# Finite Element Method Questions and Answers – One Dimensional Problems – Quadratic Shape Function

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

1. What is a shape function?
a) Interpolation function
b) Displacement function
c) Iterative function
d) Both interpolation and displacement function

Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. Lower order polynomials are chosen as shape functions. Shape function is a displacement function as well as interpolation function.

2. Quadratic shape functions give much more _______
a) Precision
b) Accuracy
c) Both Precision and accuracy
d) Identity

Explanation: The shape function is function which interpolates the solution between discrete values obtained at the mesh nodes. The unknown displacement field was interpolated by linear shape functions within each element. Use of quadratic interpolation leads to more accurate results.

3. Strain displacement relation ______
a) ε=$$\frac{du}{dx}$$
b) ε=$$\frac{du}{d\epsilon}$$
c) x=$$\frac{d\epsilon}{du}$$
d) Cannot be determined

Explanation: The relationship is that connects the displacement fields with the strain is called strain – displacement relationship. If strain is ε then strain – displacement relation is
ε=$$\frac{du}{dx}$$
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4. The _____ and ______ can vary linearly.
a) Force and load
b) Precision and accuracy
c) Strain and stress
d) Distance and displacement

Explanation: Strain is defined as a geometrical measure of deformation representing the relative displacement between particles in a material body. Stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. In quadratic shape functions strain and stress can vary linearly.

5. By Hooke’s law, stress is ______
a) σ=Bq
b) σ=EB
c) B=σq
d) σ=EBq

Explanation: Hooke’s law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid.

6. Nodal displacement as _____
a) u=Nq
b) N=uq
c) q=Nu
d) Program SOLVING

Explanation: Nodes will have nodal displacements or degrees of freedom which may include translations, rotations and for special applications, higher order derivatives of displacements.

7. At the condition, at , N1=1 at ξ=-1 which yields c=$$\frac{-1}{2}$$. Then these shape functions are called ____
a) Computer functions
b) Programming functions
c) Galerkin function
d) Lagrange shape functions

Explanation: The lagrange shape function sum to unity everywhere. At the given condition the shape functions are named as Lagrange shape functions.

8. Element body force vector is given by ______
a) fe=$$\frac{A_el_ef}{2} \int_{-1}^{1}$$ NT
b) fe= $$\frac{A_el_e}{2}\int_{}^{1}$$ NT
c) Conditioning strategies
d) fe=∫ NT

Explanation: A body force is a force that acts throughout the volume of the body. In FEM, Element body force vector is given by
fe=$$\frac{A_el_ef}{2} \int_{-1}^{1}$$ NT

9. Element traction force is given by ___
a) Te=$$\frac{l_e}{2}\int_{-1}^{1}$$NT
b) Te=$$\frac{l_eT}{2}\int_{-1}^{1}$$NT
c) Te=$$\frac{l_eT}{2}\int_{-1}^{1}$$NT
d) Undefined

Explanation: The term traction force can either refer to the total traction a vehicle exerts on a surface or the amount of total traction that is parallel to the direction of motion.
Element traction force is given by
Te=$$\frac{l_eT}{2}\int_{-1}^{1}$$NT

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