ABSTRACT
A series of meshless methods for analysis have been introduced in the literature, mostly in the late 1990s. The development of these methods may have been motivated by the shortcomings arising in the difficulty of use of the finite element methods by analysts. Some of the shortcomings were outlined in Section 6.1. Methods in the category of meshless methods include smooth particle hydrodynamics (SPH) (Swegle et al., 1994), the element-free Galerkin (EFG) method (Belytschko et al., 1994a; Lu et al., 1994), reproducing kernel particle methods (RKPMs) (Liu, 1995; Liu and Chen, 1995; Liu et al., 1996), partition of unity methods (Melenk and Babuska, 1996), h-p clouds (Duarte and Oden, 1996), the meshless local Petrov–Galerkin (MLPG) method (Atluri, 2004; Atluri and Zhu, 1998, 2000a), the natural element method (Sukumar et al., 1998), the natural neighbor Galerkin methods (Sukumar et al., 2001), and the method of finite spheres (De and Bathe, 2000, 2001). Except for the SPH methods, these methods are all based, in principle, on the finite element method. Several additional meshless methods based on the boundary element method have also been proposed. These include boundary contour methods (Mukherjee et al., 1997; Nagarajan et al., 1994, 1996), the boundary node method (Mukherjee and Mukherjee, 1997a; Chati and Mukherjee, 2000; Chati et al., 1999), and the local boundary integral equation method (Atluri et al., 2000). Most of these methods are of recent origin and are still undergoing development. Some applications of meshless methods in modeling life-cycle engineering appeared in a book by Chong et al. (2002). A popular meshless method is the EFG method. It has been developed largely in the context of elastostatics. Chapters 4 and 6 have both been presented for use in elastostatics analysis. Continuing in that vein, the EFG method is also presented in this chapter for linear elastic analysis of solid bodies.
