Which option is correct for the first derivative of the shape function S in the study of plane elasticity problems?

It is element-wise constant for both the triangular element as well as a quadrilateral element

It is element-wise constant for triangular element whereas not a constant for quadrilateral element

It is element-wise constant for both the triangular element as well as a quadrilateral element

It is not a constant for triangular element whereas element-wise constant for quadrilateral element

It is a combination of a linear function and constant for both the triangular element and a quadrilateral element

Which option is not correct with respect to the orders of the matrices in the following finite element model of plane elastic equations?Me\(\ddot{\Delta}^e\)+KeΔe=Fe+Qe

The element load vector F has order 2n x 1

Mass matrix M has order 2n x 2n

Stiffness matrix K has order 2n x n

The element load vector F has order 2n x 1

The vector of internal forces Q has order 2n x 1

What is the function on \(\frac{\partial s}{\partial n}\) if S (n, e) denotes the shape function of a linear quadrilateral element?

denotes the shape function of a linear quadrilateral element?a) Linear in e and constant in nb) Constant in e and Linear in nc) Linear in both e and nd) Constant in both e and n

What is the correct statement regarding the shape function S of a linear triangular element?

The first derivatives of S are linear, but the strains are element-wise constant

The first derivatives of S and hence, all the strains are element-wise constant

The first derivatives of S are linear, but the strains are element-wise constant

The first derivatives of S and hence the strains are linear functions

The first derivatives of S are element-wise constant, but the strains are linear

What are the simplest elements that fit for the finite element model of the plane elasticity equations?

Quadratic triangular and quadratic quadrilateral elements

Linear triangular and quadratic quadrilateral elements

Quadratic triangular and linear quadrilateral elements

Linear triangular and linear quadrilateral elements

Quadratic triangular and quadratic quadrilateral elements

Which interpolation functions must be used for the primary variables in weak forms of plane elasticity equations?

Hierarchical interpolation function

Hermite family interpolation function

Lagrange family interpolation function

Hierarchical interpolation function

Quadratic interpolation function

What can one conclude about the displacement components ux and uy in the finite element model of the plane elasticity equations?

They are primary variables and must be carried as secondary nodal degrees of freedom

They are primary variables and must be carried as primary nodal degrees of freedom

They are secondary variables and must be carried as primary nodal degrees of freedom

They are primary variables and must be carried as secondary nodal degrees of freedom

They are secondary variables and must be carried as secondary nodal degrees of freedom

13 + Mcqs in Plane Elasticity Finite Element Model in Finite Element Method Page 1 McqOptions

1.	Which option is correct for the first derivative of the shape function S in the study of plane elasticity problems?
A.	It is element-wise constant for triangular element whereas not a constant for quadrilateral element
B.	It is element-wise constant for both the triangular element as well as a quadrilateral element
C.	It is not a constant for triangular element whereas element-wise constant for quadrilateral element
D.	It is a combination of a linear function and constant for both the triangular element and a quadrilateral element
Answer» B. It is element-wise constant for both the triangular element as well as a quadrilateral element

Discussion

2.	Which form of a periodic solution is sought for the natural vibration study of plane elastic bodies?
A.	{Δ}={Δ0}eiωt
B.	{Δ}={Δ0}e-iω
C.	{Δ}={Δ0}e-iωt
D.	{Δ}={Δ0}e-iω/t
Answer» D. {Δ}={Δ0}e-iω/t

Discussion

3.	Which option is not correct with respect to the orders of the matrices in the following finite element model of plane elastic equations?Me\(\ddot{\Delta}^e\)+KeΔe=Fe+Qe
A.	Mass matrix M has order 2n x 2n
B.	Stiffness matrix K has order 2n x n
C.	The element load vector F has order 2n x 1
D.	The vector of internal forces Q has order 2n x 1
Answer» C. The element load vector F has order 2n x 1

Discussion

4.	For a linear quadrilateral element, what is the order of matrix B in the strain-displacement relation ε=BD, where D denotes the displacement matrix?
A.	6×3
B.	3×6
C.	3×8
D.	8×3
Answer» D. 8×3

