Approximate Length Scale Filter in Topology Optimization using Fourier Enhanced Neural Networks

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: exact and approximate . While exact control is desirable, its implementation requires imposing additional constraints during optimization. Here we introduce an approximate length scale filter that does not involve additional constraints. In this paper, we propose an approximate length scale filter 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 approximately 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. • A neural network-based topology optimization method with length scale control is presented. • The weights and bias associated with the NN serve as the design variables. • The length scale is controlled through Fourier projection. • The sensitivity computations are automated by expressing the computations in an end-end differentiable fashion using the NN’s library.