Optimal Design and Identification Problems in Nonsmooth Mechanics

Abstract

Some optimal design and identifications problems arising in nonsmooth mechanics are reviewed in this paper. The mechanical problems which are studied in the framework of nonsmooth mechanics involve nondifferentiable relations. These state problems are, for example, variational or hemivariational inequalities. In certain cases one is able to formulate equivalent minimization or critical point problems for appropriately defined nonsmooth and in general nonconvex potentials. The corresponding optimal design problem has some distinguished features. First, nonconvexity can not be avoinded, since the state problem is, in general, nonlinear with respect to the design variables. Furthermore, nondifferentiability is a natural concequence of the nonsmooth mechanical model. The arising sensitiviry analysis is also of a nonclassical nature. Finally, for nonconvex mechanical models, discontinuity of the response as a function of the design variables introduces discontinuous functions into the optimal desingn problem. Model applications include structural optimization, optimal design and parameter identification problems in the presence of contact or adhesion effects and in elastoplasticity.