A Chebyshev Moving Kriging Meshless Approach for Buckling Analysis of Multilayer Composite Plates

This paper proposes a new and robust numerical framework for the buckling analysis of multilayer composite plates by integrating the Chebyshev Moving Kriging (CMK) meshfree method with a Third-Order Chebyshev Shear Deformation Theory (TCSDT). The novelty of this study lies in the combined use of Chebyshev polynomials for both interpolation and shear deformation modeling. The TCSDT inherently satisfies the zero-traction boundary condition, thereby eliminating the need for shear correction factors, while the orthogonality and fast convergence of Chebyshev polynomials enhance numerical stability and accuracy compared to traditional polynomial formulations. The governing equations are systematically derived using the principle of virtual work, and the critical buckling loads are obtained through the CMK scheme. Benchmark studies demonstrate that the proposed method not only reproduces results from three-dimensional elasticity theory and established higher-order models with excellent accuracy but also offers improved robustness and efficiency. The findings confirm that the CMK–TCSDT framework provides a reliable and efficient computational tool for analyzing the buckling behavior of laminated composite structures.