A hybrid global local computational framework for ship hull structural analysis using homogenized model and graph neural network

Technical Summary: A Hybrid Global-Local Computational Framework for Ship Hull Structural Analysis

Problem Statement
Ship hull structural analysis traditionally faces a trade-off between computational efficiency and local accuracy. High-fidelity 3D finite element models (FEM) provide detailed stress and displacement fields but are computationally prohibitive for iterative design optimization. Conversely, equivalent single layer (ESL) models offer rapid global predictions but often lack the resolution to accurately capture detailed local stress concentrations within stiffened panels. This study addresses the need for a framework that efficiently predicts global structural behavior while simultaneously recovering high-fidelity local responses for any panel within the hull girder.

Methodology
The proposed framework integrates a coarse-mesh homogenized ESL model with a Graph Neural Network (GNN), specifically a Heterogeneous Graph Transformer (HGT), to bridge global and local scales. The methodology proceeds through three distinct stages:

1. Global Analysis: A coarse mesh homogenized ESL model is employed to efficiently predict the global displacement field of the ship hull girder.
2. Boundary Reconstruction: Degrees of freedom (DOFs) are extracted from the boundaries of stiffened panels within the global model. A specific global-to-local DOF mapping and reconstruction procedure is developed to recover detailed boundary kinematics, effectively translating the coarse global solution into precise boundary conditions for local analysis.
3. Local Prediction via HGT: The reconstructed boundary DOFs, combined with panel geometry and loading conditions, serve as inputs to a Heterogeneous Graph Transformer (HGT). This GNN subtype is trained on a dataset generated from high-fidelity 3D panel finite element models that utilize the reconstructed boundary conditions. Once trained, the HGT generalizes across varying panel geometries, loadings, and boundary behaviors to rapidly predict detailed stress and displacement fields for any panel in the hull.

Key Contributions

• Hybrid Architecture: The development of a computational framework that couples a physics-based homogenized ESL model with a data-driven HGT, enabling a seamless transition from global structural assessment to local stress analysis.
• DOF Mapping and Reconstruction: The formulation of a procedure to extract and reconstruct boundary kinematics from a coarse global mesh, ensuring that the local GNN receives accurate boundary conditions derived from the global solution.
• Generalizable GNN Model: The training of an HGT capable of handling heterogeneous inputs (geometry, loading, boundary conditions) to predict local responses without requiring re-meshing or re-solving of high-fidelity 3D models for every new scenario.

Results
The framework was validated using three box beam case studies. The results indicate that:

• The accuracy of the global prediction is governed primarily by the resolution of the coarse mesh ESL solution.
• The HGT component maintains high accuracy in predicting local stress and displacement fields.
• The proposed framework clearly outperforms conventional ESL-based stress estimation methods in terms of local accuracy.
• Once the HGT is trained, the framework requires only the global ESL solution to generate detailed local responses, significantly reducing computational overhead.

Significance
The paper claims that this framework is highly suitable for structural optimization tasks. By decoupling the computationally expensive high-fidelity local analysis from the iterative design process, the method allows for the rapid generation of detailed local responses based solely on global solutions. This capability addresses the bottleneck in ship hull optimization where detailed local stress checks are typically required but computationally costly to perform repeatedly.