Discussion

5.	For a linear triangular element, what is the order of matrix B in the strain-displacement relation ε=BD, where D denotes the displacement matrix?
A.	6×3
B.	3×6
C.	3×8
D.	8×3
Answer» C. 3×8

Discussion

6.	What is the function on \(\frac{\partial s}{\partial n}\) if S (n, e) denotes the shape function of a linear quadrilateral element?
A.	Linear in e and constant in n
B.	Constant in e and Linear in n
C.	Linear in both e and n
D.	Constant in both e and n
E.	denotes the shape function of a linear quadrilateral element?a) Linear in e and constant in nb) Constant in e and Linear in nc) Linear in both e and nd) Constant in both e and n
Answer» B. Constant in e and Linear in n

Discussion

7.	What is the other name of a linear triangular element for plane elasticity problems?
A.	Constant-strain triangle
B.	Linear-strain triangle
C.	Quadratic-strain triangle
D.	Variable-strain triangle
Answer» B. Linear-strain triangle

Discussion

8.	What is the correct statement regarding the shape function S of a linear triangular element?
A.	The first derivatives of S and hence, all the strains are element-wise constant
B.	The first derivatives of S are linear, but the strains are element-wise constant
C.	The first derivatives of S and hence the strains are linear functions
D.	The first derivatives of S are element-wise constant, but the strains are linear
Answer» B. The first derivatives of S are linear, but the strains are element-wise constant

Discussion

9.	What are the simplest elements that fit for the finite element model of the plane elasticity equations?
A.	Linear triangular and quadratic quadrilateral elements
B.	Quadratic triangular and linear quadrilateral elements
C.	Linear triangular and linear quadrilateral elements
D.	Quadratic triangular and quadratic quadrilateral elements
Answer» D. Quadratic triangular and quadratic quadrilateral elements

Discussion

10.	Which interpolation functions must be used for the primary variables in weak forms of plane elasticity equations?
A.	Hermite family interpolation function
B.	Lagrange family interpolation function
C.	Hierarchical interpolation function
D.	Quadratic interpolation function
Answer» C. Hierarchical interpolation function

Discussion

11.	What can one conclude about the displacement components ux and uy in the finite element model of the plane elasticity equations?
A.	They are primary variables and must be carried as primary nodal degrees of freedom
B.	They are secondary variables and must be carried as primary nodal degrees of freedom
C.	They are primary variables and must be carried as secondary nodal degrees of freedom
D.	They are secondary variables and must be carried as secondary nodal degrees of freedom
Answer» C. They are primary variables and must be carried as secondary nodal degrees of freedom

Discussion

12.	In FEM, if two independent variables are components of the same vector, then they can be approximated by two different types of interpolations.
A.	True
B.	False
Answer» C.

Discussion

13.	If only the first derivatives of ux and uy appear in the weak forms, then their interpolation must be at least bilinear.
A.	True
B.	False
Answer» B. False

Discussion

Explore topic-wise MCQs in Finite Element Method.

Which option is correct for the first derivative of the shape function S in the study of plane elasticity problems?

Which form of a periodic solution is sought for the natural vibration study of plane elastic bodies?

Which option is not correct with respect to the orders of the matrices in the following finite element model of plane elastic equations?Me\(\ddot{\Delta}^e\)+KeΔe=Fe+Qe

For a linear quadrilateral element, what is the order of matrix B in the strain-displacement relation ε=BD, where D denotes the displacement matrix?

For a linear triangular element, what is the order of matrix B in the strain-displacement relation ε=BD, where D denotes the displacement matrix?

What is the function on \(\frac{\partial s}{\partial n}\) if S (n, e) denotes the shape function of a linear quadrilateral element?

What is the other name of a linear triangular element for plane elasticity problems?

What is the correct statement regarding the shape function S of a linear triangular element?

What are the simplest elements that fit for the finite element model of the plane elasticity equations?

Which interpolation functions must be used for the primary variables in weak forms of plane elasticity equations?

What can one conclude about the displacement components ux and uy in the finite element model of the plane elasticity equations?

In FEM, if two independent variables are components of the same vector, then they can be approximated by two different types of interpolations.

If only the first derivatives of ux and uy appear in the weak forms, then their interpolation must be at least bilinear.