Minmax topology optimization

We describe a systematic approach for the robust optimal design of linear elastic structures subjected to unknown loading using minmax and topology optimization methods. Assuming only the loading region and norm, we distribute a given amount of material in the design domain to minimize the principal compliance, i.e. the maximum compliance that is produced by the worst‐case loading scenario. We evaluate the principal compliance directly by satisfying the optimality conditions which take the form of a Steklov eigenvalue problem and thus we eliminate the need of an iterative nested optimization. To generate a well‐posed topology optimization problem we use relaxation which requires homogenization theory. Examples are provided to demonstrate our algorithm.