OPTIMAL-DESIGN OF AN ELASTIC OR ELASTOPLASTIC BEAM WITH UNILATERAL ELASTIC-FOUNDATION AND RIGID SUPPORTS

A class of optimal design problems is considered, where the state problem is governed by a variational inequality. The latter includes a nonlinear monotone operator, the coefficients of which are chosen as the design (control) variables. Moreover, the set of admissible functions depends on the control, as well. Existence of an optimal design is proven on an abstract level. Some applications are presented to the optimization of a beam on a unilateral elastic foundation. Finite element approximations are proposed and a convergence result is proven.