Using the plane-stress formulation of the strain energy, and the nonlinear strain-displacement relations of von Ka´rma´n plate theory (Eqs. (8.95)) derive the strain energy in rectangular coordinates for the stretching and bending of the von Ka´rma´n theory. How does this expression simplify for the case where a deflection function w(x,y) is chosen such that, for a rectangular plate, w ¼ 0 along all the edges?
