Topology design optimization of conductive thermal problems subject to design-dependent load using density gradients

In this article, a design sensitivity analysis method is developed for topology optimization of steady-state conductive thermal problems subject to design-dependent thermal loads using density gradients–based boundary detection. In a real physical heat conduction problem, a design-dependent thermal load through the convective boundary is an important factor; however, it is not easy to impose boundary conditions in heat conduction problem due to the difficulties of exact boundary representation. Here, the detection of convection boundaries is available by the density distinction between void and materials, which is similar to a gradient operator in image processing. Applying density gradients and Dirac delta function of densities, we impose a design-dependent load effect on thermal analysis and perform the design sensitivity analysis for topology optimization. At each optimization process, it is noted that the results of thermal analysis and the design sensitivities are influenced by the design-dependent thermal load. Through demonstrative numerical examples, the proposed approach using density gradients is proven to work yielding meaningful optimization results. The developed approach is applicable to the plant engineering and nuclear industries where thermo-mechanical coupling occurs inevitably by the thermal convection.