Topology optimization with unknown-but-bounded load uncertainty

Xike Zhao, Wei Song, Hae Chang Gea, Limei Xu

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

3 Scopus citations


In this paper, convex modeling based topology optimization with load uncertainty is presented. The load uncertainty is described using the non-probabilistic based unknown-but-bounded convex model, and the strain energy based topology optimization problem under uncertain loads is formulated. Unlike the conventional deterministic topology optimization problem, the maximum possible strain energy under uncertain loads is selected as the new objective in order to achieve a safe solution. Instead of obtaining approximated solutions as used before, an exact solution procedure is presented. The problem is first formulated as a single level optimization problem, and then rewritten as a two-level optimization problem. The upper level optimization problem is solved as a deterministic topology optimization with the load which generated from the worst structure response in the lower level problem. The lower level optimization problem is to identify this worst structure response, and it is found equivalent to an inhomogeneous eigenvalue problem. Three different cases are discussed for accurately evaluating the global optima of the lower level optimization problem, while the corresponding sensitivities are derived individually. With the function value and sensitivity information ready, the upper level optimization problem can be solved through existing gradient based optimization algorithms. The effectiveness of the proposed convex modeling based topology optimization is demonstrated through different numerical examples.

Original languageEnglish (US)
Title of host publication40th Design Automation Conference
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791846322
StatePublished - 2014
EventASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014 - Buffalo, United States
Duration: Aug 17 2014Aug 20 2014

Publication series

NameProceedings of the ASME Design Engineering Technical Conference


OtherASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

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


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