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

1. The transformation relationships into strain displacement relations. Then the equation can be written as ____

a) ε=Bq

b) ε=Dq

c) ε=q

d) Elemental surface

View Answer

Explanation: For a triangular element, it can be modeled by using isoparametric formulation and then by chain rule, a jacobian matrix can be formed and then by transforming the matrix into simple form it is represented as

ε=Bq.

2. In the equation U_{e}=\(\frac{1}{2}\)2q^{T}(2∏ ∫ B^{T}DBrdA)q the quantity inside the paranthesis is _____

a) Axisymmentric

b) Strain displacement relationships

c) Stiffness matrix

d) Symmetric matrix

View Answer

Explanation: In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation.

3. The volume of ring shaped element is _____

a) A_{e}=\(\frac{1}{2}\mid detJ \mid\)

b) A_{e}=detJ

c) 2πr

d) 4πr^{2}

View Answer

Explanation: A ring-shaped object, a region bounded by two concentric circles. … Informally, it has the shape of a hardware washer. The volume of the ring-shaped element is A

_{e}=\(\frac{1}{2}\mid det J \mid\).

4. The element body force vector f^{e} is given by _____

a) Co-ordinates

b) f^{e}=\(\frac{2Πr̅A_e}{3}\)[f̅_{r},f̅_{z},f̅_{r},f̅_{z},f̅_{r},f̅_{z}]^{T}

c) f^{e}=\(\frac{2Πr̅A_e}{3}\)[f̅_{x},f̅_{y}]^{T}

d) f^{e}=\(\frac{2Πr̅A_e}{3}\)

View Answer

Explanation: A body force is a force that acts throughout the volume of a body. Forces due to gravity, electric fields and magnetic fields are examples of body forces. Body forces contrast with contact forces or the classical definition of surface forces which are exerted to the surface of an object.

5. A rotating flywheel with its axis in the z direction. We consider the flywheel to be stationary and apply the equivalent radial centrifugal (inertial) force per unit volume is _____

a) 2Πr

b) 4Πr^{2}

c) ρrω^{2}

d) ρω^{2}

View Answer

Explanation: The centrifugal force is an inertial force (also called a “fictitious” or “pseudo” force) directed away from the axis of rotation that appears to act on all objects when viewed in a rotating frame of reference.

6. Surface traction of a uniformly distributed load with components T_{1} and T_{2} is _____

a) q^{T}T^{e}=2Π∫_{e}u^{T}Trdl

b) q^{T}T^{e}=2Π

c) σ=ε

d) ε=Dσ

View Answer

Explanation: Traction, or tractive force, is the force used to generate motion between a body and a tangential surface, through the use of dry friction, though the use of shear force of the surface. Traction can also refer to the maximum tractive force between a body and a surface, as limited by available friction.

7. On summing up the strain energy and force terms over all the elements and modifying for the boundary conditions while minimizing the total potential energy. We get ______

a) σ=D

b) Kinematic energy

c) ε=Dσ

d) KQ=F

View Answer

Explanation: KQ=F by this we can obtain unknown displacement vectors. A displacement is a vector whose length is the shortest distance from the initial to the final position of a point P. It quantifies both the distance and direction of an imaginary motion along a straight line from the initial position to the final position of the point.

8. Using the connectivity of the elements, the internal virtual work can be expressed in the form _____

a) Ψ^{T}=KQ

b) Ψ^{T}=K

c) KQ=F

d) σ=Dε

View Answer

Explanation: The principle of virtual work states that in equilibrium the virtual work of the forces applied to a system is zero. Newton’s laws state that at equilibrium the applied forces are equal and opposite of the reaction, or constraint forces.

9. In axisymmetric problems, by using stress strain relation and strain displacement relation we can obtain an equation that is ____

a) σ=DB̅q

b) σ=D

c) σ=Dε

d) σ=Dε^{0}

View Answer

Explanation: The relationship between the stress and strain that a particular material displays is known as that particular material’s stress–strain curve. The strains give information about the deformation of material particles but, since they do not encompass translations and rotations, they do not give information about the precise location in space of particles.

10. The temperature effect on axisymmetric formulation. The vector ε̅_{0} is the initial strain evaluated at the centroid, representing the average temperature rise of the element is _____

a) θ^{e}=2Πr̅

b) θ^{e}=2Πr̅A_{e}B̅^{T}Dε̅_{0}

c) K=QF

d) σ=Dε_{0}

View Answer

Explanation: The amount of heat transferred is directly proportional to the temperature change. Temperature is a proportional measure of the average kinetic energy of the random motions of the constituent microscopic particles in a system (such as electrons, atoms, and molecules); but more rigorous definitions include all quantum states of matter.

11. Uniform increase in temperature of, ΔT introduces initial _____

a) Normal strain

b) Strain

c) Stresses

d) Kinetic energy

View Answer

Explanation: Strain, is a term used to measure the deformation or extension of a body that is subjected to a force or set of forces. The strain of a body is generally defined as the change in length divided by the initial length. The elongation of the bar is assumed normal, or perpendicular, to the cross section. Therefore, like stress, the strain is called a normal strain.

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