Displacement model for meshless method and its application to analysis of fracture problem

The reasonable inner core of Meshless Method (MM) was inherited. However, the theories of Meshless Method have been studied only for a short time, some questions, such as the treatment of essential boundary conditions and too expensive calculation of inverse matrix, restrict the development of meshless method seriously. The essential reasons, from which above questions originated, was studied. Then with the application of the theory of Shepard-interplanting and Taylor-expansion, a new shape function was constructed by means of limited covering technique, So the above questions were overcome successfully, and the problems about structural fracture and rock-soil engineering were analyzed.