Topology optimization of thermo-elastic structures with multiple materials under mass constraint

• Effects of the Poisson's ratios on the thermal stress coefficient is included.
• Optimization formulation is improved to avoid the possible mixed material status.
• Non-uniform initial weighting in UMMI might be advantageous in obtaining the optimum.

This work addresses the complicated design problem in which a structure of multiple materials is topologically optimized under the conditions of steady-state temperature and mechanical loading. First, the general thermal stress coefficient (GTSC) is introduced to relate the thermal stress load to the design variables and address an engineering practice need by breaking down the previous assumption that the Poisson’s ratios of all candidate materials are the same. Second, the Uniform Multiphase Materials Interpolation (UMMI) scheme and the Rational Approximation of Material Properties (RAMP) scheme are combined to parameterize material properties (e.g., the elasticity matrix and GTSC). In the problem formulation, mass constraint is adopted to automatically determine the optimal match of candidate materials instead of imposing the standard volume constraint to each material phase. An improved optimization formulation with an artificial penalty term is also proposed to avoid a possible mixed material status in the numerical results. Numerical tests illustrate the validity of the proposed method.