Graph neural network-based surrogate models for thin-walled structural analysis with application to ship hull structures

Abstract

Iterative structural design and optimization of ship hulls at the early design stage require many structural analysis evaluations. Finite element analysis (FEA) is the standard tool for evaluating stress and displacement fields, but it is computationally prohibitive at the scale required by design optimization. Existing surrogate models often rely on fixed-dimensional inputs or problem-specific encodings, making them difficult to reuse across stiffened panels and hull girder configurations with varying geometry, boundary kinematics, and loading. This thesis develops a series of graph neural network (GNN)-based surrogate models that bridge this gap, enabling fast and accurate structural analysis suitable for early stage design. The thesis builds the surrogate framework along four progressive steps. A structural unit-based graph representation is introduced to encode stiffened panels with varying geometry and stiffener layouts as homogeneous graphs. This representation is then extended to a heterogeneous graph representation that separates structural geometry, boundary kinematics, and loading into distinct node types and relation types, so that stiffened panels under spatially non-uniform boundary kinematics and loads can be effectively modeled. To bridge the panel-level surrogate model to ship hull structural analysis, a hybrid global–local framework couples the local GNN surrogate model with a coarse-mesh equivalent single-layer (ESL) global model through boundary degree-of-freedom reconstruction, so that global hull girder response and local panel fields can be predicted together. Finally, a physics-guided dual-stream heterogeneous graph neural network (DS-HGNN) introduces structural mechanics into the network architecture to improve local surrogate model accuracy and training-data efficiency. Overall, the proposed models connect panel-scale GNN surrogates with global–local hull girder analysis. The graph representations encode panels with varying geometry, stiffener layouts, boundary kinematics, and loading. The hybrid framework transfers the global hull girder response to local panels through recovered boundary kinematics, reducing repeated detailed local finite element analyses. The physics-guided DS-HGNN improves local prediction accuracy with less finite element training data. Together, these models support efficient stress and displacement field prediction for early-stage ship hull structural design optimization.