An improved meshless collocation method for elastostatic and elastodynamic problems

Abstract Meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. In this paper, an improved meshless collocation method is presented for use with either moving least square (MLS) or compactly supported radial basis functions (RBFs). A new technique referred to as an indirect derivative method is developed and compared with the direct derivative technique used for evaluation of second‐order derivatives and higher‐order derivatives of the MLS and RBF shape functions at the field point. As the derivatives are obtained from a local approximation (MLS or compact support RBFs), the new method is computationally economical and efficient. Neither the connectivity of mesh in the domain/boundary nor integrations with fundamental/particular solutions is required in this approach. The accuracy of the two techniques to determine the second‐order derivative of shape function is assessed. The applications of meshless method to two‐dimensional elastostatic and elastodynamic problems have been presented and comparisons have been made with benchmark analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd.