Stress constrained thermo-elastic topology optimization based on stabilizing control schemes

Abstract

This article proposes two effective stabilizing control schemes for addressing the stress constrained thermo-elastic topology optimization in a non-uniform temperature field. Based on the density interpolation scheme, two linear elastic equations for coupling a thermo-elastic problem are considered. For comparison, different topology problem formulations for minimizing compliance or volume subject to stress constraints are solved. By virtue of a stabilization transform method, two stabilizing control schemes combined with the grouped aggregation method are developed to handle the challenging difficulties stemming from the local nature of highly nonlinear stress constraints. Moreover, the adjoint method is adopted to perform the sensitivity analysis. The design variables are updated by utilizing the method of moving asymptotes. The results of several typical numerical examples verify the validity of the proposed methodology, including the present stabilizing control schemes which can be employed to obtain clear topological design and fast convergence rate for thermo-elastic coupling problems. Meanwhile, compliance minimization design with stress constraints is appropriate to achieve balance between stress level and stiffness.