Structural and Multidisciplinary Optimization

, Volume 46, Issue 4, pp 597–612 | Cite as

Topology optimization considering material and geometric uncertainties using stochastic collocation methods

  • Boyan S. Lazarov
  • Mattias Schevenels
  • Ole Sigmund
Research Paper
First Online:
Received:
Revised:
Accepted:

Abstract

The aim of this paper is to introduce the stochastic collocation methods in topology optimization for mechanical systems with material and geometric uncertainties. The random variations are modeled by a memory-less transformation of spatially varying Gaussian random fields which ensures their physical admissibility. The stochastic collocation method combined with the proposed material and geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The computational cost is discussed in details and solutions to decrease it, like sparse grids and discretization refinement are proposed and demonstrated as well. The method is utilized in the design of compliant mechanisms.

Keywords

Topology optimization Robust design Material uncertainties Geometric uncertainties Stochastic collocation Sparse grids 
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Notes

Acknowledgements

This work was financially supported by Villum Fonden and by a grant from the Danish Center of Scientific Computing (DCSC). The second author is a member of K.U.Leuven-BOF PFV/10/002 OPTEC-Optimization in Engineering Center.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Boyan S. Lazarov
    • 1
  • Mattias Schevenels
    • 2
  • Ole Sigmund
    • 1
  1. 1.Department of Mechanical Engineering, Solid MechanicsTechnical University of DenmarkLyngbyDenmark
  2. 2.Department of Architecture, Urbanism and PlanningK.U.LeuvenLeuvenBelgium

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