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

无网格法是一种只利用节点信息而不需要网格单元的方法。这是由于，虽然最近的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，生成分析模型也变得复杂和耗时。无网格方法比有限元方法更容易处理裂纹在模型任意部位扩展等不连续性问题，但目前对无网格方法的研究还局限于基础研究，包括三维分析在内的实际应用研究较少。其中一个原因是无网格方法与有限元方法相比，对弱形式的区域积分没有理想的格式，而且通常需要背景单元，因此，无网格方法与有限元技术相结合的新方法是值得期待的。本研究的目的是发展一种适用于三维膜结构的无网格法，并发展一种无网格法与有限元法的叠加法。最后，针对膜结构的分析，对无网格积分法、索膜摩擦模型和分析方法的系统化进行了研究。其次，介绍了新发展的叠加法，并与传统的无网格法进行了比较，阐明了叠加法的优缺点。

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.