A finite element analysis of optimal variable thickness sheets

A quasi-mixed finite element (FE) method for maximum stiffness of variable thickness sheets is analyzed. The displacement is approximated with nine no de Lagrange quadrilateral elements, and the thickness is approximated as el ementwise constant. One is guaranteed that the FE displacement solutions wi ll converge in H-1 (Omega), but in an example it is shown that, in general, one cannot expect any subsequence of the FE thickness solutions to converg e in any L-p (Omega)-norm. However, under a regularity and biaxiality assum ption on the optimal stress field, uniqueness of the optimal thickness func tion as well as convergence in L-p (Omega) (1 less than or equal to p < inf inity) of FE thickness solutions are proven.