A hybrid rigid-compliant computational framework for large-scale assembly: Integrating torsor kinematics with physics-informed graph learning

Accurate prediction of geometric and deformation-induced deviations in large-scale structural systems is essential for ensuring structural performance, serviceability, and assembly integrity. However, real-time Digital Twin (DT) applications are hindered by the computational latency of high-fidelity finite element analyses (FEA), particularly for structures involving bilateral supports and over-constrained kinematic configurations. Unlike conventional serial assembly chains, bilateral support structures present a statically indeterminate problem where the final assembled state cannot be resolved by rigid-body kinematics alone; it is fundamentally governed by the compliance of the structural components. To address this kinematic-physical coupling challenge, this study develops a hybrid rigid–compliant computational framework that unifies torsor-based structural kinematics with a physics-informed graph neural surrogate. A Bayesian-Optimized Physics-Informed Graph Neural Network (BMO-PIGNN) is proposed to learn static equilibrium on optimized mesh graphs, enabling real-time prediction of compliance-induced deformation fields at FEA-level fidelity. Complementing this, a Type-II Parallel Assembly Deviation Analysis Method (T2PADAM) is formulated to resolve the kinematic closure of statically indeterminate bilateral support systems using Small Displacement Torsor (SDT) theory. The two modules are integrated through a unified Jacobian–Torsor–Skin model, producing real-time predictions of functional geometric requirements. Validation on an industrial-scale support frame demonstrates that the proposed framework achieves a three-order-of-magnitude speed-up over FEA while maintaining R²> 0.99 accuracy. These results highlight a rigorous and efficient pathway for real-time structural DTs, providing new capabilities for deformation-aware assembly, tolerance verification, and performance-focused structural design.