Abstract: In general,it is difficult for single material thermo-elastic coupling topology optimization to obtain the comprehensive optimum of structural materials and properties.In this study,a multi-material topology optimization approach based on the ordered rational approximation of material properties(Ordered-RAMP)is proposed.In this method,the proportional and translation coefficients are established and the associated materials properties are described by a single design variable with0,1continuous distribution.The pros and cons of the proposed method were investigated and compared with the ordered solid isotropic microstructures with penalization(Ordered-SIMP).The normalized weighting method is introduced to construct the multi-objective function with minimization of structural compliance and heat dissipation,followed by sensitivity analysis of design variables.The iterative formation of thermo-elastic coupling topology optimization is derived under the multi-material and multi-objective conditions.The effects of weight coefficients and materials combination on the optimal results were analyzed through numerical examples.The results are shown that the proposed method is feasible and efficient to the multi-thermo-elastic coupling topology optimization problems.