Chebyshev polynomials in moving Kriging meshfree method for laminated composite plates

Abstract

We propose a new shape function for a meshfree method by combining of moving Kriging (MK) and Chebyshev interpolations, referred to Chebyshev moving Kriging (CMK) interpolations. This approach improves the accuracy of the numerical solutions by using Chebyshev polynomials in place of traditional polynomials. Additionally, Chebyshev polynomials are utilized to represent a higher-order shear deformation theory (HSDT), called the Chebyshev shear deformation theory (CSDT). A key advantage of the CSDT is its ability to automatically satisfy the condition of zero shear stress at both the top and bottom of the plate. This study introduces an integration of the CMK meshfree method and the CSDT to investigate the static and free vibration characteristics of laminated composite plates. Furthermore, the virtual work principle is exploited to derive the weak forms of the governing equations for laminated composite plates. The CMK meshfree method is then used to compute the displacements and natural frequencies. Numerical simulations are conducted to assess the impacts of geometric parameters, boundary conditions, length-to-thickness ratios, and fibre orientation angles on the displacements and natural frequencies of laminated composite plates. The accuracy of the numerical solutions is assessed by comparing them with the results from 3D elasticity and other shear deformation theories.