A Meshfree Tchebychev Radial Point Interpolation Method (TRPIM) for thermo-elastic analysis in two-dimensional Functionally Graded Materials

Abstract In recent years, various meshfree methods have been developed to improve accuracy and flexibility in solving thermo-elastic problems. Among these, the Tchebychev Point Interpolation Method (TPIM) and the Tchebychev–Radial Point Interpolation Method (TRPIM) are notable extensions of the traditional Point Interpolation Method (PIM). This paper presents a meshfree weak-form formulation of TRPIM for solving two-dimensional thermo-elastic problems in Functionally Graded Materials (FGMs). Unlike the conventional Radial Point Interpolation Method (RPIM), which employs basic polynomial basis functions, TRPIM enriches the approximation space with Chebyshev polynomials, thereby reducing the Runge phenomenon, achieving spectral-like accuracy, and improving numerical stability. The proposed method is applied to various FGM thermo-elastic problems, including FG plates and two types of hollow FGM cylinders. Numerical results show that TRPIM can accurately compute stress, temperature fields, and deformation characteristics. Comparisons with reference solutions indicate very small errors, clearly demonstrating the improved accuracy and robustness of the proposed approach over conventional RPIM methods.