AN APPROXIMATION-THEORY FOR OPTIMUM SHEETS IN UNILATERAL CONTACT

In this paper we give an approximation theory for the optimum variable thickness sheet problem considered in [1] and [2]. This problem, whic h is a stiffness maximization of an elastic continuum in unilateral co ntact, admits complete material removal, i.e., the design variable is allowed to take zero values. The original saddle-point problem is repl aced by a sequence of approximating problems, the solutions of which a re shown to converge weakly to exact solutions. In the case that compl ete material removal is not admissible, the state variable is shown to converge strongly in the (H-1)(2)-norm to the unique exact state solu tion. We consider a particular finite-element discretization that fits into the general theory and present the mathematical programming prob lem that results from it.