HW8solution - AE 321 – Homework 8 solution Chapter 7...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AE 321 – Homework 8 solution Chapter 7: Failure and Fatigue 1a. We start with the following trial solution. P P Note that the entries in the upper left of the stress tensor, i.e. 21 12 22 11 , , , arise from the in-plane hydrostatic case, and that all other entries are zero because the cylinder is traction-free in the x 3-direction. It can be easily shown that equilibrium is satisfied since P is constant. Using the stress-strain relation, E P E P P E P P 2 Compatibility is also satisfied because all entries in the strain tensor are constant. Boundary conditions: end faces T n 1 satisfied 33 23 13 Boundary conditions: lateral surface T n sin cos sin cos sin sin cos cos 22 12 2 12 11 1 P T P T Since the boundary conditions are satisfied, the trial solution is the solution. 1b. The stress state from part (a) is already the principal stress. Therefore, P 3 2 1 Using the Von Mises criterion, y y oct P P P P 3 2 3 2 3 1 3 1 2 2 2 1 3 2 3 2 2 2 1 max 1c. When the pressure P were also applied on the end faces, then the stress state...
View Full Document

This note was uploaded on 03/07/2011 for the course AE 311 taught by Professor Dutton,j during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 9

HW8solution - AE 321 – Homework 8 solution Chapter 7...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online