A Meshless Method Based On Weighted Least Square

Meshless method is a new numerical method .The method requires only nodes and a description of the external and internal boundaries, and no element connectivity is needed totally or partly.The main idea of this dissertation is , based on moving least square method,the governing equation of boundary value problem is diffused by least square method,no mesh is needed totally.In this paper , firstly ,foundamental theories of moving least square method is studied thoroughly,detailed research is conducted on some key problems,such as the selection of weight function,the selection of influence radius of nodes and the imposition of essential boundary condition,etc ,the shape function is constructed by Moving Least Square method;secondly, the basic formulation of the boundary value problems applied this method is conducted,in which the essential boundary conditions are imposed by the penalty method, we apply it to solve the possion equations and the bending problem of thin plates in different boundary conditions;thirdly ,in contrast to the classic results ,the numerical results of the low-order boundary value problems is very accurate, when the parameters of weight function and the influence radius get proper value ,the numerical results of the high-order problems is satisfying.