Length Scale Control in Topology Optimization using Fourier Enhanced Neural Networks

TL;DR

This paper introduces a neural network-based topology optimization method enhanced with Fourier space projection to effectively control length scales, improving design manufacturability without adding constraints.

Contribution

It extends the TOuNN framework with Fourier enhancement for length scale control, offering an efficient and constraint-free approach.

Findings

Effective length scale control demonstrated in numerical experiments.

No additional constraints required for the proposed method.

Applicable to single and multi-material designs.

Abstract

Length scale control is imposed in topology optimization (TO) to make designs amenable to manufacturing and other functional requirements. Broadly, there are two types of length-scale control in TO: \emph {exact} and \emph {approximate}. While the former is desirable, its implementation can be difficult, and is computationally expensive. Approximate length scale control is therefore preferred, and is often sufficient for early stages of design. In this paper we propose an approximate length scale control strategy for TO, by extending a recently proposed density-based TO formulation using neural networks (TOuNN). Specifically, we enhance TOuNN with a Fourier space projection, to control the minimum and/or maximum length scales. The proposed method does not involve additional constraints, and the sensitivity computations are automated by expressing the computations in an end-end differentiable fashion using the neural net's library. The proposed method is illustrated through several numerical experiments for single and multi-material designs.