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Robust topology optimization based on stochastic collocation methods under loading uncertainties. (English) Zbl 1394.74146

Summary: A robust topology optimization (RTO) approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.

MSC:

74P15 Topological methods for optimization problems in solid mechanics
49Q12 Sensitivity analysis for optimization problems on manifolds
74S05 Finite element methods applied to problems in solid mechanics
65K10 Numerical optimization and variational techniques
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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