# Finite Element Method Questions and Answers – Solid Mechanics Applications – Plane Stress, Plane Strain, and Quadrilateral Elements

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Solid Mechanics Applications – Plane Stress, Plane Strain, and Quadrilateral Elements”.

1. Plane stress is characterized by which of the following assumptions?
d) Material is anisotropic and non homogeneous

Explanation: Plane stress can be defined by making use of the following assumptions –

• Material is elastic, isotropic and homogeneous.
• Body is small in any one direction when in comparison with the other two.
• 2. Which of the following is an example of equilibrium equations for plane stress?
a) dσx/dx + dεxy/dx
b) dσx/dx + dεxy/dy
c) dσx/dy + dεxy/dx
d) dσx + dεxy/dx

Explanation: The equilibrium equations for plane stress are given by –

• x/dx + dεxy/dx
• y/dy + dεxy/dy

where, σ corresponds to the stress components
ε corresponds to the strain components respectively
• 3. Which of the following corresponds to Distributed loads?
a) Loads that arise from applied pressure only
d) Loads that are distributed over an area

Explanation: Distributed loads usually arise from applied pressure/normal stress or shearing loads. In case of plane stress situations, these loads act on element edges that lie on the global boundary. There’s no compulsion as to the area over which such loading is bound to act.

4. Which of the following defines a body force?
a) Intermittent force acting on a body
b) Contact force acting on a body
c) Non contact force acting on a body
d) Contact and intermittent force acting on a body

Explanation: Body force is a non contact force acting on any given body on a per unit mass basis. Some of the better examples of this force are the gravitational force, centrifugal force that arises from rotary motion and magnetic force.

5. When is a solid body considered to be in a state of plane strain?
a) When all assumptions except the body’s thickness of the plane stress theory are satisfied
b) When all assumptions of the plane stress theory are satisfied
c) When no assumptions of the plane stress theory are satisfied
d) Plane stress and plane strain are not related to one another

Explanation: A solid body is considered to be in a state of plane strain, if the assumptions of plane stress theory are satisfied. However, there is one exception. The body’s thickness is large when compared to the dimensions of the xy plane.
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6. Which of the following structures are eligible for plane strain analysis?
a) Dams
b) Holes
c) Plates with holes
d) Small boxes

Explanation: We know that plane strain analysis is applicable to structures that are long and are subjected to constant loading throughout. Of the given examples, only dams satisfy the prerequisites; thus, making them eligible for plane strain analysis.

7. Why is the quadrilateral element preferred for finite element formulation?
a) Ease of computation
b) User compatible
c) Small size
d) Robust mechanism

Explanation: As most element strains are constant, a large number of small elements are required for obtaining accuracy. There are many cons of using rectangular and triangular elements. However, the 4 noded quadrilateral has desirable characteristics of strain variation as well as approximation of curves.

8. Rectangular and triangular elements have many more advantages than it’s quadrilateral counterpart.
a) True
b) False

Explanation: The given statement is false. While triangular elements are preferred for modeling irregular shapes consisting of curved boundaries, rectangular elements are preferred for providing linear variation of strain components. The quadrilateral element has the right mix of both these elements.

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