# Finite Element Method Questions and Answers – Isoparametric Formulation & Axis Symmetric Elements

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Isoparametric Formulation & Axis Symmetric Elements”.

1. Large aspect ratios increase the accuracy of finite element representation.
a) False
b) True

Explanation: The given statement is false. Large aspect ratios have a negative impact on the accuracy of finite element representations in general. They in fact increase the inaccuracies in the process of finite element formulation. Large aspect ratios are also considered harmful for the convergence of finite element solutions

2. Which process is depicted in the figure below?

a) Meshing
b) Mapping
c) Mesh refinement
d) Interpolation

Explanation: The figure showcases the process of mapping. In this procedure, new elements are derived from parent elements in order to fit complex geometries in a much more easy manner. Figure specifically depicts the formation of 4 node quadrilateral element from the parent 4 node rectangular element.

3. What is isoparametric mapping?
a) Usage of different interpolation functions for field variable and element geometry description
b) Mapping of 4 node elements
c) Usage of same interpolation functions for field variable and element geometry description
d) Mapping of 3 node elements

Explanation: When same interpolation functions are used for both the field variable and element geometry description, then the process is referred to as isoparametric mapping. Elements that are defined by this procedure are referred to as isoparametric elements.

4. What is a Jacobian matrix?
a) Representation of the interpolation functions
b) Representation of global mass matrix
c) Representation of global element matrix
d) Measure of distortion undergone by the element while mapping

Explanation: Jacobian matrix represents the measure of distortion that an element undergoes while mapping from Cartesian to natural coordinates. The determinant of this matrix should not be negative. A negative value indicates that the geometric constraints are not met.

5. Which of the following is a prerequisite for an axisymmetric problem?
a) Problem must possess an axis of symmetry
b) There shouldn’t be any axis of rotation
d) Only equivalent loads can be applied

Explanation: There are many prerequisites for an axisymmetric problem. Some of them include –

• Problem must possess an axis of symmetry
• Boundary conditions must be symmetric about the axis of revolution
• Material properties must be symmetric about axis of revolution

6. When is an axisymmetric problem treated as a two dimensional problem?
a) When there is no symmetry in any of the elements
c) When the third dimension is negligible
d) Only if geometry is axially symmetric

Explanation: When the geometry, support conditions and constraints, loading, and the material properties are symmetric about the axis of revolution; then the axisymmetric problem under discussion can be treated as a two dimensional problem.

7. Which of the following is an example of an axisymmetric problem?
a) Cantilever beam subjected to axial load
b) Cantilever beam subjected to bending load
d) Beam subjected to a combination of bending and axial loads

Explanation: A rocket nozzle subjected to thermal and pressure loading is an example of axisymmetric loading. Some other examples include – soil masses subjected to footing loads, thick/thin walled pressure vessels, engine valve and pressure vessel etc.

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