Evolutionary topology optimization of continuum structures under uncertainty using sensitivity analysis and smooth boundary representation

This paper presents an evolutionary approach for the Robust Topology Optimization (RTO) of continuum structures under loading and material uncertainties. The method is based on an optimality criterion obtained from the stochastic linear elasticity problem in its weak form. The smooth structural topology is determined implicitly by an iso-value of the optimality criterion field. This iso-value is updated using an iterative approach to reach the solution of the RTO problem. The proposal permits to model the uncertainty using random variables with different probability distributions as well as random fields. The computational burden, due to the high dimension of the random field approximation, is efficiently addressed using anisotropic sparse grid stochastic collocation methods. The numerical results show the ability of the proposal to provide smooth and clearly defined structural boundaries. Such results also show that the method provides structural designs satisfying a trade-off between conflicting objectives in the RTO problem.The authors would like to thank Dr. Francisco Periago for constructive suggestions and discussions. This work has been partially supported by the AEI/FEDER and UE under the contract DPI2016-77538-R and by the “Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia” under the contract 19274/PI/14