Optimization of a plate with holes

Abstract

We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented, based on a fictitious domain approach and the control variational method. The algorithm that we introduce is of gradient type and performs simultaneous topological and boundary variations. Numerical experiments are also included and show its efficiency.

Topological optimization and minimal compliance in linear elasticity

“…It is a new approach and another important property is that it may be applied to many boundary value problems as governing systems. For other fixed domain approaches, we quote [14], [15], [19], [20] and the survey [16] with its references. For multi-layered composite materials, one can consult [9].…”

“…For instance, already [13] used a penalization/regularization method in free boundary problems. A survey on this subject is the paper [16] and in [19], [17] such approaches are extended to the optimization of plates with holes and other problems. In general, Dirichlet boundary conditions are taken into account, while the approximation defined in (2.9), (2.10) can be used for other boundary conditions as well.…”