First-Order Bilevel Topology Optimization for Fast Mechanical Design

TL;DR

This paper introduces a fast, low-cost bilevel topology optimization algorithm for mechanical design that significantly reduces computational resources by using approximate matrix inversions and first-order methods, enabling interactive design previews.

Contribution

The paper presents a novel bilevel topology optimization approach that replaces exact matrix inversions with approximate solutions, enabling faster and more interactive mechanical design processes.

Findings

The proposed method reduces iterative computational cost compared to traditional FEA-based algorithms.

Theoretical convergence of the algorithm is established.

Numerical experiments demonstrate the efficiency and effectiveness of the approach.

Abstract

Topology Optimization (TO), which maximizes structural robustness under material weight constraints, is becoming an essential step for the automatic design of mechanical parts. However, existing TO algorithms use the Finite Element Analysis (FEA) that requires massive computational resources. We present a novel TO algorithm that incurs a much lower iterative cost. Unlike conventional methods that require exact inversions of large FEA system matrices at every iteration, we reformulate the problem as a bilevel optimization that can be solved using a first-order algorithm and only inverts the system matrix approximately. As a result, our method incurs a low iterative cost, and users can preview the TO results interactively for fast design updates. Theoretical convergence analysis and numerical experiments are conducted to verify our effectiveness. We further discuss extensions to use high-performance preconditioners and fine-grained parallelism on the Graphics Processing Unit (GPU).