Meshfree Weak-strong(MWS) Form Method For Moderately Thick Plates

Meshless methods possess many outstanding adantages over traditional numerical methods such as finite elemet method, boundary element method etc. A lot of the important pioneering effort has been done on meshless methods by scholars in a recent decade, and further investigation into many problems of meshless methods should be made.The mesh free weak-strong (MWS) form method is a new numerical technique presented in the recent years, because it doesn't need any finite element or boundary element meshes. Furthermore, for the most inner nodes it eliminates the numerical integration, it can analyze the problem flexibly and conveniently and is named as"a truly meshless method"with great applied prospect. In recent years, G.R.Liu etc. have successfully applied the MWS into 2-D solids and imcompressible flow problems. On the basis of their work, applications of the MWS method to the moderately thick plates are presented in this dissertation, which enriches theory of the MWS and extends its applications.At the beginning of the dissertation, recent developments of meshless methods are briefly reviewed. Three kinds of meshless methods are proposed based on different models: 1) collation methods; 2) weak form method; 3) weak and strong form method. Characteristics, advantages and disadvantages for a variety of meshless methods are pointed out. Among which, the research and development on meshless methods of plate and shell problems are reviewed in detail. Then, the basic ideas of the mesh free weak-strong (MWS ) method are presented.In the dissertation, the MWS method to the static problem of the moderately thick plates is prosposed. For the nodes on essential boundaries and those nodes whose local quadrature domain does not intersect with the natural boundaries, the strong form is used. Otherwise, the local weak form is used. For the strong form, which eliminates numerical intergration, has high efficiency, and the essential boundary condtion is enforced as simply as FEM. As natural boundary condition is naturally included in the weak form, it doesn't need extra treatment. Through examples with various supported conditions under various loads, the optimal shape and size of the support domain of weighted functions are discussed, and the validity and the feasibility of the MWS method in the solution of the static problem for moderately thick plates are examined. For the dynamic analysis of moderately thick plates, the MWS method is used to discrete the spatial domain as the static problems. The Newmark family of the method is adapted to discrete the time domain, and the subspace interation method is used to analyze the natural vibration problem of plates. Through calculating examples, the free vibration characteristics, the deformation and internal force response under forced vibration are studied.Examples analysed show, not only the boundary value problem but alse the initial proble of moderately thick plates can be effectively solved by the mesh free weak-strong (MWS) form method. A good stability, a high rate of convergence and a reasonable accuracy to both deflection and internal forces can be obtained. Also it can appropriately treat the two types of boundaries. The MWS has all advantages possessed by the other meshfree methods, and without much numerical integration, the MWS has higher efficiency. Compared with the FEM, the MWS constructed high order interpolation more easily, and its coding is simple and easy, and has better versatility and less data preparation. Therefore, the MWS method is an attractive, prospective method in solving the engineering problems.