A deterministic approach for shape and topology optimization under uncertain loads

Abstract : The present work aims at handling uncertain loads in shape and topology optimization. More specifically, we minimize objective functions combining mean values and variances of standard cost functions and assume that uncertainties are small and generated by a finite number N of random variables. A deterministic approach that relies on a second-order Taylor expansion of the cost function has been proposed by Allaire & Dapogny. 1 That method requires a computational effort comparable to the one for an N-load problem. This work presents a general framework to handle uncertainties on arbitrary static load cases where perturbations on both surface forces and body forces are considered. We demonstrate the effectiveness of the approach in the context of level-set-based topology optimization for the robust compliance minimization on three-dimensional test cases.
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Chetra Mang, Julien Cortial, Chiara Nardoni, Felipe Bordeu. A deterministic approach for shape and topology optimization under uncertain loads. Eurogen 2019, Sep 2019, Guimarães, Portugal. ⟨hal-02471986⟩

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