Thermo-elastic topology optimization with stress and temperature constraints

A thermo-elastic topology optimization with stress and temperature constraints is proposed to attack the complex multiphysics problem in this paper. Based on the rational approximation of material properties (RAMP), the coupled equations of mechanic and temperature field are solved. Two optimization problems, volume minimization with temperature and stress constraints, and traditional compliance minimization with volume and temperature constraints, are discussed for comparison. The stress stabilizing control scheme (SSCS) combined with global stress measure is presented to tackle highly nonlinear and local nature of stress with thermal expansion in varying temperature field. The adjoint method is applied to achieve the sensitivity of multiphysics field and the density function is updated utilizing the method of moving asymptotes (MMA). Representative examples are investigated to demonstrate the effectiveness and utility of the proposed method. Clear topology and stable iterative process can be obtained for complex coupled problem by means of the SSCS. Meanwhile, the topology with stress and temperature constraints has obvious sensitivity to even subtle change in temperature. The optimization design considering several stress constraints under multithermal conditions can work well in different temperature ranges.