Robust multiphase topology optimization accounting for manufacturing uncertainty via stochastic collocation

Vahid Keshavarzzadeh, Kai A. James

Research output: Contribution to journalArticlepeer-review


This paper presents a computational framework for multimaterial topology optimization under uncertainty. We combine stochastic collocation with design sensitivity analysis to facilitate robust design optimization. The presence of uncertainty is motivated by the induced scatter in the mechanical properties of candidate materials in the additive manufacturing process. The effective elastic modulus in each finite element is obtained by an interpolation scheme which is parameterized with three distinct elastic moduli corresponding to the available design materials. The parametrization enables the SIMP-style penalization of intermediate material properties, thus ensuring convergence to a discrete manufacturable design. We consider independent random variables for the elastic modulus of different materials and generate designs that minimize the variability in the performance, namely structural compliance. We use a newly developed quadrature rule, designed quadrature, to compute statistical moments with reduced computational cost. We show our approach on numerical benchmark problems of linear elastic continua where we demonstrate the improved performance of robust designs compared with deterministic designs. We provide the MATLAB implementation of our approach.

Original languageEnglish (US)
Pages (from-to)2461-2476
Number of pages16
JournalStructural and Multidisciplinary Optimization
Issue number6
StatePublished - Dec 1 2019


  • Additive manufacturing
  • Multimaterial topology optimization
  • Robust design optimization
  • Stochastic collocation

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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