Research On Key Technologies For Numerical Simulation Of Large Deformation Of Plates And Shells Based On Meshless Method

While FEM is applied to simulate forming of body panels and high speed impact, if the local emerges large deformation, mesh may be serious distortion, so it will reduce the accuracy of the simulation analysis and even make computation stop. As a new numerical method, Meshless method provides a new channel to solve this problem. Meshless method constructs shape functions strictly based on nodes, partially or completely separates from the grid, and residual grid is only used for the integral, so it is suitable for large deformation analysis. Based on Element Free Galerkin method, numerical simulation of the large shell deformation is presented in the dissertation.Firstly, the current research status of both at home and abroad is overviewed. Combined with shortcoming of FEM about large deformation, corresponding advantages of meshless methods are described, and the basic idea is established, which is related to simulate large deformation by Element Free Galerkin method.Secondly, the basic principle of EFGM is elaborated. By the application of KD tree combined with the domain search algorithm, the method of quick searching node is bulided, which improves the efficiency of the nodes search. The finite element background mesh is established through the use of finite element analysis software to obtain the node and grid information, and then use it for numerical integration. Through the penalty function method, the essential boundary has been resolved.Thirdly, the knowledge of the elastic-plastic finite element deformation and updated Lagrange description method are described. By the above ideas, combined with EFGM, solving equations of large deformation about shell and plane are deduced. In order to establish the mapping between the space node and two-dimensional node, a neutral-surface node parameterization method based on Mindlin shell theory is found.Finally, some key factors affecting calculation accuracy of the meshless method are presented. By studying the calculation example, the optimal applied scopes are obtained, and thus the calculation accuracy is improved. So as to verify the solving precision, solving equations of the meshless method are used in practical examples about large deformation.