# Finite element procedure and modelling

## Practice Problems

1. Which of the following is finite element software?

1. ANSYS
2. COMSOL Multiphysics
3. ABAQUS
4. All of these

Correct option- d

Explanation: ABAQUS, ANSYS, and COMSOL Multiphysics are all finite element software. This software contains algorithms of FEM which aids in performing the finite element analysis. The specialty of this software is it can handle millions of finite elements and account for better accuracy of solutions.

2. Which of the following is also known as basis functions?

1. Polynomial function
3. Cubic function
4. None of these

Correct option- a

Explanation: The polynomial functions are also known as basis functions. The basis functions are greatly used in numerical analysis like the FEM. They are also known as blending functions. These functions act as an extensive tool for mathematical interpolations.

3. Which of the following is the first step in the FEM?

1. Formation of PDEs
2. Discretization
3. Formation of the stiffness matrix
4. None of these

Correct option- b

Explanation: Discretization of the domain is the first and primary step in the FEA. In this step, the domain is subdivided into multiple subdomains by using specific finite elements. Each of the finite elements is characterized by nodes and degree of freedom.

4. Which of the following is true for the Galerkin method?

1. It minimizes domain residual.
2. It minimizes the complexity of the problem.
3. It solves the PDEs.
4. All of these

Correct option- a

Explanation: The Galerkin method is used to minimize the domain residual. The Galerkin method is an integral method, which does so by introducing specific weights. It also transforms the governing PDEs into weak forms.

5. Which of the following is true for a stiffness matrix?

1. It relates the force and deformation
2. It is derived by considering the material properties
3. It denotes the amount of deformation a member undergoes
4. Both a and b

Correct option- d

Explanation: The stiffness matrix relates the force and deformations of a member. They are derived using the material properties of the member. The stiffness matrix acts as an essential parameter for solving the equation and aids in the determination of the unknowns, especially deformations. For instance, the force and deformation matrix can be related to the stiffness matrix.