Neural Co-Optimization of Structural Topology, Manufacturable Layers, and Path Orientations for Fiber-Reinforced Composites

TL;DR

This work presents a neural co-optimization framework that jointly optimizes structural topology, curved manufacturing layers, and fiber orientations for fiber-reinforced composites using three implicit neural fields. By embedding strength-based Hoffman criteria and manufacturability constraints as differentiable losses, the approach yields designs that achieve higher failure loads while remaining fabricable on multi-axis filament printers. The method supports varying motion degrees of freedom (5-axis, 3-axis, 2.5-axis) and demonstrates up to 33.1% improvement in measured failure loads over sequential optimization in physical tests. Extensive computational experiments, ablations, and physical fabrication validate the effectiveness of co-optimization in balancing mechanical performance with manufacturing feasibility. The framework is general, extensible to shape control, and highlights key trade-offs between stiffness-based and strength-based design in anisotropic, additively manufactured composites.

Abstract

We propose a neural network-based computational framework for the simultaneous optimization of structural topology, curved layers, and path orientations to achieve strong anisotropic strength in fiber-reinforced thermoplastic composites while ensuring manufacturability. Our framework employs three implicit neural fields to represent geometric shape, layer sequence, and fiber orientation. This enables the direct formulation of both design and manufacturability objectives - such as anisotropic strength, structural volume, machine motion control, layer curvature, and layer thickness - into an integrated and differentiable optimization process. By incorporating these objectives as loss functions, the framework ensures that the resultant composites exhibit optimized mechanical strength while remaining its manufacturability for filament-based multi-axis 3D printing across diverse hardware platforms. Physical experiments demonstrate that the composites generated by our co-optimization method can achieve an improvement of up to 33.1% in failure loads compared to composites with sequentially optimized structures and manufacturing sequences.

Figures (18)

• Figure 1: Strong anisotropic mechanical properties can be observed on specimens fabricated by filament-based 3D printing. In our tests, Young's modulus, tensile strength, compression strength, and shearing strength are measured by using the ASTM standards of E111, D638, D695, and D5379 respectively.
• Figure 2: The planar case with the tensile strengths $(X_t, Y_t)$ and the compression strengths $(X_c, Y_c)$ is employed to illustrate the Hoffman criterion ellipsoid. Re-orienting the anisotropic material effectively rotates the Hoffman criterion ellipsoid to enclose the yield point $\boldsymbol{\sigma}_{d}$, thereby preventing material failure under the given stress.
• Figure 3: An example of MBB beam with dimensions as $135 \times 45 \times 45 \, \text{mm} (w \times h \times d)$ having its structural topology optimized by the Hoffman criterion for strength (top row) and the compliance energy for stiffness (bottom row) -- both having manufacturability constraints incorporated and a target volume fraction of $25\%$. From left to right, the layers for multi-axis 3D printing, the failure index distribution $\Gamma(\cdot)$ and the strain energy distribution.
• Figure 4: Our computational pipeline for co-optimizing structural topology and manufacturing sequences employs a neural network-based representation. Structural solids, manufacturing layers (as the printing sequence), and fiber orientations (as the printing path direction) are represented by the density field $\rho(\mathbf{x},\theta_\rho)$, the material deposition field $m(\mathbf{x},\theta_m)$ and the auxiliary field $a(\mathbf{x},\theta_a)$ together. The network coefficients $\theta_\rho$, $\theta_m$ and $\theta_a$ serve as design variables and are optimized using backpropagation to minimize loss functions defined according to both design and manufacturing objectives, where the anisotropic FEA is employed to evaluate the mechanical performance for design objectives.
• Figure 5: Illustrations of curvature based evaluations. (a) For a point $\mathbf{x}$ on the implicit surface defined by $m(\mathbf{x})=c_i$, whether there is local collision can be evaluated by the maximal curvature $K_{\max}$. Note that directions of the minimum curvature $\boldsymbol{\kappa}_{min}$ and the maximum curvature $\boldsymbol{\kappa}_{max}$ are specified by arrows. (b) The abrupt tool orientation change is prevented by controlling the curvature along the fiber-path direction $\mathbf{f}(\mathbf{x})$, denoted by $K_f$.