Application Of Meshless Method To Calculation Of Reinforced Concrete Plates

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.The paper systematically introduces present development of Element Free Method and the basic theory of EFGM, and mainly describes the equation by which the Moving least square(MLS) is approximately used to deduce EFGM, meanwhile, deduces the EFGM stiffness matrix of bending plates .the calculation shows that this method is feasible in practice .