TreeTOp: Topology Optimization using Constructive Solid Geometry Trees

TL;DR

This paper introduces a novel feature-mapping topology optimization framework that uses an expanded set of Boolean operations within a differentiable tree structure, enabling more flexible and precise geometry design.

Contribution

It extends FMTO by incorporating union, intersection, and subtraction operations in a differentiable framework, enhancing design flexibility and optimization accuracy.

Findings

Demonstrates improved design flexibility with multiple Boolean operations.

Shows successful application through various numerical examples.

Achieves gradient-based optimization using a unified, differentiable Boolean approach.

Abstract

Feature-mapping methods for topology optimization (FMTO) facilitate direct geometry extraction by leveraging high-level geometric descriptions of the designs. However, FMTO often relies solely on Boolean unions, which can restrict the design space. This work proposes an FMTO framework leveraging an expanded set of Boolean operations, namely, union, intersection, and subtraction. The optimization process entails determining the primitives and the optimal Boolean operation tree. In particular, the framework leverages a recently proposed unified Boolean operation approach. This approach presents a continuous and differentiable function that interpolates the Boolean operations, enabling gradient-based optimization. The proposed methodology is agnostic to the specific primitive parametrization and is showcased through various numerical examples.