MCQ Questions and Answers on Finite Element Analysis

Answer :   Option:- D

Discretization is the process of breaking down a structure into smaller, manageable parts (called elements) to facilitate analysis, especially in computational methods like the Finite Element Method (FEM). This allows for approximate solutions to complex physical problems.

Answer :   Option:- A

The Finite Element Method (FEM) divides a complex problem into smaller and simpler parts known as finite elements. These elements are interconnected at nodes and collectively approximate the solution to the entire problem.

Answer :   Option:- C

In Finite Element Analysis (FEA), the problem domain is divided into smaller, simpler parts called "elements." These elements help to make complex problems easier to solve by breaking them down into smaller units. Think of it like cutting a large piece of fabric into smaller pieces to analyze each part more effectively.

Answer :   Option:- A

FEA is a method used to approximate numerical solutions to complex engineering and physics problems. It allows us to solve problems that cannot be solved easily with traditional analytical methods, such as predicting how structures will behave under loads or how heat flows through materials.

Answer :   Option:- D

A fixed support in FEA means that the object or structure is securely held in place, and it cannot move in any direction. Therefore, the displacements (movement) at a fixed support are zero, as no shifting or rotation is allowed at that point.

Answer :   Option:- B

A 1D element in FEA is a simple line or rod, and it has two nodes, one at each end of the element. These nodes represent the points where the element connects to other elements or the boundary of the problem. The nodes help define how the element behaves in the analysis.

Answer :   Option:- C

The stiffness matrix of a structure is determined by both its material properties (such as Young's Modulus and Poisson's ratio) and its geometry (such as length, area, and shape). Material properties influence how the material resists deformation, while geometry affects the distribution and magnitude of forces. Both factors are essential in determining the overall stiffness of the structure.

Answer :   Option:- B

In finite element analysis (FEA), the stiffness matrix represents the relationship between the nodal displacements and forces. For a 1-D bar element, each node typically has one degree of freedom (DOF), which is the axial displacement. Now, let's break it down: 1-D bar element: This type of element resists axial forces, and each node has one degree of freedom for axial displacement. 3 nodes: If the structure consists of 3 nodes, then the total number of degrees of freedom for the system is 3 (one for each node). Stiffness matrix size: The stiffness matrix is a square matrix where the order of the matrix corresponds to the total number of degrees of freedom in the system. Since there are 3 nodes and each node has 1 degree of freedom, the total number of degrees of freedom is 3. Thus, the stiffness matrix will have an order of 3x3 (one degree of freedom per node). The 3x3 matrix will represent the relationship between the forces and displacements at the 3 nodes.

Answer :   Option:- A

Shape functions are used in finite element analysis to express the displacement of an element in terms of its nodal displacements. These functions interpolate the displacement within the element based on the values at the nodes, allowing the calculation of displacements at any point in the element.

Answer :   Option:- B

Bar -> 1D element\nHexahedron -> 3D element\nTetrahedron -> 3D element,\nOnly Triangle is 2D element.