Stress Distribution of Rectangular Sandwich Composite Plates under Nonuniform Loading via a Refined Shear–Normal Strain Formulation

A third-order displacement-based formulation is utilized to model transverse shear and normal deformation phenomena in the bending analysis of simply supported square and rectangular sandwich plate structures. The plate is subjected to transverse loading in five forms: sinusoidal, uniformly distributed, linearly varying, concentrated, and parabolic. The kinematics adopt a displacement field in which both in-plane and transverse components vary nonlinearly across the plate thickness. By enforcing zero transverse shear traction on the top and bottom surfaces, the formulation obviates the shear correction factors typically invoked in first-order shear deformation models. The governing equations and boundary conditions are obtained via the virtual work principle, and closed-form solutions are provided for simply supported sandwich plates. Flexural analysis encompasses square and rectangular sandwich plates with different aspect ratios. The complete numerical solution framework is developed using MATLAB software. Validation is performed by cross-checking the present formulation against benchmarks from classical plate theory, first-order shear deformation theory, multiple higher-order shear deformation models, and exact solutions from three-dimensional elasticity wherever available.