Comparative analysis of sandwich panel resultants under varying ply orientations using mathematica

This study presents a unified computational framework for analyzing the influence of ply orientation on the in-plane force and bending moment resultants of three-layered functionally graded sandwich panels with a soft porous core. The face sheets comprise laminated SiC-Al plies with continuous axial gradation governed by a powerlaw distribution, with effective properties estimated through the Voigt rule of mixtures. The core elastic behaviour is characterized by a closed-cell foam porosity model governed by a non-dimensional porosity coefficient. Each ply is modelled as a linear elastic orthotropic continuum under plane stress, with laminate-level stiffness matrices assembled following Classical Laminate Plate Theory, while the full sandwich assembly is governed by Higher-Order Shear Deformation Theory to capture transverse shear deformation in the compliant core. Complete trigonometric expansions rigorously satisfy natural boundary conditions at all plate edges. Four representative stacking sequences-Distinct, quasi-isotropic, symmetric balanced, and antisymmetric-are systematically examined to establish laminate architecture as an independent structural design parameter. The framework enables quantitative identification of global stress resultant extrema and their spatial distributions, providing a theoretical basis for performance-based design of porous-core FGM sandwich panels in aerospace, automotive, and civil engineering applications.