For plane elasticity problems, which option represents the essential boundary conditions among the governing equations?

Surface traction at the boundary

Displacements, ux and uy at the boundary

Surface traction at the boundary

The displacements (ux and uy) and surface traction at the boundary

In the weak form of the principle of virtual displacements applied to a plane elastic finite element, what does the term ( int_{V_e} )( u i ui)dV correspond to?

Virtual work done by the body force

Virtual work done by the surface traction

What is the correct form of the principle of virtual displacements applied to plane finite elastic element If Ve is the volume of element and se is its surface?

0= ( int_{V_e} )( ij ij+ u i ui)dV- ( int_{V_e} )fi uidV- se ( hat{t_i} ) uids

0= ( int_{V_e} )( ij ij+ u i ui)dV+ ( int_{V_e} )fi uidV- se ( hat{t_i} ) uids

0= ( int_{V_e} )( ij ij+ u i ui)dV ( int_{V_e} )fi uidV+ se ( hat{t_i} ) uids

In FEM, which method is not used to construct the weak forms and associated finite element model of the plane elasticity equations?

Principle of virtual displacements

The principle of minimum total potential energy

Weak form of governing differential equations

10 + Mcqs in Plane Elasticity Weak Formulations in Finite Element Method Page 1 McqOptions

1.	If the equation _{_c}h_e (( frac{ partial w_1}{ partial x} sigma_{xx}+ frac{ partial w_1}{ partial y} ) _xy-w₁f_x+ w₁ ( ddot{u_x}) )dxdy-&oint;_{_c}h_ew₁( _xxn_x+ _xyn_y)ds=0 represents the weak form of plane elasticity equations, then the weight functions w₁ and w₂ are the first variations of u_x and u_y, respectively.
A.	True
B.	False
Answer» B. False

Discussion

2.	For plane elasticity problems, which option represents the essential boundary conditions among the governing equations?
A.	Displacements, u<sub>x</sub> and u<sub>y</sub> at the boundary
B.	Surface traction at the boundary
C.	The displacements (u<sub>x</sub> and u<sub>y</sub>) and surface traction at the boundary
D.	Stresses in the element
Answer» B. Surface traction at the boundary

Discussion

3.	For a plane elasticity problem, which term in the weak form of the principle of virtual displacements is affected by a change in the applied surface traction forces?
A.	( int_{V_e} )( <sub>ij</sub> <sub>ij</sub>)dV
B.	<sub>s<sub>e</sub></sub>t <sub>i</sub> u<sub>i</sub>ds
C.	( int_{V_e} )( u <sub>i</sub> u<sub>i</sub>)dV
D.	( int_{V_e} )f<sub>i</sub> u<sub>i</sub>dV
Answer» C. ( int_{V_e} )( u <sub>i</sub> u<sub>i</sub>)dV

Discussion

4.	Under plane elasticity, which force is responsible for doing the virtual work ( int_{V_e} )f_i u_idV in the weak form of the principle of virtual displacements?
A.	Body force
B.	Concentrated loads
C.	Surface traction force
D.	Pressure force
Answer» B. Concentrated loads

Discussion

5.	In the weak form of the principle of virtual displacements applied to a plane elastic finite element, what does the term ( int_{V_e} )( u _i u_i)dV correspond to?
A.	Virtual strain energy
B.	Kinetic energy
C.	Virtual work done by the body force
D.	Virtual work done by the surface traction
Answer» C. Virtual work done by the body force

Discussion

6.	In the weak form of the principle of virtual displacements, 0= ( int_{V_e} )( _ij _ij+ u _i u_i)dV- ( int_{V_e} )f_i u_idV- _{s_e}t _i u_ids , applied to plane finite elastic element,which term corresponds to virtual strain energy stored in the body?
A.	( int_{V_e} )( <sub>ij</sub> <sub>ij</sub>)dV
B.	<sub>s<sub>e</sub></sub>t <sub>i</sub> u<sub>i</sub>ds
C.	( int_{V_e} )( u <sub>i</sub> u<sub>i</sub>)dV
D.	( int_{V_e} )f<sub>i</sub> u<sub>i</sub>dV
Answer» B. <sub>s<sub>e</sub></sub>t <sub>i</sub> u<sub>i</sub>ds

Discussion

7.	In the weak formulation of the plane elasticity equations, even though the methods, the principle of virtual displacements and the three-step weak formulation, give, mathematically different finite element models, they are the same in their algebraic forms.
A.	True
B.	False
Answer» C.

