Structural topology optimization using graph based neural methods
HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization
Machine Learning
Summary
Designing the best shape for a structure to be strong yet lightweight is usually done by tweaking materials and testing repeatedly, which can be slow. This paper introduces a new approach that uses a graph representation of the structure’s mesh to directly model materials and their physical behavior more naturally. The authors show this method can achieve similar quality results with less computing power and works for complex 3D shapes and materials that stretch or deform. This approach combines material layout and structural analysis into a single framework that reflects how elements connect, improving efficiency.
What this means in practice
- •For structural engineers: Create optimized lightweight designs for complex and irregular structures with reduced computational cost.
- •For mechanical design teams: Use a unified graph-based method to efficiently simulate and optimize components undergoing large deformations and plastic behavior.
Authors
Kangzheng Liu, Uday Kumar Punna, Leixin Ma
Abstract
Density-based topology optimization is typically structured as a nested sequence of material updates, structural analyses, and sensitivity assessments. While neural density parameterization and dual-field physics-informed approaches provide data-free alternatives, most existing methods represent density and displacement as coordinate fields and make limited use of the discrete relationships inherent in the finite element mesh. The present study introduces HGTO, a unified graph-based formulation that extends complete neural topology optimization from coordinate space to finite-element graph space. Element densities are parameterized on the element graph derived from the mesh, and the structural state is determined on the corresponding node--element hypergraph. Finite element kinematics, numerical quadrature, constitutive response, and force assembly remain explicitly defined operations within the differentiable computation. The material field and equilibrium state are therefore coupled through a common finite-element incidence structure. Numerical studies show compliance comparable to conventional density-based optimization at substantially lower computational cost than a representative coordinate-based dual-field neural method. The same coupled formulation accommodates high-resolution and irregular meshes, three-dimensional structures, finite deformation, and elastoplastic response.