Analysis of laminated composite plates and shallow shells with radial basis functions and QR-stabilized polynomial augmentation

The aim of this paper is to develop and assess a stable strong-form meshless collocation formulation for the static bending and free vibration of laminated composite plates and shallow shells. The formulation is based on the first-order shear deformation theory (FSDT) and uses polyharmonic spline (PHS) radial basis functions with polynomial augmentation. A QR transformation is introduced in the polynomial block to replace raw monomials by an orthonormal basis, thereby improving the conditioning of the augmented interpolation system while preserving the same approximation space. A single five-degree-of-freedom collocation framework is written for laminated shallow shells of constant principal curvature; laminated flat plates and isotropic Mindlin plates are recovered as limiting cases. The novelty of the work is the combination of PHS-based differentiation, QR-stabilized polynomial augmentation, and a unified five-field shallow-shell FSDT operator for laminated composite structures. The method is validated against isotropic plate benchmarks, finite element and analytical plate solutions, exact FSDT Navier solutions for laminated plates and shallow shells, and free-vibration mode shapes. The results demonstrate accurate static and dynamic predictions over thin-to-thick regimes, while also identifying conditioning limits on very fine grids.