Multiscale topology optimization of functionally graded lattice structures based on physics-augmented neural network material models
arXiv:2408.00510 · doi:10.1016/j.cma.2025.117808
Abstract
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization problem falls into the class of NP-complete mixed-integer nonlinear programming problems. To tackle this difficulty, we obtain a relaxed problem from a multiplicative split of the relative density and a penalization approach. The sensitivities of the objective function are derived such that any gradient-based solver might be applied for the iterative update of the design variables. In a next step, we introduce a material model that is parametric in the design variables of interest and suitable to describe the isotropic deformation behavior of quasi-stochastic lattices. For that, we derive and implement further physical constraints and enhance a physics-augmented neural network from the literature that was formulated initially for rhombic materials. Finally, to illustrate the applicability of the method, we incorporate the material model into our computational framework and exemplary optimize two-and three-dimensional benchmark structures as well as a complex aircraft component.
References in corpus (7)
- A new family of Constitutive Artificial Neural Networks towards automated model discovery
- Learning Constitutive Relations using Symmetric Positive Definite Neural Networks
- Neural networks meet hyperelasticity: A guide to enforcing physics
- Physics-Informed Neural Networks for Shell Structures
- A comparative study on different neural network architectures to model inelasticity
- Finite electro-elasticity with physics-augmented neural networks
- Neural Network Layers for Prediction of Positive Definite Elastic Stiffness Tensors