In Finite Element Analysis, which option is correct for computation of load due to specified boundary stress?

Can be computed using a local coordinate system but not one-dimensional interpolation functions

Can be computed using a local coordinate system and one-dimensional interpolation functions

Can be computed using a local coordinate system but not one-dimensional interpolation functions

Cannot be computed using a local coordinate system but one-dimensional interpolation functions can be used

Neither a local coordinate system nor one-dimensional interpolation functions can be used

In Finite Element Analysis, what are the values of nodal forces in the following element if the line 2-4 is 160 in long?

0 and 800 along the DOF 7 and 8 respectively

1600 along both the DOF 3 and 7

800 and 0 along the DOF 3 and 4 respectively

0 and 800 along the DOF 7 and 8 respectively

0 and 800 along the DOF 3 and 4 respectively

What is the global load vector in Finite Element Analysis of the following structure if the local load vector is \(\begin{bmatrix}0\\0\\2\\0\\1\\0\end{bmatrix}\) and θ=0?

\(\begin{bmatrix}0\\0\\2\\0\\0\\1\end{bmatrix}\)

\(\begin{bmatrix}0\\0\\0\\2\\0\\1\end{bmatrix}\)

\(\begin{bmatrix}0\\0\\2\\0\\0\\1\end{bmatrix}\)

\(\begin{bmatrix}0\\0\\2\\0\\1\\0\end{bmatrix}\)

\(\begin{bmatrix}0\\0\\0\\2\\1\\0\end{bmatrix}\)

In transformations, what is the transformation matrix R in the relation F=RQ if the load vector in global coordinates is F and the load vector in element coordinates is Q?

\(\begin{bmatrix}cos \alpha & -sin \alpha & 0 & 0 & \\sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & -sin \alpha & \\0 & 0 & sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)

\(\begin{bmatrix}cos \alpha & sin \alpha & 0 & 0 & \\-sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & sin \alpha & \\0 & 0 & -sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)

\(\begin{bmatrix}cos \alpha & -sin \alpha & 0 & 0 & \\sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & -sin \alpha & \\0 & 0 & sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)

\(\begin{bmatrix}cos \alpha & sin \alpha & 0 & 0 & \\-sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & -sin \alpha & \\0 & 0 & sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)

\(\begin{bmatrix}cos \alpha & -sin \alpha & 0 & 0 & \\sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & sin \alpha & \\0 & 0 & -sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)

Which option is not correct concerning the internal load vector in the finite element model of plane elasticity problems?

Its computation doesn’t involve evaluation of line integrals for any type of element

It is computed at all the nodes interior of the element

It is computed only when the element falls on the boundary of the domain on which tractions are known

Its computation doesn’t involve evaluation of line integrals for any type of element

It is evaluated in global coordinates but not in element coordinates

In the Finite Element Method, which expression is correct for a linear triangular element if S is the shape function, Ae is its area, and K is a constant?

\(\frac{\partial S}{\partial y}=\frac{K}{A_e^2}\)

\(\frac{\partial S}{\partial x}=\frac{K}{A_e}\)

\(\frac{\partial S}{\partial y}=\frac{K}{A_e^2}\)

\(\frac{\partial S}{\partial x}\)=KAe

\(\frac{\partial S}{\partial y}\)=KAe2

12 + Mcqs in Plane Elasticity Evaluation Integrals in Finite Element Method Page 1 McqOptions

1.	In the Finite Element Method, which element is known for the slowest convergence?
A.	Linear triangular element
B.	Quadratic triangular element
C.	Linear rectangular elements
D.	Quadratic rectangular elements
Answer» B. Quadratic triangular element

Discussion

2.	In Finite Element Analysis, which option is correct for computation of load due to specified boundary stress?
A.	Can be computed using a local coordinate system and one-dimensional interpolation functions
B.	Can be computed using a local coordinate system but not one-dimensional interpolation functions
C.	Cannot be computed using a local coordinate system but one-dimensional interpolation functions can be used
D.	Neither a local coordinate system nor one-dimensional interpolation functions can be used
Answer» B. Can be computed using a local coordinate system but not one-dimensional interpolation functions

Discussion

3.	In vibration and transient analysis of beams, if the linear acceleration scheme predicts the solution,then it is unstable for the first several time steps, but it eventually becomes stable.
A.	True
B.	False
Answer» C.

Discussion

4.	In Finite Element Analysis, what are the values of nodal forces in the following element if the line 2-4 is 160 in long?
A.	1600 along both the DOF 3 and 7
B.	800 and 0 along the DOF 3 and 4 respectively
C.	0 and 800 along the DOF 7 and 8 respectively
D.	0 and 800 along the DOF 3 and 4 respectively
Answer» C. 0 and 800 along the DOF 7 and 8 respectively

Discussion

5.	What is the expression for the traction term tn in the element load vector Qe=∮┌cheψTtds of the following figure where L23 is the length of the line 2-3?
A.	tn=-T(-1+\(\frac{s}{L_{23}})\)
B.	tn=T(-1+\(\frac{s}{L_{23}})\)
C.	tn=-T(1+\(\frac{s}{L_{23}})\)
D.	tn=T(1+\(\frac{s}{L_{23}})\)
Answer» C. tn=-T(1+\(\frac{s}{L_{23}})\)

