This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Two Dimensional Problems – Constant Strain Triangle”.

1. Finite element method uses the concept of _____

a) Nodes and elements

b) Nodal displacement

c) Shape functions

d) Assembling

View Answer

Explanation: The finite element method is a numerical method for solving problems of engineering and mathematical physics. Finite element method uses the concept of shape functions in systematically developing the interpolations.

2. For constant strain elements the shape functions are ____

a) Spherical

b) Quadratical

c) Polynomial

d) Linear

View Answer

Explanation: The constant strain triangle element is a type of element used in finite element analysis which is used to provide an approximate solution in a 2D domain to the exact solution of a given differential equation. For CST shape functions are linear over the elements.

3. Linear combination of these shape functions represents a ______

a) Square surface

b) Linear surface

c) Plane surface

d) Combinational surface

View Answer

Explanation: A constant strain element is used to provide an approximate solution to the 2D domain to the exact solution of the given differential equation. The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes.

4. In particular, N_{1}+N_{2}+N_{3} represent a plane at a height of one at nodes ______

a) One

b) Two

c) Three

d) One, two and three

View Answer

Explanation: Any linear combination of these shape functions also represents a plane surface. In particular, N

_{1}+N

_{2}+N

_{3}represents a plane height of one at nodes one, two, and, three and thus it is parallel to the triangle 123.

5. If N_{3} is dependent shape function, It is represented as ____

a) N_{3}=ξ

b) N_{3}=1-ξ

c) N_{3}=1-η

d) N_{3}=1-ξ-η

View Answer

Explanation: The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. N

_{1}, N

_{2}, N

_{3}are not linearly independent only one of two of these are independent.

6. In two dimensional problems x-, y- co-ordinates are mapped onto ____

a) x-, y- co-ordinates

b) x-, ξ – co-ordinates

c) η-, y- co-ordinates

d) ξ-η-Co-ordinates

View Answer

Explanation: The similarity with one dimensional element should be noted ; in one dimensional problem the x- co-ordinates were mapped onto ξ- co-ordinates and the shape functions were defined as functions of ξ. In the two dimensional elements the x-, y-, co-ordinates are mapped onto ξ-,,η – co-ordinates.

7. The shape functions are physically represented by _____

a) Triangular co-ordinates

b) ξ-,η-Co-ordinates

c) Area co-ordinates

d) Surface co-ordinates

View Answer

Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. Therefore appropriate functions have to be used and as already mentioned; low order typical polynomials are used in shape functions. The shape functions are physically represented by area co-ordinates.

8. A_{1} is the first area and N_{1} is its shape function then shape function N_{1}= ___

a) A_{1}/A

b) A-A_{1}

c) A_{1}+A

d) A_{1}

View Answer

Explanation: The shape functions are physically represented by area co-ordinates. A point in a triangle divides into three areas. The shape functions are precisely represented as

N

_{1}=A

_{1}/A .

9. The equation u=Nq is a _____ representation.

a) Nodal

b) Isoparametric

c) Uniparametric

d) Co-ordinate

View Answer

Explanation: The isoparametric representation of finite elements is defined as element geometry and displacements are represented by same set of shape functions.

10. For plane stress or plane strain, the element stiffness matrix can be obtained by taking _____

a) Shape functions, N

b) Material property matrix, D

c) Iso parametric representation, u

d) Degrees of freedom, DoF

View Answer

Explanation: The material property matrix is represented as ratio of stress to strain that is σ=Dε . Therefore by this relation element stiffness matrix can be obtained by material property matrix.

11. In a constant strain triangle, element body force is given as ____

a) f^{e}=[f_{x},f_{y},f_{x},f_{y},f_{x},f_{y}]^{T}

b) f^{e}=\(\frac{t_eA_e}{3}\)

c) f^{e}=\(\frac{t_eA_e}{3}\)[f_{x},f_{y},f_{x},f_{y},f_{x},f_{y}]^{T}

d) f^{e}=\(\frac{t_eA_e}{3}\)[f_{x},f_{y}]^{T}

View Answer

Explanation: A body force is a force which acts through the volume of the body. Body forces contrast with the contact forces or the classical definition of the surface forces which are exerted to the surface of the body.

12. Traction force term represented as ___

a) ∫u^{T} Tl

b) ∫u^{T}T

c) ∫u^{T}

d) u^{T}Tl

View Answer

Explanation: Traction force or tractive force are used to generate a motion between a body and a tangential surface, through the use of dry friction, through the use of shear force of the surface is also commonly used.

13. In the equation KQ=F, K is called as ____

a) Stiffness matrix

b) Modified stiffness matrix

c) Singular stiffness matrix

d) Uniform stiffness matrix

View Answer

Explanation: The stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. The stiffness and force modifications are made to account for the boundary conditions.

14. Principal stresses and their directions are calculated by using ____

a) Galerkin approach

b) Rayleigh method

c) Potential energy method

d) Mohr’s circle method

View Answer

Explanation: Mohr’s circle is two dimensional graphical representation of the transformation law. While considering longitudinal stresses and vertical stresses in a horizontal beam during bending.

15. I the distribution of the change in temperature ΔT, the strain due to this change is ____

a) Constant strain

b) Stress

c) Initial strain

d) Uniform strain

View Answer

Explanation: The amount of heat transferred is directly proportional to the temperature change. The distribution of change in temperature, the strain due to this change is initial strain.

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