This book contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures,...

The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past...

This updated second edition provide a thorough introduction to the latest methods for solving engineering problems. These methods move beyond finite difference and finite element methods, which have inherent limitations in flexibility, effectiveness, and speed when applied to present-day complex engineering analysis. This edition presents the latest developments in the field, including X-FEM, crack tip enrichment, gradient smoothing methods (GSM), and other specific technologies. The programming code found in the final chapter has also been updated.