| During the last three decades, a new kind of numerical method which is named meshless method or meshfree method has been developed. The distinct feature of meshfree methods compared to conventional numerical method such as finite element methods is that the new class of numerical methods has been developed which approximates partial differential equations only based on a set of nodes without the need for an additional mesh. Because of the feature, meshfree method can overcome some difficulties which FEM has ever met.A detailed retrospection has been given in this dissertation. The basic theory has been expatiated in depth, and also different meshfree methods have been introduced comprehensively. Based on the large amount of work by the pioneers, a new type of meshfree method has been developed which introduces the generalized node to conventional meshfree methods. So it can be termed generalized-node-based meshfree method (GNBMM). The technique of the generalized node is originated from the manifold method and can be also thought as one of the partition of unity methods. This new method is therefore more general than the traditional meshfree method. And based on GNBMM, the collocation method is used to discrete the system equations, which result in collocation type GNBMM. The system formulation obtained by collocation method can be more simply than which obtained by Galerkin method. It can be considered a true meshfree method, because of that no background cells are needed. And also, if higher generalized node interpolation functions are used, it can overcome the intrinsic flaw of collocation method.And in this dissertation, the developed methods are applied to elastic problems, elastic-plastic problems, consolidation problems, material discontinuous problems, and so on. The results obtained from the developed methods are in good accordance with the analysis method or FEM, which means that the developed method is effective and feasible.
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