Discussion

6.	What is the global load vector in Finite Element Analysis of the following structure if the local load vector is \(\begin{bmatrix}0\\0\\2\\0\\1\\0\end{bmatrix}\) and θ=0?
A.	\(\begin{bmatrix}0\\0\\0\\2\\0\\1\end{bmatrix}\)
B.	\(\begin{bmatrix}0\\0\\2\\0\\0\\1\end{bmatrix}\)
C.	\(\begin{bmatrix}0\\0\\2\\0\\1\\0\end{bmatrix}\)
D.	\(\begin{bmatrix}0\\0\\0\\2\\1\\0\end{bmatrix}\)
Answer» B. \(\begin{bmatrix}0\\0\\2\\0\\0\\1\end{bmatrix}\)

Discussion

7.	In transformations, what is the transformation matrix R in the relation F=RQ if the load vector in global coordinates is F and the load vector in element coordinates is Q?
A.	\(\begin{bmatrix}cos \alpha & sin \alpha & 0 & 0 & \\-sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & sin \alpha & \\0 & 0 & -sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)
B.	\(\begin{bmatrix}cos \alpha & -sin \alpha & 0 & 0 & \\sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & -sin \alpha & \\0 & 0 & sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)
C.	\(\begin{bmatrix}cos \alpha & sin \alpha & 0 & 0 & \\-sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & -sin \alpha & \\0 & 0 & sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)
D.	\(\begin{bmatrix}cos \alpha & -sin \alpha & 0 & 0 & \\sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & sin \alpha & \\0 & 0 & -sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)
Answer» B. \(\begin{bmatrix}cos \alpha & -sin \alpha & 0 & 0 & \\sin \alpha & cos \alpha & 0 & 0 & \\0 & 0 & cos \alpha & -sin \alpha & \\0 & 0 & sin \alpha & cos \alpha & \\& & & & \ddots\end{bmatrix}\)

Discussion

8.	Which option is not correct concerning the internal load vector in the finite element model of plane elasticity problems?
A.	It is computed at all the nodes interior of the element
B.	It is computed only when the element falls on the boundary of the domain on which tractions are known
C.	Its computation doesn’t involve evaluation of line integrals for any type of element
D.	It is evaluated in global coordinates but not in element coordinates
Answer» C. Its computation doesn’t involve evaluation of line integrals for any type of element

Discussion

9.	In the Finite Element Method, the vector of internal forces is computed only when the element falls on the boundary of the domain on which tractions are absent.
A.	True
B.	False
Answer» C.

Discussion

10.	In Finite Element Analysis, what is the correct load vector for the linear quadrilateral element with area Ae, thickness he and uniform body force vector f?
A.	\(\frac{A_e h_e}{4} \)f
B.	\(\frac{A_e h_e}{3}\)f
C.	\(\frac{h_e}{3A_e}\)f
D.	\(\frac{h_e}{4A_e}\)f
Answer» B. \(\frac{A_e h_e}{3}\)f

Discussion

11.	In Finite Element Analysis, what is the correct load vector for a linear triangular element with area Ae, thickness he and uniform body force vector f?
A.	\(\frac{A_e h_e}{4}\)f
B.	\(\frac{A_e h_e}{3}\)f
C.	\(\frac{h_e}{3A_e}\)f
D.	\(\frac{h_e}{4A_e}\)f
Answer» C. \(\frac{h_e}{3A_e}\)f

Discussion

12.	In the Finite Element Method, which expression is correct for a linear triangular element if S is the shape function, Ae is its area, and K is a constant?
A.	\(\frac{\partial S}{\partial x}=\frac{K}{A_e}\)
B.	\(\frac{\partial S}{\partial y}=\frac{K}{A_e^2}\)
C.	\(\frac{\partial S}{\partial x}\)=KAe
D.	\(\frac{\partial S}{\partial y}\)=KAe2
Answer» B. \(\frac{\partial S}{\partial y}=\frac{K}{A_e^2}\)

Discussion

Explore topic-wise MCQs in Finite Element Method.

In the Finite Element Method, which element is known for the slowest convergence?

In Finite Element Analysis, which option is correct for computation of load due to specified boundary stress?

In vibration and transient analysis of beams, if the linear acceleration scheme predicts the solution,then it is unstable for the first several time steps, but it eventually becomes stable.

In Finite Element Analysis, what are the values of nodal forces in the following element if the line 2-4 is 160 in long?

What is the expression for the traction term tn in the element load vector Qe=∮┌cheψTtds of the following figure where L23 is the length of the line 2-3?

What is the global load vector in Finite Element Analysis of the following structure if the local load vector is \(\begin{bmatrix}0\\0\\2\\0\\1\\0\end{bmatrix}\) and θ=0?

In transformations, what is the transformation matrix R in the relation F=RQ if the load vector in global coordinates is F and the load vector in element coordinates is Q?

Which option is not correct concerning the internal load vector in the finite element model of plane elasticity problems?

In the Finite Element Method, the vector of internal forces is computed only when the element falls on the boundary of the domain on which tractions are absent.

In Finite Element Analysis, what is the correct load vector for the linear quadrilateral element with area Ae, thickness he and uniform body force vector f?

In Finite Element Analysis, what is the correct load vector for a linear triangular element with area Ae, thickness he and uniform body force vector f?

In the Finite Element Method, which expression is correct for a linear triangular element if S is the shape function, Ae is its area, and K is a constant?