Mee-658 – Theory of Plates and Shells Spring 2012

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MEE-658 – Theory of Plates and Shells

Spring 2012
Homework Assignment #2
Report results in a professional manner by due date listed above.

  1. A clamped circular plate of radius, a, is under a rotationally symmetric lateral load which increases from the center to the edge of the plate according to:

Where po is constant.

Derive the expression for the deflected shape, w.

  1. Given a clamped circular plate under uniform loading where

r = 20" material=Steel p= 5.5psi t=0.375"

  1. Derive a general expression for the deflected shape and moments as a function of r.

  2. Determine the maximum deflection

  3. Determine the maximum stresses, r and 

  4. Compare the results to a finite element analysis.

  1. Repeat the problem above for a plate with a 5" diameter hole at the center.

  1. A clamped circular plate of thickness, t, carries a concentrated load at the center of magnitude P. This force acts on an area with a radius 0.6t. Determine the maximum value of P knowing that the allowable stress is 60MPa, t=15mm, a=180mm, E=210GPA and =0.3.

  1. For the plate given in Problem 2; increase the load to 100 psi. Assume the in-plane boundary is immovable.

  1. Plot the load vs. peak deflection, compare to theory. (incrementally increase the load in at least 10 steps)

  2. Plot the load vs. Von Mises stress at the edge of the plate.

  3. Comment on the small deflection vs large deflection solution.

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