Topology Optimization of Thermal Insulators considering Thermal–Structural Multi-Objective Function

This study develops a two-dimensional design sensitivity analysis and topology optimization method for multi-objective problems considering both thermal insulation and structural stiffness. The objective function is defined by introducing a weight factor that combines the thermal total energy and compliance for the thermal and structural problems. The derived design sensitivities are validated using the finite difference sensitivities. The Pareto front for designing thermal insulation is obtained by varying the weight function of the objective function and size of the domain. This meant that the geometric feature of the thermal bottleneck outweighed the load-supporting structures as the relative importance of the thermal insulation increased. Compared with the existing designs, the obtained designs are both structurally reliable and thermally insulative in terms of quantitative performance measures.