Structural and Multidisciplinary Optimization

, Volume 42, Issue 5, pp 725–738 | Cite as

Topology optimization involving thermo-elastic stress loads

  • Tong Gao
  • Weihong Zhang
Research Paper


Structural topology optimization of thermo-elastic problems is investigated in this paper. The key issues about the penalty models of the element stiffness and thermal stress load of the finite element model are highlighted. The penalization of thermal stress coefficient (TSC) measured by the product between thermal expansion coefficient and Young’s modulus is proposed for the first time to characterize the dependence of the thermal stress load upon the design variables defined by element pseudo-densities. In such a way, the element stiffness and the thermal stress load can be penalized independently in terms of element pseudo-density. This formulation demonstrates especially its capability of solving problems with multiphase materials. Besides, the comparison study shows that the interpolation model RAMP is more advantageous than the SIMP in our case. Furthermore, sensitivity analysis of the structural mean compliance is developed in the case of steady-state heat conduction. Numerical examples of two-phase and three-phase materials are presented.


Topology optimization Thermo-elastic problems Thermal stress Design-dependent load Thermal stress coefficient 



This work is supported by the National Science Fund for Distinguished Young Scholars (10925212), the National Natural Science Foundation of China (50775184, 90916027) and the Aeronautical Science Foundation (2008ZA53007).


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Engineering Simulation and Aerospace Computing (ESAC), The Key Laboratory of Contemporary Design and Integrated Manufacturing TechnologyNorthwestern Polytechnical UniversityXi’anChina

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