# Finite Element Method Questions and Answers – Interpolation Functions – Polynomial Forms

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Interpolation Functions – Polynomial Forms”.

1. Which of the following defines an interior node?
a) A node that is not connected to any other node
b) Node that is interconnected to every node in the model
c) Node that is interior to the elements
d) Node that is exterior to the elements

Explanation: An interior node is one that is not connected to any other node in any element of the model. Inclusion of the same is seen as a mathematical tool used for increasing the order of approximation in the field variable.

2. What is considered as the first step in the development of interpolation functions?
a) Expressing the field variable as a trigonometric function
b) Expressing the field variable as a polynomial
c) Mesh refinement
d) Process of meshing

Explanation: The general procedure starts off with expressing the field variable as a polynomial; usually with order lesser than the degrees of freedom exhibited by the element. Following this, the nodal boundary conditions are applied and the polynomial coefficients are computed accordingly.

3. Which of the following defines geometrical isotropy?
a) Function does not change under translation only
b) Function changes under translation and rotation
c) Function does not change under translation or rotation
d) Function does not change under rotation only

Explanation: If a functional form does not change under translation or rotation of its coordinates; then it is said to follow geometric isotropy. This is considered as a prerequisite for two and three dimensional elements exhibiting compatibility and completeness conditions respectively.

4. What is a Pascal’s triangle?
a) Graphical method of representing one dimensional polynomials
b) Graphical method of representing three dimensional polynomials
c) Graphical method of plotting results in the finite element analysis
d) Graphical method of representing two dimensional polynomials

Explanation: The Pascal’s triangle is the graphical method of representing complete two dimensional polynomials. Each horizontal line in this triangle corresponds to a polynomial of order M; where M is any arbitrary positive integer.

5. Only complete polynomials are capable of exhibiting geometric isotropy.
a) True
b) False

Explanation: The given statement is false. Incomplete polynomials are also capable of exhibiting geometric isotropy; if and only if they are symmetric. Symmetry corresponds to the independent variables appearing as equal and opposite pairs; ensuring that each independent variable has a role to play in the polynomial.
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