Topological Sensitivity Analysis for Two-Dimensional Heat Transfer Problems Using the Boundary Element Method

Abstract

The objective of the current chapter is to present the application of a hard kill material removal algorithm for topology optimization of heat transfer problems. The boundary element method is used to solve the governing equations. A topological-shape sensitivity approach is used to select the points showing the lowest sensitivities, where material is removed by opening a cavity. As the iterative process evolves, the original domain has holes progressively introduced, until a given stop criteria is achieved. In a topological optimization process, final shapes with irregular boundaries are usual. Instead of applying boundary smoothing techniques at a postprocessing level, this work adopts a procedure in which smooth boundaries are ensured as a direct outcome of the original optimization code. The strategy employs Bézier curves for boundary parameterization. An algorithm is also developed to detect, during the optimization process, which curve of the intermediary topology must be smoothed. For the purpose of dealing with non-isotropic materials a linear coordinate transformation is implemented.