Handed Out: 2/19/98
Due: 2/26/98
1. A uniform circular plate (thickness h, bending stiffness D, Poisson's ratio v) has radius R, a clamped boundary, and a concentrated force F applied in the center. Find the deflection in the center dF as a function of the applied force F and the radius R.
2. The same plate above is loaded with a uniform pressure p on one side. Find the deflection in this case dp as function of p and R.
3. A disk of silicon (thickness 0.030", E = 15.5 Msi, v = 0.3) is held against a processing platen by a uniform pressure p=1 psi. A 0.001" particle gets on the platen, holding the silicon off the platen. Use the above to relations to model this situation and find the force F applied to the particle. Hints: p and dtot = dF + dp are known. Assume the boundary, where the plate touches the platen, is clamped (critique this assumption if you like). The unknowns are F and R; the conditions to be satisfied are the above, plus vertical equilibrium. Be careful of the last condition- don't forget the shear resultant at the boundary when writing the equilibrium equation.