Application Of Meshless Method To Calculation Of Plates And Shells

Element-free Galerkin method(EFGM), similar to Finite element method, is a new numerical method developed recently. In EFGM, in order to get a numerical solution for a partial diferential equation, the shape function is constructed by moving least squares (MLS), the control equation is derived from the weak form of variational equation and essential boundary conditions are imposed by penalty function method. The advantages of EFGM are: (1) only nodal datas are necessary, i. e. there is no need to join nodes into elements; (2) high accuracy can be achieved:(3)postprocess is easy, etc.The mathematical basis of EFGM is moving least squares method. To use MLS it is only necessary to construct an array of nodes in the domain under consideration Just because of this, EFGM is completely free. Moving least squares interpolants do not pass through the data because the interpolation functions are not equal to unity the nodes unless the weight functions are singular. This is of disadvantage in EFGM for it complicates the imposition of essential boundary conditions and the application of point loads. However, these disadvantages are heavily outweighted by its advantages.In the calculation of bending plates, penalty parameters are introduced to satisfy the essential boundary conditions in this dissertation. In the light of the theory of Reissner-Mindlin plate, the governing equations of meshless method are derived for problems of bending plates. The proposed method can be applied to both the thick and thin plates and good results canbe obtained with a few nodes.Finally, the implementation of the element free Galerkin method(EFG) for spatial thin shell structures is presented in this paper. Basesing on the shell theory under orthogonal curvilinear coordinate system, moving least squares approximation is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approxi -mation of general spatial shell geometry. Discrete system equations are obtained by incorporating these interpolations into the Galerkin weak form. This is a new calculation method. Then the corresponding computer program is developed and several examples are given. The EFG results compare favorably with closed-form solutions and that of finite element analyses.