Self Evolving Structural Optimization - A Novel Approach To Topology Optimization

Abstract

Topology optimization is utilized to determine the optimal distribution of material in a domain subject to specific load and boundary conditions. The main methods utilized in this field include Solid Isotropic Material with Penalization (SIMP), (Bidirectional) Evolutionary Structural Optimization ((B)ESO) and Level Set Method (LSM). Most mainstream approaches rely on a continuous design domain or material field, which introduces two artifacts: intermediate densities (where the normalized density is a fraction rather than 0 or 1, also known as grey-scaling) and alternating densities or patterns in the design domain (checkerboarding). Grey-scaling creates non-physical regions, an area that has the same material but with a partial density and increases the stiffness, while checkerboards artificially lowers compliance and makes the designs mesh-dependent; mitigating these effects typically requires use of additional filters, knowledge of the optimizer and post processing to create a manufacturable design. The SIMP method dominates the field as it is computationally efficient and easily applied to individual cases. To address these issues while maintaining efficiency, this dissertation proposes Self-Evolving Structural Optimization (SESO): a stress-driven, derivative-free, discrete algorithm that removes a prescribed amount of inefficient (under utilized) material each iteration based on the Von Mises stress. A stress-averaging filter promotes continuity and suppresses checkerboarding while preserving a binary (0–1) design; compliance is monitored as a guard and for reporting rather than driving the update scheme. SESO avoids sensitivity calculations, post-processing and converges in a fixed, preset number of iterations. On eight canonical cases, SESO reduced compliance relative to the best SIMP result per case by at least 3.7% and up to 31%, and required 73–87% fewer iterations than SIMP when density filtering was utilized. Across these cases the designs remained binary with no observed checkerboarding.