Discussion

8.	What is the correct form of the principle of virtual displacements applied to plane finite elastic element If V_e is the volume of element and s_e is its surface?
A.	0= ( int_{V_e} )( <sub>ij</sub> <sub>ij</sub>+ u <sub>i</sub> u<sub>i</sub>)dV- ( int_{V_e} )f<sub>i</sub> u<sub>i</sub>dV- <sub>s<sub>e</sub></sub> ( hat{t_i} ) u<sub>i</sub>ds
B.	0= ( int_{V_e} )( <sub>ij</sub> <sub>ij</sub>+ u <sub>i</sub> u<sub>i</sub>)dV- ( int_{V_e} )f<sub>i</sub> u<sub>i</sub>dV- <sub>s<sub>e</sub></sub> ( hat{t_i} ) u<sub>i</sub>ds
C.	0= ( int_{V_e} )( <sub>ij</sub> <sub>ij</sub>+ u <sub>i</sub> u<sub>i</sub>)dV+ ( int_{V_e} )f<sub>i</sub> u<sub>i</sub>dV- <sub>s<sub>e</sub></sub> ( hat{t_i} ) u<sub>i</sub>ds
D.	0= ( int_{V_e} )( <sub>ij</sub> <sub>ij</sub>+ u <sub>i</sub> u<sub>i</sub>)dV ( int_{V_e} )f<sub>i</sub> u<sub>i</sub>dV+ <sub>s<sub>e</sub></sub> ( hat{t_i} ) u<sub>i</sub>ds
Answer» B. 0= ( int_{V_e} )( <sub>ij</sub> <sub>ij</sub>+ u <sub>i</sub> u<sub>i</sub>)dV- ( int_{V_e} )f<sub>i</sub> u<sub>i</sub>dV- <sub>s<sub>e</sub></sub> ( hat{t_i} ) u<sub>i</sub>ds

Discussion

9.	In constructing the weak forms of plane elasticity problems, which option is not related to the principle of virtual displacements?
A.	Displacements to strains
B.	Strains to stresses
C.	The equations of motion
D.	Body forces
Answer» E.

Discussion

10.	In FEM, which method is not used to construct the weak forms and associated finite element model of the plane elasticity equations?
A.	Principle of virtual displacements
B.	The principle of minimum total potential energy
C.	Weak form of governing differential equations
D.	Hamiltonian principle
Answer» E.

Discussion

Explore topic-wise MCQs in Finite Element Method.

For plane elasticity problems, which option represents the essential boundary conditions among the governing equations?

For a plane elasticity problem, which term in the weak form of the principle of virtual displacements is affected by a change in the applied surface traction forces?

Under plane elasticity, which force is responsible for doing the virtual work ( int_{V_e} )fi uidV in the weak form of the principle of virtual displacements?

In the weak form of the principle of virtual displacements applied to a plane elastic finite element, what does the term ( int_{V_e} )( u i ui)dV correspond to?

In the weak form of the principle of virtual displacements, 0= ( int_{V_e} )( ij ij+ u i ui)dV- ( int_{V_e} )fi uidV- set i uids , applied to plane finite elastic element,which term corresponds to virtual strain energy stored in the body?

In the weak formulation of the plane elasticity equations, even though the methods, the principle of virtual displacements and the three-step weak formulation, give, mathematically different finite element models, they are the same in their algebraic forms.

What is the correct form of the principle of virtual displacements applied to plane finite elastic element If Ve is the volume of element and se is its surface?

In constructing the weak forms of plane elasticity problems, which option is not related to the principle of virtual displacements?

In FEM, which method is not used to construct the weak forms and associated finite element model of the plane elasticity equations?

Under plane elasticity, which force is responsible for doing the virtual work ( int_{V_e} )f_i u_idV in the weak form of the principle of virtual displacements?

In the weak form of the principle of virtual displacements applied to a plane elastic finite element, what does the term ( int_{V_e} )( u _i u_i)dV correspond to?

In the weak form of the principle of virtual displacements, 0= ( int_{V_e} )( _ij _ij+ u _i u_i)dV- ( int_{V_e} )f_i u_idV- _{s_e}t _i u_ids , applied to plane finite elastic element,which term corresponds to virtual strain energy stored in the body?

What is the correct form of the principle of virtual displacements applied to plane finite elastic element If V_e is the volume of element and s_e is its surface?