FINITE ELEMENT ANALYSISTEST # 3PART-A

Tick all relevant answers

1. In plane stress analysis the following stress components are zero.

a) xx (b) yy (c) zz (d) xy (e) yz (f) xz

2. In plane strain analysis the following strain components are present.

a) xx (b) yy (c) zz (d) xy (e) yz (f) zx

3. The convergence requirement that requires representation of states of constant strain by the

displacement model is satisfied by the following terms of the polynomial.

a) constant term (b) linear term (c) Quadratic term (d) All of the above

4. In a 2D field problem involving vector variables. where the variation of field variable is very high

we have to

a) Provide more no. of small size triangular elements.

b) Provide less no. of large size triangular elements

c) Provide same size triangular elements.

5. A cantilever beam, which is idealized by 5 beam elements results in a stiffness matrix of size.

a) 12 x 12 (b) 5 x 5 (c) 10 x 10 (d) 6 x 6

6. In solving for axial displacements of a bar of varying cross section subject to self weight alone it

is desirable to

a) go in for a single quadratic polynomial displacement model.

b) go in for a no. of linear polynomial displacement model

c) go in for a single beam element

7. If the no. of nodes for field displacement is more than the no. of nodes for geometric

transformation then we call the element as

a) Sub parametric (b) isoparametric (c) super parametric

8. In the torsion problem the field of variable occurring in the governing equation is

a) shear stress (b) Torque (c) Stress function (d) Shear strain

9. If (x1, y1) (x2, y2) and (x3, y3) represent the coordinates of the vertices taken in order clockwise the determinant

1 x1 y1 gives 1 x2 y2

1 x3 y3

a) 2A (b) –2A (c) A (d) –A

10. Evaluation of the integral N1 dx dy for a constant strain triangular element gives

(a) 2A (b) A (c) A/3 (d) 2A/d.

11. The Jacobian of transformation from Cartesian to natural co-ordinates for a one dimensional 2

noded element is

a) L (b) 2L (c) L/4 (d) L/2 (f) L/3

12. In the torsion problem the shear stress xz and yz are given respectively

- - - - a) ------ & ------ (b) ------ & ------ (c) ------ & ------ (d) ------ & ------

x y y x y x x y

13. In a thermal problem involving heat flow through a fin the boundary condition when the end is

left open to the atmosphere is given by

dTa) hp (T - T ) = KA ---- (b) hp (T - T ) = 0

dx

dT dTc) KA ---- = 0 (d) hp (T - T ) = KA ----

dx dx

2. The best numbering scheme to reduce hand width is given by

3. The minimum no. of elements needed to discretize the beam given in Fig.1 is

a) 4 (b) 5 (c) 6 (d) 7

4. A serendipity element is

a) 9 noded quadrilateral element (b) 8 noded quadrilateral element

c) 4 noded quadrilateral element (d) 4 noded cubic element

5. When higher order elements are included in the strain displacement relations we consider it as a case of

a) Geometric Non linearity (b) Material Non Linearity (c) Both a and b

d) None of the above.

6. The error in not satisfying the Governing Equation is termed as

a) error in solution (b) Discretization error (c) Residue (d) Flux

PART-B

7. Discuss how you will discretize the following domains. What are the matrices you will use.

8. What are Serendipity elements? Derive the shape functions for one corner node and one mid

side node for such on element.

9. Write short notes on

i) Numerical integration for evaluation of stiffness matrices

ii) Serendipity elements

iii) Convergence criteria.

10. Evaluate the Jacobian of transformation for the element shown in Fig.

11. Triangular elements are used for the stress analysis of a plate subjected to inplane loads. The

components of displacement parallel to (x, y) axes at the nodes i,j and k of an element are

found to be (-0.001. 0.01), (-0.002, 0.01( and (-0.002, 0.02) cm respectively. If the (x, y) co-

ordinates o the nodes shown in figure below are in cm, find (i) the distribution of the (x,y)

displacement components inside the element and (ii) the components of displacement of the

point (xp, yp) = (30, 25) cm.

ASSIGNMENT

1. Discuss the use of Pascal’s Triangle.

2. Explain what is meant by Co and C1 continuity element with respect to finite element method.

3. What are the conditions to be satisfied by the displacement model to ensure convergence of

solution?

4. Distinguish between Material and Geometric Non-linearity.

5. Explain very briefly about the various Non-Linear solution techniques.

Best of luck for your exams.