields a good approximate solution
B. Insensitive to the growth of round-off errors
C. Gaussian elimination method is an example
D. Starts with an initial approximation
Answer» D. Starts with an initial approximation
Discussion
12.

Which option is not correct about direct methods for solving system of linear equations?

A. In the absence of errors it yields exact solution
B. Errors arising from round off and truncation may give useless results
C. Gaussian elimination method is an example
D. Starts with an initial approximation
Answer» E.
Discussion
13.

The simultaneous linear equations used in FEM for solution of static problems are KX=F, the methods available for solving these equations are divided into two types: direct and iterative.

A. True
B. False
Answer» B. False
Discussion