Research on Nonlinear Superposition Meshfree Analysis for Detection of Moving Discontinuous Surface

最近，人们开始关注所谓的无网格方法，这种方法只利用节点信息，不需要单元或网格。这是因为，尽管近年来计算机技术的快速发展使我们能够分析更复杂的有限元模型，但分析模型的生成也变得复杂和耗时。此外，无网格方法可以很容易地处理不连续性，如裂纹在模型任意部分的扩展，而不是有限元方法，但无网格方法的研究仍然局限于基础性研究，包括三维分析在内的实用研究很少。原因之一是与有限元方法相比，无网格方法对于弱形式的区域积分没有理想的格式，通常需要背景单元。因此，无网格方法和有限元技术相结合的新方法是被期待的。从这些角度出发，本研究的目的是发展一种实用的三维膜结构的无网格方法，并发展一种无网格方法和有限元方法的叠加法。最后，对膜结构分析中的无网格积分、索膜摩擦模型和分析方法的系统化进行了研究。其次，介绍了叠加法的最新发展，阐明了叠加法与传统无网格法的优缺点。

Recently an attention is paid on so-called Meshfree methods, which utilize the only nodal information and require no elements or grids. It is due to that although the recent rapid progress of computer technology enables us to analyze more complicated finite element model, generating analyses model also becomes complicated and time consuming. Furthermore, meshfree methods can easily handle discontinuity, such as crack propagating in the arbitrary part of the model rather than the finite element method.However, the research regarding meshfree methods is still limited to the fundamental study and there are few practical researches including three-dimensional analyses. One of the reason is that comparing with the finite element methods, the meshfree methods have no ideal scheme for the domain integration of weak form and usually require background cells for it. Therefore the new method combining meshfree methods with the finite element techniques is anticipated.From these points of view, the purposes of this study are to develop a practical meshfree method for 3-dimensional membrane structures and to develop a superposition method of the meshfree and the finite element method. Finally, for the analyses of membrane structures, the meshfree integration, the friction model of cable and membrane and systemization of the analyses method are investigated. Secondly, the superposition method is newly developed and clarifies the advantages and disadvantages comparing with the conventional meshfree methods.