Topology optimization under independent multi-load with uncertainty

Hae Chang Gea, Xing Liu, Euihark Lee, Limei Xu

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

1 Scopus citations


In this paper, topology optimization under multiple independent loadings with uncertainty is presented. In engineering practice, load uncertainty can be found in many applications. From the literature, researchers have focused mainly on problems containing only a single uncertain external load. However, such idealistic problems may not be very useful in engineering practice. Problems involving multi-loadings with uncertainty are more commonly found in engineering applications. This paper presents a method to solve a system which contains multiple independent loadings with load uncertainty. First, a two-level optimization problem is formulated. The upper level problem is a typical topology optimization problem to minimize the mean compliance in the design using the worst case conditions. The lower level optimization problem is to solve for the worst loadings corresponding to the critical structure response. At the lower level formulation, an unknown-but-bounded model is used to define uncertain loadings. There are two challenges in finding the worst loading case: non-convexity and multi-loadings. The non-convexity problem is addressed by reformulating the problem as an inhomogeneous eigenvalue problem by applying the KKT optimality conditions and the multi-uncertain loadings problem is solved by an iterative method. After the worst loadings are generated, the upper level problem can be solved by a general topology optimization method. The effectiveness of the proposed method is demonstrated by numerical examples.

Original languageEnglish (US)
Title of host publication42nd Design Automation Conference
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791850107
StatePublished - 2016
EventASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016 - Charlotte, United States
Duration: Aug 21 2016Aug 24 2016

Publication series

NameProceedings of the ASME Design Engineering Technical Conference


OtherASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation


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