MCQOPTIONS
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MCQOPTIONS
This section includes 14 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?- ew3 (( 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 | |
| 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 | |
| 3. |
For the vector form of the finite element model of momentum and continuity equations M +K11 +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 | |
| 4. |
For the vector form of the finite element model of momentum and continuity equations M +K11 +K12P=0, what is the correct expression for mass matrix M? |
| A. | M= <sub> <sub>c</sub></sub> <sup>T</sup> dx |
| B. | M= <sub> <sub>c</sub></sub>f <sup>T</sup> dx |
| C. | M= <sub> <sub>c</sub></sub>t <sup>T</sup> dx |
| D. | M= <sub> <sub>c</sub></sub>P <sup>T</sup> dx |
| Answer» B. M= <sub> <sub>c</sub></sub>f <sup>T</sup> dx | |
| 5. |
Which equation is the correct vector form of the finite element model of momentum and continuity equations in the flow domain? |
| A. | M +K<sup>11</sup> +K<sup>12</sup>P=0 |
| B. | M +K<sup>11</sup> +K<sup>22</sup>P=F<sup>1</sup> |
| C. | M +K<sup>22</sup> +K<sup>12</sup>P=F<sup>1</sup> |
| D. | M +K<sup>11</sup> +K<sup>12</sup>P=F<sup>1</sup> |
| Answer» E. | |
| 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 | |
| 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 | |
| 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 | |
| 9. |
Using constitutive relations, what is the value of xyif =0.3 and v=4xy-6y? |
| A. | 0.24x |
| B. | 2.4x |
| C. | 0.12x |
| D. | 1.2x |
| Answer» E. | |
| 10. |
Using constitutive relations, what is the value of xxif =0.3 and v=4x? |
| A. | 0.24 |
| B. | 2.4 |
| C. | 0.12 |
| D. | 1.2 |
| Answer» C. 0.12 | |
| 11. |
In FEM, which option is the correct weak form of the following momentum equation? ( frac{ partial v_x}{ partial t}- frac{ partial sigma _{xx}}{ partial x}- frac{ partial sigma_{xy}}{ partial y}-f_x )=0 |
| A. | l ( int_{ Omega_e}[ rho w_1 frac{ partial v_x}{ partial t}+ frac{ partial w_1}{ partial x} sigma_{xx}+ frac{ partial w_1}{ partial y} sigma_{xy}-w_1 f_x] )dxdy+ <sub> <sub>c</sub></sub> w<sub>1</sub>( <sub>xx</sub>n<sub>x</sub>+ <sub>xy</sub>n<sub>y</sub>)ds=0 |
| B. | l ( int_{ Omega_e}[ rho w_1 frac{ partial v_x}{ partial t}+ frac{ partial w_1}{ partial x} sigma_{xx}+ frac{ partial w_1}{ partial y} sigma_{xy}-w_1 f_x] )dxdy=0 |
| C. | l ( int_{ Omega_e}[ rho w_1 frac{ partial v_x}{ partial t}+ frac{ partial w_1}{ partial x} sigma_{xx}+ frac{ partial w_1}{ partial y} sigma_{xy}-w_1 f_x] )dxdy+ <sub> <sub>c</sub></sub> w<sub>1</sub>( <sub>xx</sub>+ <sub>xy</sub>)ds=0 |
| D. | l ( int_{ Omega_e} w_1[ rho frac{ partial v_x}{ partial t}- frac{ partial sigma_{xx}}{ partial x}- frac{ partial sigma_{xy}}{ partial y}-f_x] )dxdy++ <sub> <sub>c</sub></sub> w<sub>1</sub>( <sub>xx</sub>n<sub>x</sub>+ <sub>xy</sub>n<sub>y</sub>)ds=0 |
| Answer» B. l ( int_{ Omega_e}[ rho w_1 frac{ partial v_x}{ partial t}+ frac{ partial w_1}{ partial x} sigma_{xx}+ frac{ partial w_1}{ partial y} sigma_{xy}-w_1 f_x] )dxdy=0 | |
| 12. |
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 | |
| 13. |
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 | |
| 14. |
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. | |