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.

What is the physical interpretation of the weight function w3 in the following weak form of the continuity equation?-∫Ωew3\((\frac{\partial v_x}{\partial x}+\frac{\partial v_y}{\partial y})\)dxdy=0

A. Hydrostatic pressure
B. Axial force
C. Surface traction
D. Body force
Answer» B. Axial force
Discussion
2.

In matrix algebra, if a matrix is positive definite, then all its eigenvalues are greater than zero.

A. True
B. False
Answer» B. False
Discussion
3.

For the vector form of the finite element model of momentum and continuity equations MΔ+K11Δ+K12P=0 what is the order of matrix F if the order of M is 2n x 2n?

A. 2n x 1
B. 1 x 2n
C. m x 2n
D. 2n x m
Answer» B. 1 x 2n
Discussion
4.

For the vector form of the finite element model of momentum and continuity equations MΔ+K11Δ+K12P=0, what is the correct expression for mass matrix M?

A. M=∫ΩcρψTψdx
B. M=∫ΩcfψTψdx
C. M=∫ΩctψTψdx
D. M=∫ΩcPψTψdx
Answer» B. M=∫ΩcfψTψdx
Discussion
5.

Which equation is the correct vector form of the finite element model of momentum and continuity equations in the flow domain?

A. MΔ+K11Δ+K12P=0
B. MΔ+K11Δ+K22P=F1
C. MΔ+K22Δ+K12P=F1
D. MΔ+K11Δ+K12P=F1
Answer» E.
Discussion
6.

Which option is not correct concerning the velocity variables, vx and vy in the weak form of the momentum and continuity equation?

A. They are primary variables
B. The minimum continuity requirement for interpolation is that they are linear in x and y
C. The minimum continuity requirement for interpolation is that they are constant
D. They are continuous across the inter-element boundary
Answer» D. They are continuous across the inter-element boundary
Discussion
7.

Which option is not correct concerning the pressure variable, P in the weak form of the momentum and continuity equation?

A. P is a primary variable
B. P is a part of the secondary variables
C. P=constant is the minimum continuity requirement for interpolation
D. It is discontinuous across inter-element boundaries
Answer» B. P is a part of the secondary variables
Discussion
8.

If a governing equation represents volume change in an element, then the weight function in its weak form must be like a force that causes the volume change.

A. True
B. False
Answer» B. False
Discussion
9.

Using constitutive relations, what is the value of τxyif μ=0.3 and v=4xy-6y?

A. 0.24x
B. 2.4x
C. 0.12x
D. 1.2x
Answer» E.
Discussion
10.

Using constitutive relations, what is the value of τxxif μ=0.3 and v=4x?

A. 0.24
B. 2.4
C. 0.12
D. 1.2
Answer» C. 0.12
Discussion
11.

For a governing equation, what does one conclude from the weak formulation if it does not contain boundary integral involving weight function?

A. Integration by parts is used
B. Integration by parts is not used
C. The weight function is as a primary variable
D. The weight function is to be made continuous across inter-element boundaries
Answer» C. The weight function is as a primary variable
Discussion
12.

In the formulation of governing equations, which option does not signify the characteristics of a weight function?

A. Weight functions are multiplied to governing equations to obtain weak forms
B. Weight functions are interpreted from the physical setup of the problem
C. Weight function must denote a non-dimensional quantity
D. Weight function can be interpreted as a velocity
Answer» D. Weight function can be interpreted as a velocity
Discussion
13.

In velocity-pressure formulation in FEM, which step is not used in the development of a weak form?

A. Multiply governing equations with weight functions
B. Integrating over the element domain
C. Integrating by parts
D. Performing coordinate transformation
Answer» E.
Discussion