{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

View Full Document Right Arrow Icon
AE 321 Homework 8 solution Chapter 7: Failure and Fatigue 1a. We start with the following trial solution.   0 0 0 0 0 0 0 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 0 0 0 0 0 0 Compatibility is also satisfied because all entries in the strain tensor are constant. Boundary conditions: end faces T n 1 0 0 satisfied 0 0 0 33 23 13 Boundary conditions: lateral surface T n 0 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.
Background image of page 1

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

View Full Document Right Arrow Icon
1b. The stress state from part (a) is already the principal stress. Therefore, P 3 2 1 0 Using the Von Mises criterion, y y oct P P P P 3 2 3 2 0 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 becomes P P P 0 0 0 0 0 0 Nothing that P
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}