Extruded-geometric-component-based 3D topology optimization

Abstract

A three-dimensional (3D) topology optimization approach based on extruded geometric components (EGCs) is proposed. Each EGC is constructed by extruding a convex/non-convex polygon along the axis of the EGC and rounding the ends of the EGC. Using an adaptive mapping technique which allows mapping each ECG onto a support domain, the EGCs are mapped onto an analytical grid to obtain an effective density field for material interpolation. Moreover, 2D-plane calculations can be utilized to replace 3D-space calculations to enhance computing efficiency. The positions and the cross-sectional areas of the ECGs are simultaneously optimized through the determination of an optimum set of geometry parameters. Some structural benchmark problems were investigated to verify the applicability of the proposed approach. Compared with the solid isotropic material penalization (SIMP) approach, the underlying approach does not require any filtering or projection techniques. Hence, it can produce a stiffer optimum design with an explicit boundary description whilst the number of design variables dramatically reduces.