This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “One Dimensional Problems – Finite Element Modelling”.

1. If the structure is divided into discrete areas or volumes then it is called an _______

a) Structure

b) Element

c) Matrix

d) Boundaries

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Explanation: An element is a basic building block of finite element analysis. An element is a mathematical relation that defines how the degrees of freedom of node relate to next. The structure is divided into discrete areas or volumes known as elements.

2. In finite element modeling nodal points are connected by unique ________

a) Surface

b) Shape

c) Eigen values

d) Matrix

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Explanation: A node is a co-ordinate location in a space where the degrees of freedom can be defined. A node may be limited in calculated motions for a variety of reasons. Element boundaries are defined when nodal points are connected by unique polynomial curve or surface.

3. In finite element modeling every element connects to _______

a) 4 nodes

b) 3 nodes

c) 2 nodes

d) Infinite no of nodes

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Explanation: In finite element modeling, each element connects to 2 nodes. Better approximations are obtained by increasing the number of elements. It is convenient to define a node at each location where the point load is applied.

4. In one dimensional problem, each node has _________ degrees of freedom.

a) 2 degrees of freedom

b) 3 degrees of freedom

c) No degrees of freedom

d) 1 degree of freedom

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Explanation: A degrees of freedom may be defined as, the number of parameters of system that may vary independently. It is the number of parameters that determines the state of a physical system. In one dimensional problem, every node is permitted to displace only in the direction. Thus each node has only one degree of freedom.

5. Which relations are used in one dimensional finite element modeling?

a) Stress-strain relation

b) Strain-displacement relation

c) Total potential energy

d) Total potential energy; Stress-strain relation; Strain-displacement relation.

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Explanation: The basic procedure for a one dimensional problem depends upon total potential energy, stress-strain relation and strain-displacement relation are used in developing the finite element modeling.

6. One dimensional element is the linear segments which are used to model ________

a) Bars and trusses

b) Plates and beams

c) Structures

d) Solids

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Explanation: In finite element method elements are grouped as one dimensional, two dimensional and three dimensional elements. One dimensional element is the linesegment which is used to model bars and trusses.

7. Modeling is defined as ________________

a) Elemental area with uniform cross section

b) Elemental area with non uniform cross section

c) Structural area with uniform cross section

d) Non structural area with non uniform cross section

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Explanation: Modeling is one of the basic steps in finite element method. Let us model a stepped shaft consists of discrete no of elements each having a uniform cross sectional area. Average cross section area within each region is evaluated and used to define elemental area with uniform cross sectional area.

A1=A

_{1}’+A

_{2}’/2.

8. Discretization includes __________ numbering.

a) Element and node

b) Only nodal

c) Only elemental

d) Either nodal or elemental

View Answer

Explanation: The process of dividing a body into equivalent number of finite elements associated with nodes is called discretization. Discretization includes both node and element numbering, in this model every element connects two nodes.

9. The loading on an element includes _______

a) Body force

b) Traction force

c) Point load

d) Body force, Traction force & Point load

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Explanation: The loading on an element includes body force; traction force & point load. Body force is distributed force acting on every elemental volume. Traction force is a distributed load along the surface of a body.

10. Global nodes corresponds to _______

a) Entire body

b) On surface

c) On interface

d) On element

View Answer

Explanation: Global coordinate system corresponds to the entire body. It is used to define nodes in the entire body.

11. Local node number corresponds to ______________

a) Entire body

b) On element

c) On interface

d) On surface

View Answer

Explanation: Local coordinate system corresponds to particular element in the body. The numbering is done to that particular element neglecting the entire body.

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