An improved Tchebychev-radial point interpolation method for large deformation analysis of hyperelastic model

In this study, an improvement for the Tchebychev-radial point interpolation method (TRPIM) is proposed for the finite deformation analysis of the hyperelastic structure. The TRPIM shape function is developed by integrating the radial basis function with the Tchebychev polynomial basis function instead of traditional polynomial basis functions, and this combination produces a more accurate interpolation. Both the first and second kinds of Tchebychev polynomial are tested and evaluated for the proposed method. The modification revolves around integrating the Cartesian transformation method into the TRPIM approach to make it a truly meshfree method that does not use background cells system for numerical integration. The nonlinear behavior of hyperelastic models (Neo-Hookean, Mooney–Rivlin, and Ogden) under a finite deformation state is simulated with the total Lagrange formulation and standard Newton–Raphson algorithm. To assess the large deformation behavior of two-dimensional hyperelastic problems, a series of numerical tests are carried out. The reliability and performance of the proposed method is confirmed by comparing its results with those of available solutions. • Improved weak-form meshless method via Tchebychev-RPIM and CTM integration • The improved TRPIM is evaluated with the two types of Tchebychev polynomial. • Method applied to nonlinear analysis of Neo-Hookean, Mooney-Rivlin and Ogden models. • Numerical tests evaluate the advantageous aspects of the proposed method.