Jeffrey Doyon

HW#2

Due 10/20/08

List of References:

(a) Callister, William D. (2000). Materials Science And Engineering, An Introduction, 5th Edition. John Wiley & Sons, Inc.

(b) Budynas, Richard G. (1999). Advanced Strength and Applied Stress Analysis, 2nd Edition. McGraw-Hill.

1. The Airy stress function Ф(x,y) is applicable to 2D plane elasticity problems where body forces don’t exist, and is defined such that:

Solving for compatibility yields the biharmonic equation:

Written out for rectangular coordinates, this biharmonic equation is:

2.From the notes, for an isotropic linear elastic solid,

Values of E or υ are given for this problem as stated below.

E = 210 GPa

υ = .3

from Ref (b)

#3. A 2D plate element model was created using PATRAN software that represented linear-elastic (small deflections), isotropic material. All nodes at x=0 were fixed (All DOFs=0), and a point load of 105 was applied to one node at the edge of the beam (at x=1) and in the middle of the breadth (at z=0.5). Below the deflected shape is represented in red and the undelfected shape is in black. The predicted maximum deflection is 0.00358.

=-.004 From Beam Theory closed form solution.

#4.a and b

4c.

4d. If there is not stress then there is no strain as they are directly proportional in linear elastic theory.

4e. See 4c.

4.g

4.f

5.a The solutions seen below can be obtain from the notes.

Sigma_z=0

Hoop stress

Displacement

Sigma_r

Esilon_phi

Epsilon_r

6.a Creep compliance is equal to the ratio of elasticity to anelatisity or E/neta.

b. Assume propertie of steel. E=30X10^6psi=206842MPa. Assume strain an instant before the stress is released at t=10^3