7/25/2019 CE5610_assign7_2013

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Finite Element Analysis

Assignment 7 (Due Date: April 29, 2013)

1. The state of stress at a point is given as follows:

2 2 2

2 2 2

2 2

( , )

0

xx

yy

zz

xy

yz xz

y c x y

x c y xx y

f x y

Determine ( , )f x y so that the stress distribution may be in equilibrium in the absence of

body forces.

2. Develop a deformation field ( , ), ( , )u x y v x y that describe the deformation of the finite

element shown in the following figure. From this determine , ,x y xy

. Interpret your

answer.

3. Compute stresses and strains at a point located at 2 2, for the problem shown in thefollowing figure, using only one quadrilateral element. Assume plane strain conditions. E =

30106psi, = 0.25, thickness = 1.

(0, 0) (5, 0)

(0, 10) (5, 10)

(4, 0) (9, 0)

(5, 10) (10, 10)