Optimization of a plate with holes

TL;DR

This paper presents a gradient-based optimization method for shape and topology design of a simply supported plate with holes, using a fictitious domain approach and control variational method, demonstrated through numerical experiments.

Contribution

It introduces a fixed domain, easy-to-implement optimization algorithm that performs simultaneous topological and boundary variations for plates with holes.

Findings

Efficient optimization algorithm demonstrated through numerical experiments.

Method effectively handles shape and topology variations.

Applicable to plates with complex multiply connected domains.

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.