A new level-set based approach to shape and topology optimization under geometric uncertainty

Shikui Chen, Wei Chen*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Geometric uncertainty refers to the deviation of the geometric boundary from its ideal position, which may have a non-trivial impact on design performance. Since geometric uncertainty is embedded in the boundary which is dynamic and changes continuously in the optimization process, topology optimization under geometric uncertainty (TOGU) poses extreme difficulty to the already challenging topology optimization problems. This paper aims to solve this cutting-edge problem by integrating the latest developments in level set methods, design under uncertainty, and a newly developed mathematical framework for solving variational problems and partial differential equations. Contributions of this work lie in the following three aspects: First, geometric uncertainty is quantitatively modeled by combing level set equation with a random normal boundary velocity field characterized by K-L expansion. Multivariate Gauss quadrature is employed to propagate the geometric uncertainty, which also facilitates shape sensitivity analysis by transforming a TOGU problem into a weighted summation of deterministic topology optimization problems. Second, a PDE-based approach is employed to overcome the deficiency of conventional level set model which cannot explicitly maintain the point correspondences between the current and the perturbed boundaries during the boundary perturbation process. With the explicit point correspondences, shape sensitivity defined on different perturbed designs can be mapped back to the current design, which makes it possible to create a single design velocity field to optimize the performances defined on different geometries. The proposed method is demonstrated with a bench mark structural design. Robust designs achieved with the proposed TOGU method are compared with their deterministic counterparts.

Original languageEnglish (US)
Title of host publication13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2010
DOIs
StatePublished - Dec 1 2010
Event13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, MAO 2010 - Ft. Worth, TX, United States
Duration: Sep 13 2010Sep 15 2010

Publication series

Name13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2010

Other

Other13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, MAO 2010
CountryUnited States
CityFt. Worth, TX
Period9/13/109/15/10

ASJC Scopus subject areas

  • Aerospace Engineering
  • Mechanical Engineering

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