Research On Adaptive Method Coupling Meshless Method And Finite Element For Distortion Elements Of Plates And Shells

The finite element method (FEM) has been the most popular tool which is widely commercialized for solving plate and shell problems. Due to too large deformation of material or the contact between blank and tools or inhomogeneous material flow for large deformation of plates and shells, such as sheet metal forming and crash problems, local high gradient region of stress can be introduced, the mesh distortions will be resulted from excssive deformation during FEM analysis, and subsequent incremental analysis has to be conducted based on meshes of inferior quality, which can lost considerable accuracy, furthermore, cause no convergence for solving because of severe element distortions.The meshless local Petrov-Galerkin (MLPG) method can avoid the computational difficulty caused by mesh distortions and is suitable for large deformation and adaptive analysis, but its computational efficiency is rather low with comparison to that of FEM. Based on localization and high gradient of distortional elements, the adaptive method, which converts the FEM analysis into the meshless computation to preserve the accuracy in the region where meshes have been distorted and still employs the FE method to ensure high computational efficiency in the region where the quality of the FE meshes is acceptable, has been proposed. The main content of this thesis can be summarized as following:1.The weighted residual method with compactly supported trial functions is summarized as the theoretical basis of the meshless method, and then the basic principles of the MLPG method is discussed in detail. Algorithms determining the nodal support domain and searching the coverage nodes are presented. The penalty factor imposing the essential boundary conditions is proposed.2.The meshless representation of the field variables for plates and shells is established based on moving least square (MLS) method, and then the MLPG method of Mindlin plates and shells for small deformation is presented. Numerical investigation shows the size of quadrature domain plays the greatest effect on the computational precision and the optimal combination of the impact parameters is given.3. An h-adaptive MLPG method is presented by the two-scale decomposition of field variables based on multi-resolution analysis. Based on multi-resolution analysis from B spline wavelets, the two scale decomposition technology of field variables is established, by which field variables can be decomposed into high and low scales and the high scale component can commonly represent the gradient of solution according to inherent characteristic of wavelets, and then the extremum detection technology of the wavelet theory is applied to implement an algorithm searching high gradient nodes. Finally, an h-adaptive MLPG method is presented without posterior estimation, an extra process needed in FEM analysis. 4. According to the basic ideas of the MLPG method, updated- Lagrange principles are applied to establish the MLPG equations of plates and shells for large deformation and the solving procedure is implemented.5. Finally, the adaptive method coupling FE and MLPG method for plates and shells is presented. In order to give full play to their advantages of MLPG and FEM method, by constructing interface elements in the interface zone between the FE regions and the meshless regions, the adaptive algorithm has been proposed to convert FEM analysis to meshless approximation for the region where meshes are distorted, and then the coupling method of MLPG-FEM for plates and shells is implemented. Numerical examples show that the present method exploits the respective advantages of both FEM whose computational efficiency is rather high and meshless methods which is suitable for large deformation and adaptive analysis and can eliminate computational difficulty caused by mesh distortions.Based on the existing research achievements and practical experiences, this dissertation achieves some creativity work that focused on the coupling method of MLPG-FEM analysis of plates and shells:1. The MLPG method of Mindlin plates and shells is presented. Parameters impacting on the computational precision are discussed in detail and their optimal combination is proposed.2. Based on the multi-resolution characteristic of the B spline wavelets, the two scale decomposition technology of field variables is established and then an h-adaptive MLPG method is presented without posterior estimation.3. By constructing interface elements in the interface zone between the FEM regions and the meshless regions, the adaptive algorithm is presented which converts FEM into meshless analysis for the region where meshes are distorted, and then the coupling method of MLPG-FEM for plates and shells is implemented.