Nonlinear Analysis of Corrugated Core Sandwich Plates Using the Element-Free Galerkin Method

This paper presents a meshless Galerkin method for analyzing the nonlinear behavior of corrugated sandwich plates. A corrugated sandwich plate is a composite structure comprising two flat face sheets and a corrugated core, which can be approximated as an orthotropic anisotropic plate with distinct elastic properties in two perpendicular directions. The formulation is based on the first-order shear deformation theory (FSDT), where the shape functions are constructed using the moving least-square (MLS) approximation. Nonlinear stress and strain expressions are derived according to von Kármán’s large deflection theory. The virtual strain energy functionals of the individual plates are established, and their nonlinear equilibrium equations are formulated using the principle of virtual work. The governing equations for the entire corrugated sandwich structure are obtained by incorporating boundary conditions and displacement continuity constraints. A Newton–Raphson iterative scheme is employed to solve the nonlinear equilibrium equations. The computational program is implemented in C++, and extensive numerical examples are analyzed. The accuracy and reliability of the proposed method are validated through comparisons with ANSYS finite element solutions using SHELL181 elements. The method used in this paper can avoid the problems of mesh reconstruction and mesh distortion in the finite element method. In practical application, it simplifies the simulation calculation and understands the mechanical behavior of sandwich plates closer to actual engineering practice.