A novel PD-HSDT application for the mechanical response of laminated and sandwich composite plates under static loading

This study presents a PD-HSDT formulation that combines Higher-Order Shear Deformation Theory (HSDT) with the Peridynamic Differential Operator (PDDO) for the static analysis of laminated and sandwich composite plates. Accurate analysis of such composites is challenging due to layered anisotropy and sensitivity to bending-induced stresses. The PDDO reformulates local spatial derivatives as nonlocal integral expressions, facilitating the numerical treatment of higher-order field equations. When coupled with HSDT, which is applicable to both thin and thick plates, the proposed framework enables a nonlocal, meshless treatment of higher-order derivatives and allows direct modeling of complex bending behavior and discontinuities. HSDT captures transverse shear deformation and cross-sectional warping without requiring shear correction factors. The governing equations and boundary conditions are derived using the principle of virtual work and solved using the PDDO framework. Numerical examples for plates with various aspect ratios and laminate configurations, including cross-ply, angle-ply, and sandwich structures with different face stiffnesses, are presented. The computed displacement and stress fields show close agreement with exact and benchmark solutions, with accurate representation of transverse shear effects. The formulation provides a basis for extension to more complex loading conditions and damage analyses.