Multi-material topology optimization using neural networks for plates with variable thickness

Abstract

This paper proposes a novel multi-material topology optimization (MMTO) method for plates with variable thickness, based on neural network (NN) representations and the Reissner--Mindlin plate theory. The proposed methodology leverages the expressive power of fully-connected neural networks to define continuous, mesh-independent material distributions, effectively addressing typical numerical challenges such as mesh-dependency, checker-boarding, and shear-locking. The neural network outputs material volume fractions at any spatial point, guaranteeing partition-of-unity via a softmax activation, and utilizes automatic differentiation for precise sensitivity analyses. A penalty-based loss function combines structural compliance minimization with mass constraints, driving efficient gradient-based optimization of NN parameters. The structural response is evaluated using the robust MITC4 finite element formulation to accurately model bending and shear deformation in thick-to-thin plate regimes. Through several benchmark examples and aerospace-oriented case studies, the method demonstrates improved structural performance, sharp and manufacturable material interfaces, and reduced computational overhead compared to conventional gradient-free and mesh-based techniques. The presented NN-based MMTO framework thus provides an effective computational tool for designing optimized multi-material structures, particularly suited to advanced engineering applications.