Topology Optimisation For Heat Conduction Problems In 2D With Heat Transfer Boundary Condition And Heat Flux Objective Function Defined On Morphing Boundaries Using BEM

Topological derivative is a significant and indispensable quantity in topology optimisation processes. It is defined as the limit of the variation of the objective functional caused when an infinitely small part of the material is removed in the domain. Since the topological derivatives have different expressions depending on the boundary conditions on the boundary of the cavity generated by removing the material, the derivation of the topological derivative becomes an important task before proceeding to the topology optimisation. This paper presents a topological derivative expression for two-dimensional heat conduction problems with the objective function of heat flux defined on the morphing boundaries generated through the topology optimisation process. The obtained topological derivative is used to update the distribution of the level set function, which gives the boundary of the material as its iso-surface corresponding to zero value. The effectiveness of the present approach is demonstrated through numerical examples.