Sensitivity Analysis in Shape Optimization using Voxel Density Penalization

Abstract

Shape optimization in the context of technical design is the process by which mechanical demands (e.g. loads, stresses) govern a sequence of piece instances, which satisfy the demands, while at the same time evolving towards more attractive geometric features (e.g. lighter, cheaper, etc.). The SIMP (Solid Isotropic Material with Penalization) strategy seeks a redistribution of local densities of a part in order to stand stress / strain demands. Neighborhoods (e.g. voxels) whose density drifts to lower values are considered superfluous and removed, leading to an optimization of the part shape. This manuscript presents a study on how the parameters governing the voxel pruning affect the convergence speed and performance of the attained shape. A stronger penalization factor establishes the criteria by which thin voxels are considered void. In addition, the filter discourages punctured, chessboard pattern regions. The SIMP algorithm produces a forecasted density map on the whole piece voxels. A post-processing is applied to effectively eliminate voxels with low density, to obtain the effective shape. In the literature, mechanical performance finite element analyses are conducted on the full voxel set with diluted densities by linearly weakening each voxel resistance according to its diluted density. Numerical tests show that this approach predicts a more favorable mechanical performance as compared with the one obtained with the shape which actually lacks the voxels with low density. This voxel density - based optimization is particularly convenient for additive manufacturing, as shown with the piece actually produced in this work. Future endeavors include different evolution processes, albeit based on variable density voxel sets, and mechanical tests conducted on the actual sample produced by additive manufacture.