Meshfree analysis of the vibration behavior of functionally graded graphene origami-enabled auxetic metamaterial plates on a Pasternak foundation under blast loading in a thermal environment

Abstract

This study presents a meshfree computational framework for analyzing the vibration behavior of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) plates resting on a Pasternak foundation and subjected to blast loading in a thermal environment. The work is motivated by the demand for efficient tools to model advanced functionally graded metamaterials, which exhibit complex mechanical responses due to multiphysics coupling and auxetic characteristics. The governing equations of motion are derived using the refined first-order shear deformation theory (r-FSDT) combined with Hamilton’s principle. To solve these equations, a meshfree computational framework based on moving Kriging (MK) interpolation is developed. The proposed framework benefits from the Kronecker delta property, which enables the direct and efficient enforcement of boundary conditions, and further enhances accuracy by eliminating the need for pre-defined correlation parameters. The method is validated against benchmark results from the literature, confirming its accuracy and reliability. A series of simulations is then carried out to systematically explore the influence of the number of layers, temperature, foundation stiffness, boundary conditions, graphene origami (Gori) weight fraction, and Gori distribution patterns on the vibration behavior of FG-GOEAM plates. The findings demonstrate that the proposed method not only improves accuracy compared with conventional finite element method (FEM) and other mesh-based approaches but also provides new insights into the complex interplay among input parameters. These results highlight the feasibility of the proposed framework for optimizing the design and guiding the practical application of FG-GOEAM plates in engineering structures.