# Finite Element Method Questions and Answers – Computer Implementation, Element Computation, and FEM2DV2 Applications

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Computer Implementation, Element Computation, and FEM2DV2 Applications”.

1. What is the reason for increased element calculations in 2D elements?
a) Usage of mixed order integrations
b) Time limitations
c) Computation difficulty
d) User complexity

Explanation: When it comes to two dimensional structures, there is an increase in element calculations. This is because of – variety of geometrical shapes of elements, multivariable problems, integration over areas, and usage of mixed order integrations in certain formulations of the finite element method.

2. What is the difference between MSH2DR and MSH2DG?
a) MSH2DR is used to generate meshes over non rectangular domains
b) MSH2DR is used to generate meshes over rectangular domains
c) There is no difference between the two
d) MSH2DG is used to generate meshes over rectangular domains

Explanation: In the preprocessor section, MSH2DR is used to generate triangular and rectangular -element meshes over rectangular domains. This requires minimal input. MSH2DG is a more generalized subroutine and is used to generate meshes over non rectangular domains.

3. What is the purpose of using the RELEM subroutine?
a) Used to end the program
b) Used for computation of eigenvalues
c) Used to generate element data
d) Used for mesh generation

Explanation: The RELEM subroutine is used for generation of element data. It is not called explicitly; but called inside the MSH2G subroutine. MSH2G is a subroutine that carries out mesh generation. All the above mentioned subroutines are part of the preprocessor stage of the finite element method.

4. What is the difference between the ELKMFT and ELKMFR subroutines?
a) ELKMFT computes element matrices and vectors for triangular elements
b) ELKMFR computes element matrices and vectors for triangular elements
c) ELKMFT computes element matrices and vectors for rectangular elements
d) No difference between the two

Explanation: The ELKMFT and ELKMFR subroutines are part of the processor stage of the finite element methodology. While the ELKMFT is used to compute the element matrices and vectors for triangular elements, the ELKMFR subroutine is used for computation of element matrices and vectors for the rectangular elements.

5. Which of the following is not a step involved in the element matrix computation process?
a) Development of subroutine for evaluation of interpolation functions
b) Structural aesthetic comparison
c) Numerical integration of element matrices
d) Setting up of element matrices subject to type of problems

Explanation: Structural aesthetic comparison is not involved in the element matrix computation process. The main steps involved are:

• Development of subroutines for the evaluation of interpolation functions along with their derivatives.
• Numerical integration of the coefficients of element matrices using respective quadrature formulae.
• Setting up of element matrices with respect to the type of problems encountered.
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6. What are the functions of SHPTRI and SHPRCT subroutines respectively?
a) Used for generating mesh
b) Used for application of boundary conditions
c) Used for evaluation of interpolation functions along with their derivatives

Explanation: The subroutines SHPTRI and SHPRCT are used for evaluation of interpolation functions along with their derivatives. While SHPTRI corresponds only to triangular elements, SHPRCT corresponds to rectangular elements. These subroutines are called in a do loop based on the number of quadrature points.

7. In multivariable problems, the element matrices are themselves defined in terms of submatrices.
a) True
b) False

Explanation: The given statement is true. In multivariable problems, the element matrices are themselves defined in terms of submatrices. This is also the case for plane elasticity, fluid flow and plate bending etc. In such specific cases, the nodal degrees of freedom are renumbered in order to reduce the half bandwidth of the assembled coefficient matrix.

8. Which of the following can be solved using the FEM2DV2 program?
a) Plane elasticity problems
b) Plane rigidity problems
c) One dimensional problems
d) Multi dimensional problems

Explanation: The FEM2DV2 program can solve plane elasticity problems. In addition to this, it can solve single variable problems (convective type boundary conditions), Viscous continuous fluid flow type, and plate problems making use of classical and shear deformation theories.

9. In heat transfer problems, what is the variable ICONV used for?
a) It is not used for indicating boundaries presence
b) Indicating presence of convective boundaries
c) Indicating presence of conductive boundaries
d) Indicating presence of radioactive boundaries

Explanation: ICONV is used for indicating the presence or absence of convective boundaries. When ICONV = 1, it corresponds to presence of convective boundaries. Whereas, when ICONV = 0, it indicates the absence of convective boundaries. Additional contributions to coefficient matrices are observed when convective boundaries are present.

10. Which of the following is a limitation of the FEM2DV2 program?
a) Response analysis
b) Element classification
c) Mesh generation
d) Computation

Explanation: A major drawback of the FEM2DV2 lies in its mesh generation. Due to this, it becomes a tedious task for the user to input mesh data; especially for problems having more number of elements. MSH2DR and MSH2DG are two subroutines that are used for mesh generation in this program.

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