This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Computer Implementation and FEM1DV2 Applications”.

1. Which of the following is not performed during the preprocessor stage of a finite element analysis?

a) Assembling element matrices

b) Reading input data

c) Plotting mesh

d) Constraint application

View Answer

Explanation: The preprocessor stage is the first step in the finite element method. In this method, input data is taken and used to plot mesh, apply loads and constraints among many other various functions. Assembling of element matrices takes place in the Processing stage.

2. Which stage does the generation of element matrices fall into?

a) Post processor

b) Processor

c) Preprocessor

d) It is present in all stages of the finite element method

View Answer

Explanation: Generation of element matrices takes place in the processor stage of the finite element method. This stage is the second in chronological order. Assembly of element equations, boundary conditions application, computation of the finite element model are some other functions of the processor stage.

3. Plotting of solution takes place in the preprocessor stage.

a) True

b) False

View Answer

Explanation: The given statement is false. Plotting of solution takes place in the post processor stage. This also happens to be the penultimate stage of the finite element method. Result comparison, Gradient computation are some other functions of this stage.

4. Which of the following defines a subroutine?

a) Algorithm of the program

b) User input routine

c) Sequence of steps that are used to perform a specific task

d) Interpolation of eigenvalue functions

View Answer

Explanation: A subroutine is basically a sequence of steps that are used to perform specific tasks. All the three stages of a finite element analysis have many subroutines in them in order to perform the operations and computations. ASSMBL, BONDRY are some examples of subroutines used in the finite element method.

5. Which of the following subroutine is used in the preprocessing stage?

a) ASSMBL

b) BONDRY

c) SOLVER

d) MESH1D

View Answer

Explanation: MESH1D is a subroutine that is used to generate the mesh in the preprocessing stage. Whereas, ASSMBL, BONDRY and SOLVER are subroutines used in the processing stage. Each subroutine has a specific task associated with it.

6. Which stage of the finite element analysis is considered to have the most number of subroutines?

a) Processor stage

b) Preprocessor stage

c) Post processor stage

d) All stages have equal number of subroutines

View Answer

Explanation: The Processor stage is considered to have the most number of subroutines. This is due to the fact that, major portion of the finite element method(computation) takes place in this stage. Some of the subroutines available in the processor are ASSMBL, BONDRY, SOLVER, AXLBX, COEFNT etc. ASSMBL is used to assemble the equations, whereas BONDRY is used to impose boundary conditions.

7. We can help save storage and computing time by making use of the upper banded form for assembly of element matrices.

a) True

b) False

View Answer

Explanation: The given statement is true. Most element matrices are symmetric in nature. Upon computing, the resulting global matrix would also turn out to be symmetric. In order to save computation time and storage while solving finite element problems, it is considered sufficient to store only the upper part/band of the element matrix.

8. Which of the following is not a type of boundary condition?

a) Dirichlet boundary conditions

b) Rayleigh boundary conditions

c) Neumann boundary conditions

d) Newton boundary conditions

View Answer

Explanation: Rayleigh boundary conditions is not an existing type of the boundary conditions. Dirichlet boundary conditions correspond to boundary conditions on primary variables. Neumann boundary conditions correspond to boundary conditions on secondary variables. Newton boundary conditions correspond to boundary conditions on mixed type of variables.

9. Which program is depicted in the flowchart given below?

a) FEM1DV2

b) FEM2DV2

c) FEM3DV2

d) MESH3D

View Answer

Explanation: Program FEM1DV2 is depicted in the figure given. This is a revision of program FEM1D, and helps solve 2

^{nd}and other higher order problems. A number of subroutines are included in this program. Some of them include ECHO, PSTPRC, SOLVER etc.

10. Match the following subroutines to their corresponding functions.

1) SHP1D i) Calculating reactions of truss and frame problems 2) REACTN ii) Determining eigenvalues and vectors 3) AXLBX iii) Generating mesh for the given structure 4) MESH1D iv) Computing shape functions and their derivatives

a) 1-i, 2-ii, 3-iii, 4-iv

b) 1-iv, 2-i, 3-ii, 4-iii

c) 1-ii, 2-i, 3-iv, 4-iii

d) 1-iv, 2-ii, 3-iv, 4-iii

View Answer

Explanation: Subroutines SHP1D, AXLBX correspond to the processor stage. Whereas, MESH1D corresponds to the preprocessor stage, REACTN corresponds to the post processor stage. MESH1D is used for mesh generation, AXLBX is used for determining eigenvalues and vectors, SHP1D is used for computing shape functions and their derivatives, and REACTN is used for calculating the reactions of truss and frame members.

11. Match the key variables to their corresponding abbreviations.

1) NDF i) Number of equations per model 2) NEQ ii) Total degrees of freedom in the element 3) NPE iii) Number of degrees of freedom per node 4) NN iv) Number of nodes per element

a) 1-iii, 2-i, 3-iv, 4-ii

b) 1-ii, 2-i, 3-iv, 4-iii

c) 1-i, 2-ii, 3-iv, 4-iii

d) 1-iii, 2-i, 3-iv, 4-ii

View Answer

Explanation: Key variables are abbreviations that are used in the program FEM1DV2. These variables replace the need to type out huge wordings in the program. NDF corresponds to number of degrees of freedom per node, NEQ corresponds to the number of equations per model, NPE corresponds to the number of nodes per element, and NN corresponds to the total degrees of freedom in the element.

12. What should be used as a prefix to the key variables in order to demonstrate max values of the same?

a) MX

b) MAX

c) MAXI

d) MAXM

View Answer

Explanation: The prefix MX is used for key variables in order to demonstrate maximum values. Some examples include MXNEQ and MXNOD. They correspond maximum number of equations per model and maximum nodes per mesh respectively.

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