1. For constant strain elements the shape functions are ____
a) Spherical
b) Quadratical
c) Polynomial
d) Linear
Explanation: The constant strain triangle element is a type of element used in finite element analysis which is used to provide an approximate solution in a 2D domain to the exact solution of a given differential equation. For CST shape functions are linear over the elements.
2. Linear combination of these shape functions represents a ______
a) Square surface
b) Linear surface
c) Plane surface
d) Combinational surface
Explanation: A constant strain element is used to provide an approximate solution to the 2D domain to the exact solution of the given differential equation. The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes.
3. In particular, N1+N2+N3 represent a plane at a height of one at nodes ______
a) One
b) Two
c) Three
d) One, two and three
Explanation: Any linear combination of these shape functions also represents a plane surface. In particular, N1+N2+N3 represents a plane height of one at nodes one, two, and, three and thus it is parallel to the triangle 123.
4. If N3 is dependent shape function, It is represented as ____
a) N3=ξ
b) N3=1-ξ
c) N3=1-η
d) N3=1-ξ-η
Explanation: The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. N1, N2, N3 are not linearly independent only one of two of these are independent.
5. In two dimensional problems x-, y- co-ordinates are mapped onto ____
a) x-, y- co-ordinates
b) x-, ξ – co-ordinates
c) η-, y- co-ordinates
d) ξ-η-Co-ordinates
Explanation: The similarity with one dimensional element should be noted ; in one dimensional problem the x- co-ordinates were mapped onto ξ- co-ordinates and the shape functions were defined as functions of ξ. In the two dimensional elements the x-, y-, co-ordinates are mapped onto ξ-,,η – co-ordinates.
6. The shape functions are physically represented by _____
a) Triangular co-ordinates
b) ξ-,η-Co-ordinates
c) Area co-ordinates
d) Surface co-ordinates
Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. Therefore appropriate functions have to be used and as already mentioned; low order typical polynomials are used in shape functions. The shape functions are physically represented by area co-ordinates.
7. A1 is the first area and N1 is its shape function then shape function N1= ___
a) A1/A
b) A-A1
c) A1+A
d) A1
Explanation: The shape functions are physically represented by area co-ordinates. A point in a triangle divides into three areas. The shape functions are precisely represented as
N1=A1/A .
8. The equation u=Nq is a _____ representation.
a) Nodal
b) Isoparametric
c) Uniparametric
d) Co-ordinate
Explanation: The isoparametric representation of finite elements is defined as element geometry and displacements are represented by same set of shape functions.
9. For plane stress or plane strain, the element stiffness matrix can be obtained by taking _____
a) Shape functions, N
b) Material property matrix, D
c) Iso parametric representation, u
d) Degrees of freedom, DoF
Explanation: The material property matrix is represented as ratio of stress to strain that is σ=Dε . Therefore by this relation element stiffness matrix can be obtained by material property matrix.
10. In a constant strain triangle, element body force is given as ____
a) fe=[fx,fy,fx,fy,fx,fy]T
b) fe=\(\frac{t_eA_e}{3}\)
c) fe=\(\frac{t_eA_e}{3}\)[fx,fy,fx,fy,fx,fy]T
d) fe=\(\frac{t_eA_e}{3}\)[fx,fy]T
Explanation: A body force is a force which acts through the volume of the body. Body forces contrast with the contact forces or the classical definition of the surface forces which are exerted to the surface of the body.