# Finite Element Method Questions and Answers – Axis Symmetric Formulation

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Axis Symmetric Formulation”.

1. Consider an Axisymmetric problem of which is having a radius of r, rotational angle θ and length l. Then r dl dθ is known as ____
a) Elemental volume
b) Element
c) Elemental surface area
d) Elemental surface

Explanation: Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. Surface element may refer to an infinitesimal portion of a 2D surface, as used in a surface integral in a 3D space.

2. The stress vector is correspondingly defined as ___________
a) σ=[σyzyzθ]T
b) σ=[σyz]T
c) u=[u, w]T
d) T=[Ty,Tz]T

Explanation: The stress is expressed by the Cauchy traction vector T defined as the traction force F between adjacent parts of the material across an imaginary separating surface S, divided by the area of S.

3. Problems involving three- dimensional axisymmetric solids or solids of revolution, subjected to _____ loading.
a) Rotational
b) Two-dimensional
c) Three-dimensional

Explanation: Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. Surface element may refer to an infinitesimal portion of a 2D surface, as used in a surface integral in a 3D space.

4. All deformations and stresses are independent of _______
a) Co-ordinates
b) Number of nodes
c) Rotational angle, θ
d) Area

Explanation: The point around which you rotate is called the center of rotation, and the smallest angle you need to turn is called the angle of rotation. The angle of rotation is a measurement of the amount, the angle, by which a figure is rotated counterclockwise about a fixed point, often the center of a circle.

5. Revolving bodies like fly wheels can be analyzed by introducing _______ in body force term.
a) Gravitational force
b) Revolving force
c) Centrifugal force
d) Centripetal force

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.
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6. The stress- strain relation is given as ___________
a) σ=D
b) σ=Dε
c) σ=ε
d) ε=Dσ

Explanation: The Hook’s law, states that within the elastic limits the stress is proportional to the strain since for most materials it is impossible to describe the entire stress – strain curve with simple mathematical expression, in any given problem the behavior of the materials is represented by an idealized stress – strain curve, which emphasizes those aspects of the behaviors which are most important is that particular problem.

7. Axisymmetric problems are totally defined in ______
a) xy planes
b) yz planes
c) rz planes
d) rθ planes

Explanation: Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. Surface element may refer to an infinitesimal portion of a 2D surface, as used in a surface integral in a 3D space. Thus, the problem needs to be looked at as a two dimensional problem in rz, defined on revolving area.

8. For axisymmetry solids gravity forces can be considered if deformation and stresses act on _____
a) X direction
b) Z direction
c) Y direction
d) Parallel to plane

Explanation: Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward (or gravitate toward) one another, including objects ranging from atoms and photons, to planets and stars. Gravity forces can be considered if acting in z direction.

9. In axisymmetric solids, stress- strain law can be defined as ______
a) σ=D(ε-ε0)
b) σ=D
c) σ=Dε
d) σ=Dε0

Explanation: The relationship between the stress and strain that a particular material displays is known as that particular material’s stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress).

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