Finite Element Method Questions and Answers Part-18

1. On Belleville spring the load is applied in ______
a) X direction
b) Z direction
c) Y direction
d) Axial direction

Answer: d
Explanation: A Belleville washer, also known as a coned-disc spring, [1] conical spring washer, [2] disc spring, Belleville spring or cupped spring washer, is a conical shell which can be loaded along its axis either statically or dynamically. A Belleville washer is a type of spring shaped like a washer. It is the frusto-conical shape that gives the washer a spring characteristic.

2. In the Belleville spring, the load-deflection curve is _____
a) Linear
b) Curved
c) Non linear
d) Parabolic

Answer: c
Explanation: A Belleville washer, also known as a coned-disc spring, [1] conical spring washer, [2] disc spring, Belleville spring or cupped spring washer, is a conical shell which can be loaded along its axis either statically or dynamically.

3. A steel sleeve inserted into a rigid insulated wall. The sleeve fits snugly, and then the temperature is raised by _____
a) Uniform
b) Non uniform
c) σ
d) ΔT

Answer: d
Explanation: A sleeve is a tube of material that is put into a cylindrical bore, for example to reduce the diameter of the bore or to line it with a different material. Sometimes there is a metal sleeve in the bore to give it more strength. The pistons run directly in the bores without using cast iron sleeves.

4. In a Belleville spring, load-deflection characteristics and stress distribution can be obtained by dividing the area into ____
a) Surfaces
b) Nodes
c) Elements
d) Loads

Answer: c
Explanation: A Belleville washer, also known as a coned-disc spring, [1] conical spring washer, [2] disc spring, Belleville spring or cupped spring washer, is a conical shell which can be loaded along its axis either statically or dynamically.

5. In two dimensional isoparametric elements, we can generate element stiffness matrix by using ____
a) Numerical integration
b) Differential equations
c) Partial derivatives
d) Undefined

Answer: a
Explanation: The term isoparametric is derived from the use of the same shape functions (or interpolation functions) [N] to define the element’s geometric shape as are used to define the displacements within the element.

6. The vector q=[q1,q2………q8]T of a four noded quadrilateral denotes ____
a) Load vector
b) Transition matrix
c) Element displacement vector
d) Constant matrix

Answer: c
Explanation: 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.

7. For a four noded quadrilateral, we define shape functions on _____
a) X direction
b) Y direction
c) Load vector
d) Master element

Answer: d
Explanation: Master Element (ME) is the main point of reference in our analysis. The ME represents the person itself, and it gives us a primary layer of our personality. To determine the quality of ME, and overall chart, we have to analyze what kind of connection and access ME has to other Elements. The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes.

8. The master element is defined in ______
a) Co-ordinates
b) Natural co-ordinates
c) Universal co-ordinates
d) Radius

Answer: b
Explanation: Master Element (ME) is the main point of reference in our analysis. The ME represents the person itself, and it gives us a primary layer of our personality. To determine the quality of ME, and overall chart, we have to analyze what kind of connection and access ME has to other Elements.

9. Shape function can be written as _____
a) Nt=(1-ξ)(1-η)
b) Nt=(1-ξ)
c) Nt=(1-η)
d) Nt=\(\frac{1}{4}\)(1-ξ)(1-η)

Answer: d
Explanation: The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions.

10. For a four noded element while implementing a computer program, the compact representation of shape function is ____
a) Nt=\(\frac{1}{4}\)(1-ξ)(1-η)
b) Nt=(1-ξ)(1-η)
c) Nt=\(\frac{1}{4}\)(1+ξξi)(1+ηηi)
d) Undefined

Answer: c
Explanation: FourNodeQuad is a four-node plane-strain element using bilinear isoparametric formulation. This element is implemented for simulating dynamic response of solid-fluid fully coupled material, based on Biot’s theory of porous medium. Each element node has 3 degrees-of-freedom (DOF): DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p).