Generative Design of Bionic Structures Via Concurrent Multiscale Topology Optimization and Conformal Geometry Method

Topology optimization has been proved to be an efficient tool for structural design. In recent years, the focus of structural topology optimization has been shifting from single material continuum structures to multimaterial and multiscale structures. This paper aims at devising a numerical scheme for designing bionic structures by combining a two-stage parametric level set topology optimization with the conformal mapping method. At the first stage, the macro-structural topology and the effective material properties are optimized simultaneously. At the second stage, another structural topology optimization is carried out to identify the exact layout of the metamaterial at the mesoscale. The achieved structure and metamaterial designs are further synthesized to form a multiscale structure using conformal mapping, which mimics the bionic structures with orderly chaos features. In this research, a multi-control-point conformal mapping (MCM) based on Ricci flow is proposed. Compared with conventional conformal mapping with only four control points, the proposed MCM scheme can provide more flexibility and adaptivity in handling complex geometries. To make the effective mechanical properties of the metamaterials invariant after conformal mapping, a variable-thickness structure method is proposed. Three 2D numerical examples using MCM schemes are presented, and their results and performances are compared. The achieved multimaterial multiscale structure models are characterized by the orderly chaos features of bionic structures while possessing the desired performance.

Automated summary

Topology optimization has been proven to be an efficient tool for structural design, with recent focus shifting towards multimaterial and multiscale structures. This paper proposes a numerical scheme for designing bionic structures using a two-stage parametric level set topology optimization combined with the conformal mapping method. The study introduces a multi-control-point conformal mapping (MCM) based on Ricci flow to handle complex geometries and a variable-thickness structure method to maintain effective mechanical properties of metamaterials after conformal mapping. Three 2D numerical examples using MCM schemes are presented, demonstrating the orderly chaos features of bionic structures in achieved multimaterial multiscale structure models while maintaining desired performance.