Fast topological-shape optimization with boundary elements in two dimensions

Igor A. Ostanin, Denis N. Zorin, Ivan V. Oseledets

Research output: Contribution to journalArticle

Abstract

Wide variety of engineering design problems can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches were developed to address the problem of finding optimal design of an engineered structure. Recent works [10, 23] have demonstrated the feasibility of boundary element method as a tool for topological-shape optimization. However, it was noted that the approach has certain drawbacks, and in particular high computational cost of the iterative optimization process. In this short note we suggest ways to address critical limitations of boundary element method as a tool for topological-shape optimization. We validate our approaches by supplementing the existing complex variables boundary element code for elastostatic problems with robust tools for the fast topological-shape optimization. The efficiency of the approach is illustrated with a numerical example.

Original languageEnglish (US)
Pages (from-to)127-133
Number of pages7
JournalRussian Journal of Numerical Analysis and Mathematical Modelling
Volume32
Issue number2
DOIs
StatePublished - Apr 1 2017

Keywords

  • Elasticity
  • boundary element method
  • topological derivative
  • topological-shape optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation

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