MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 12 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. |
If the equation ∫Ωche\((\frac{\partial w_1}{\partial x}\sigma_{xx}+\frac{\partial w_1}{\partial y}\)σxy-w1fx+ρw1\(\ddot{u_x})\)dxdy-∮Γchew1(σxxnx+σxyny)ds=0 represents the weak form of plane elasticity equations, then the weight functions w1 and w2 are the first variations of ux and uy, respectively. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 2. |
For plane elasticity problems, which option represents the essential boundary conditions among the governing equations? |
| A. | Displacements, ux and uy at the boundary |
| B. | Surface traction at the boundary |
| C. | The displacements (ux and uy) and surface traction at the boundary |
| D. | Stresses in the element |
| Answer» B. Surface traction at the boundary | |
| 3. |
If Fx, Fy denotes the components of the force vector, then which option is the correct secondary degrees of freedom present in the following figure of a plane elasticity problem? |
| A. | \(F_6^x=F_6^y\)≠0 |
| B. | \(F_7^x=F_7^y\)≠0 |
| C. | \(F_6^x\ne F_6^y\)=0 |
| D. | \(F_7^x\ne F_7^y\)=0 |
| Answer» E. | |
| 4. |
If U,V denotes the components of the displacement vector, then which option is the correct primary nodal degrees of freedom present in the following figure of a plane elasticity problem? |
| A. | U1=V1=0 |
| B. | U2≠0, V2=0 |
| C. | U2=0, V2≠0 |
| D. | U1=V1≠0 |
| Answer» B. U2≠0, V2=0 | |
| 5. |
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. | \(\int_{V_e}\)(σijδεij)dV |
| B. | ∮set̂ iδuids |
| C. | \(\int_{V_e}\)(ρü iδui)dV |
| D. | \(\int_{V_e}\)fiδuidV |
| Answer» C. \(\int_{V_e}\)(ρü iδui)dV | |
| 6. |
Under plane elasticity, which force is responsible for doing the virtual work \(\int_{V_e}\)fiδuidV 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 | |
| 7. |
In the weak form of the principle of virtual displacements applied to a plane elastic finite element, what does the term \(\int_{V_e}\)(ρü iδui)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 | |
| 8. |
In the weak form of the principle of virtual displacements, 0=\(\int_{V_e}\)(σijδεij+ρüiδui)dV-\(\int_{V_e}\)fiδuidV-∮set̂iδuids , applied to plane finite elastic element,which term corresponds to virtual strain energy stored in the body? |
| A. | \(\int_{V_e}\)(σijδεij)dV |
| B. | ∮set̂ iδuids |
| C. | \(\int_{V_e}\)(ρü iδui)dV |
| D. | \(\int_{V_e}\)fiδuidV |
| Answer» B. ∮set̂ iδuids | |
| 9. |
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. | |
| 10. |
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? |
| A. | 0=\(\int_{V_e}\)(σijδεij+ρüiδui)dV-\(\int_{V_e}\)fiδuidV-∮se\(\hat{t_i}\)δuids |
| B. | 0=\(\int_{V_e}\)(σijδεij+ρu̇iδui)dV-\(\int_{V_e}\)fiδuidV-∮se \(\hat{t_i}\)δuids |
| C. | 0=\(\int_{V_e}\)(σijδεij+ρüiδui)dV+\(\int_{V_e}\)fiδuidV-∮se \(\hat{t_i}\)δuids |
| D. | 0=\(\int_{V_e}\)(σijδεij+ρu̇iδui)dV\(\int_{V_e}\)fiδuidV+∮se \(\hat{t_i}\)δuids |
| Answer» B. 0=\(\int_{V_e}\)(σijδεij+ρu̇iδui)dV-\(\int_{V_e}\)fiδuidV-∮se \(\hat{t_i}\)δuids | |
| 11. |
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. | |
| 12. |
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. | |