Analysis Of Stability Of Composite Laminates Plates Based On Meshfree Local Petrov-Galerkin Method

Because of its mesh-dependency the finite element method(FEM) is known to have difficulties in solving the problems with large deformation and moving boundaries.Some well-developed Meshfree Galerkin methods,such as EFG and RKPM,can solve such problems,but they need background cells to conduct numerical integration,and are inefficient in solving large-scale problems.The Meshfree local Petrov-Galerkin(MLPG) method has the advantages of "truly Meshfree",high efficiency and accuracy.In this paper some numerical schemes for stability of composite laminates are presented in the frame of MLPG and verified by numerical examples.The main contributions are:At the beginning of the dissertation,recent developments of Meshfree methods are briefly reviewed.All kinds of Meshfree methods are reviewed and commented. Characteristics,advantages and disadvantages for a variety of Meshfree methods are pointed out.Among them,the research and development on Meshfree methods of plate and shell problems are reviewed in detail.In the dissertation,the MLPG method to the stability of the composite laminates is proposed.The symmetric weak forms of the equivalent integration equations to the governing differential equations for the composite laminates in local subdomains are formulated by the weighted residual method(WRM).The deflection is interpolated by using the moving least squares(MLS) approximation.All integrals are carried out in subdomains and their boundaries with a regular shape.For the moving least square approximation does not possess properties of the Kronecker-delta function,the essential boundary condition can not be enforced directly,and the penalty method is used to imposed on the essential boundary condition.The validity and feasibility of the MLPG method in the solution of the stability problem for composite laminates are examined.