Element-free Galerkin Method(efgm) And Its Application In The Stability Of Symmetrically Laminated Composite Plates

Elerment-free method is a new numerical method. This dissertation studies in detail the fundamental theories of Element-free Galerkinm method(EFGM)and applies it to bending, buckling of Symmetrically Laminated Composite Plates. Numerical examples show that the method is feasible.The contents of this dissertation can divide into two parts:In the first part, the fundamental theories of Moving Least Square Method (MISM) which is the mathematical basis of EFGM are studied thoroughly. The shape function of EFGM are also deduced. Several hot problems, such as the selection of weight function and basis function, the size of influence radius of nodes, the collocation of boundary condition and the method of integral and implementation etc., are deeply researched.In the second part, this dissertation applied EFGM to solve elastic problem and buckling problem of Symmetrically Laminated Composite Plates. The corresponding stiffness matrix of EFGM is derived using variational principle. The corresponding computer programs are also developed. Comparing the results to FEM results, we can see that the method is reasonable and feasible . At the same time penalty function is applied to enforce the essential boundary conditions in this dissertation. The corresponding energy formulas are derived. Penalty function solves thoroughly the problem which collocation of boundary condition is difficult by EFGM.Research shows that EFGM solving elastic bending problem and buckling problem of Symmetrically Laminated Composite Plates is reasonable and feasible. Numerical examples show that EFGM has the advantage of simple before and after process, high accuracy in solving static and dynamic analysis of plates. In a word, EFGM has a promising prospect in engineering practice.