Free Vibration, Buckling, and Static Analysis of Sandwich Panels with a Square Honeycomb Core Using a Meshfree Method

Meshless methods are a relatively modern approach that has garnered significant interest in analyzing and investigating complex structural problems thanks to distinctive features such as high accuracy, flexibility, rapid calculation speed, and cost–effectiveness. In the present study, the element-free Galerkin method is employed as a meshless approach, wherein a set of arbitrary nodes is distributed across the problem’s geometry, including its boundaries, to define the problem domain. The Moving Least Squares approximation is also utilized to formulate the shape functions. Given the intricate geometry of the honeycomb core within sandwich panels, the study employs the generalized method to derive the effective mechanical properties of the honeycomb core. Furthermore, to acquire displacement fields and establish relationships for the problem, the classic plate theory and the first-order shear deformation theory are independently applied. These relationships are then formulated using the Galerkin meshless method. Finally, the obtained parameters are evaluated, and the validity of these relationships is confirmed by comparing the results of this study with those presented in existing articles. The outlined procedure has been systematically simulated through a step-by-step MATLAB program. Subsequently, the impact of different boundary conditions, individual layer thicknesses, dimension ratios, and core wall spacing on the panel’s displacement, free-vibration, and buckling behaviors is thoroughly investigated. The obtained results substantiate the efficacy of the utilized methodology, demonstrating a favorable combination of accuracy and convergence rate.