Post-Processing of Topology Optimized Results

Abstract

Structural design optimization is the process of obtaining an optimized structure while satisfying a set of criteria. The process can be divided into three stages: topology optimization (stage one), geometry extraction (stage two) and shape optimization (stage three). The last two stages are regarded to be the post-processor of topology optimized results and this MSc. Thesis proposes a new method for this part. At stage one, topology optimized results show unwanted features, namely jagged boundaries (i.e. poor smoothness) and intermediate densities (i.e. poor crispness). The post-processor should overcome these unwanted properties.
During post-processing the geometry is described implicitly by a Level Set Function (LSF). The zero-level contour of the LSF describes the actual geometry. The LSF is constructed by summing a set of Radial Basis Functions (RBFs) each multiplied with a weight, resulting in a smooth summation. At stage two, a geometry is extracted by setting up and solving a set of equations linking the RBFs to the densities obtained at stage one.
At stage three, a shape optimization is done to compensate the loss of structural performance, which resulted from translating the densities to an LSF at stage two. The geometry described by the LSF does not match the mesh created for stage one. A fictitious domain method called the Finite Cell Method (FCM) is used to perform a structural analysis on the non-matching mesh. A sensitivity analysis is done to provide gradient information to the gradient-based optimizer, the Method of Moving Asymptotes (MMA). Controlling the slope of the LSF is needed to make sure the sensitivities do not become zero throughout the domain. The maximum possible slope of the LSF can be fixed by setting a bound on the weights of the RBFs. Furthermore, intermediate densities are penalized such that these provide relatively low stiffness compared to its material use.
Several case studies are done using the proposed method. The post-processor: (1) improves the smoothness due to the use of the smooth LSF, (2) decreases the amount of intermediate densities by an average factor of 5.5 and (3) achieves an average 10\% improve in performance between stage two and three. The computation time is strongly problem dependent, test cases are either: slower, equally fast or faster than the topology optimization of stage one.