Potential Energy Approach - One Dimensional Problems Questions and Answers

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “One Dimensional Problems – Potential Energy Approach”.

1. Continuum is discretized into_______ elements.
a) Infinite
b) Finite
c) Unique
d) Equal
View Answer

Answer: b
Explanation: The continuum is a physical body structure, system or a solid being analyzed and finite elements are smaller bodies of equivalent system when given body is sub divided into an equivalent system.

2. U_e=\(\frac{1}{2}\int\) σ^T εA dx is a _____________
a) Potential equation
b) Element strain energy
c) Load
d) Element equation
View Answer

Answer: b
Explanation: The given equation is Element strain energy equation. The strain energy is the elastic energy stored in a deformed structure. It is computed by integrating the strain energy density over the entire volume of the structure.

3. Which is the correct option for the following equation?
K^e=\(\frac{E_eA_e}{l_e}\begin{bmatrix}
1 & -1 \\ -1 & 1 \end{bmatrix}\)
a) Load vector
b) Energy matrix
c) Node matrix
d) Element stiffness matrix
View Answer

Answer: d
Explanation: The given matrix is element stiffness matrix. A stiffness matrix represents the system of linear equations that must be solved in order to as certain an approximate solution to the differential equation. The stiffness matrix is a inherent property of a structure. Stiffness matrix is positive definite. K_e is linearly proportional to the product E_eA_e and inversely proportional to length l_e.

4. Body force vector f^e = _____________
a) \(\frac{A_el_ef}{2}\begin{Bmatrix}1 \\ 1 \end{Bmatrix}\)
b) \(\frac{A_el_e}{2}\begin{Bmatrix}1 \\ 1 \end{Bmatrix}\)
c) A_el_e\(\begin{Bmatrix}1 \\ 1 \end{Bmatrix}\)
d) A_el_ef \(\begin{Bmatrix}1 \\ 1 \end{Bmatrix}\)
View Answer

Answer: a
Explanation: A Body force is a force that acts throughout the volume of the body. Forces due to gravity, electric and magnetic fields are examples of body forces.

5. Between wheel and ground how much of traction force is required?
a) High traction force
b) Low traction force
c) Infinite traction force
d) No traction force
View Answer

Answer: a
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, through the use of shear force of the surface. In the design of wheeled or tracked vehicles, high traction between wheel and ground should be more desirable.

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6. Element traction force is given by ___
a) T^e=Tl_e\(\begin{Bmatrix}1 \\ 1 \end{Bmatrix}\)
b) T^e=Tl_e
c) T^e=\(\frac{Tl_e}{2}\begin{Bmatrix}1 \\ 1 \end{Bmatrix}\)
d) Undefined
View Answer

Answer: c
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, through the use of shear force of the surface.

7. ∏ = \(\frac{1}{2}\) Q^TKQ-Q^T F In this equation F is defined as _________
a) Global displacement vector
b) Global load vector
c) Global stiffness matrix
d) Local displacement vector
View Answer

Answer: b
Explanation: Global load vector is assembly of all local load vectors. This load vector is obtained by due to given load. In the given equation F is defined as global load vector.

8. What are the basic unknowns on stiffness matrix method?
a) Nodal displacements
b) Vector displacements
c) Load displacements
d) Stress displacements
View Answer

Answer: a
Explanation: Stiffness matrix represents systems of linear equations that must be solved in order to as certain an approximate solution to the differential equation. In stiffness matrix nodal displacements are treated as basic unknowns for the solution of indeterminate structures. The external loads and the internal member forces must be in equilibrium at the nodal points.

9. Write the element stiffness for a truss element.
a) K=\(\frac{A}{l}\)
b) K=\(\frac{AE}{l}\)
c) K=\(\frac{E}{l}\)
d) K=AE
View Answer

Answer: b
Explanation: Truss is a structure that consists of only two force members only. Where the members are organized so that the assemblage as a whole behaves as a single object.

10. Formula for global stiffness matrix is ____________
a) No. of nodes*Degrees of freedom per node
b) No. of nodes
c) Degrees of freedom per node
d) No. of elements
View Answer

Answer: a
Explanation: Generally global stiffness matrix is used to complex systems. Stiffness matrix method is used for structures such as simply supported, fixed beams and portal frames. Size of stiffness matrix is defined as:
Size of global stiffness matrix=No. of nodes*Degrees of freedom per node.

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