Topology optimization of heat conduction problem involving design-dependent heat load effect

Topology optimization of steady heat conduction problem under both design-independent and design-dependent heat loads is studied by means of a modified bidirectional evolutionary structural optimization (BESO) method. Two types of problems are distinguished by their physical meanings and particularly design-dependent load effect is highlighted in the following two points. At the stage of sensitivity analysis, both the heat conductivity matrix and the design-dependent heat generation load associated with the void element are penalized in the same manner. The rationality is illustrated based on numerical tests. Furthermore, as the sensitivity of the objective function changes its sign during the iteration, a modified BESO procedure is presented to deal with the non-monotonicity of the objective function defined by the heat potential capacity. Detailed steps of the BESO procedure are presented for the element removal and growth while the inequality volume constraint is imposed. To conclude the work, numerical results and the element sensitivity obtained are discussed to show the effect of design-dependent load.