A new closed-form analytical solution for PFG shells and honeycomb sandwich plates with auxetic cores via the unified formulation and boundary discontinuous Fourier method

This research conducts a static analysis of fully clamped rectangular plates and shells made from porous functionally graded (PFG) materials, and a sandwich part with two isotropic face sheets and an auxetic core, utilizing the Carrera unified formulation (CUF) alongside the boundary-discontinuous Fourier method. The CUF models the displacement field with expansion orders ranging from 1 to 4 through an equivalent single-layer (ESL) approach. PFG material properties follow a power-law distribution across the shell’s thickness and are expressed using Taylor functions. The governing equilibrium equations and boundary conditions are derived using the partial virtual displacements principle and resolved using the boundary-discontinuous Fourier series approach. To validate the results, we compare the results with existing solutions, highlighting the benefits of using variable kinematic models for analyzing PFG shells and honeycomb sandwich plates with auxetic cores. The research investigates how varying porosity distributions, porosity ratios, volume fraction coefficients, radius ratios, and auxetic cell wall angles affect the mechanical properties of these structures. This approach provides a distinctive framework that serves as a reference standard for verifying novel shell theories and finite element models.