A new hybrid boundary node method based on taylor expansion and the shepard interpolation method

Abstract

Summary: A novel meshless method based on the Shepard and Taylor interpolation method (STIM) and the hybrid boundary node method (HBNM) is proposed. Based on the Shepard interpolation method and Taylor expansion, the STIM is developed to construct the shape function of the HBNM. In the STIM, the Shepard shape function is used as the basic function, which is the zero-level shape function, and the high-power basic functions are constructed through Taylor expansion. Four advantages of the STIM are the interpolation property, the arbitrarily high-order consistency, the absence of inversion for the whole process of shape function construction, and the low computational expense. These properties are desirable in the implementation of meshless methods. By combining the STIM and the HBNM, a much more effective meshless method is proposed to solve the elasticity problems. Compared with the traditional HBNM, the STIM can improve accuracy because of the use of high-power basic functions and can also improve the computational efficiency because there is no inversion for the shape function construction process. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method.