Mechanics-Informed Non-Dimensionalisation and Physics-Constrained Neural Surrogates for the Buckling of Laminated Composite Plates, with Independent Cross-Ply External Validation

Buckling governs the design of thin laminated composite plates, yet parametric finite-element (FE) exploration of the design space is computationally expensive. Machine learning surrogates reduce this computational cost, but are usually judged on predictive accuracy alone, not on whether the learned response respects known invariances and classical theory bounds. This work treats accuracy, invariance, analytical compliance, and external generalization as distinct properties. A layered-shell FE model is verified against the exact closed-form solution of classical laminated plate theory, reproducing the benchmark critical load to within 0.0237% and the first five eigenvalues to within 0.226%. A 500-case Latin hypercube campaign spans ply orientation, thickness, and longitudinal modulus from 25 to 250 GPa. Mechanics-informed features help only when paired with a non-dimensional target, cutting the hold-out relative error to 1.625%. Four backbone-matched networks with graded constraints are compared over twenty seeds. Statistical feature importance does not establish pointwise invariance, and soft penalties leave criterion compliance uncertified. On 120 cross-ply configurations generated after model freezing, the soft-constrained network transfers best (coefficient of determination 0.9605, relative error 1.638%) and the bounded network satisfies the criterion for all 2400 predictions. On cross-ply laminates, the exact closed form outperforms every surrogate; thus, the surrogates target anisotropic layups that have none.