Multimaterial topology design for optimal elastic and thermal response with material-specific temperature constraints

Ziliang Kang, Kai A. James

Research output: Contribution to journalArticlepeer-review


We present an original method for multimaterial topology optimization with elastic and thermal response considerations. The material distribution is represented parametrically using a formulation in which finite element–style shape functions are used to determine the local material properties within each finite element. We optimize a multifunctional structure that is designed for a combination of structural stiffness and thermal insulation. We conduct parallel uncoupled finite element analyses to simulate the elastic and thermal response of the structure by solving the two-dimensional Poisson problem. We explore multiple optimization problem formulations, including structural design for minimum compliance subject to local temperature constraints so that the optimized design serves as both a support structure and a thermal insulator. We also derive and implement an original multimaterial aggregation function that allows the designer to simultaneously enforce separate maximum temperature thresholds based upon the melting point of the various design materials. The nonlinear programming problem is solved using gradient-based optimization with adjoint sensitivity analysis. We present results for a series of two-dimensional example problems. The results demonstrate that the proposed algorithm consistently converges to feasible multimaterial designs with the desired elastic and thermal performance.

Original languageEnglish (US)
Pages (from-to)1019-1037
Number of pages19
JournalInternational Journal for Numerical Methods in Engineering
Issue number10
StatePublished - Mar 9 2019


  • elasticity
  • finite element methods
  • structures
  • thermal effects
  • topology design

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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