The Complex Variable Meshless Local Petrov-Galerkin Method For Thin Plate Bending Problems

The meshless method is a numerical simulation method developed in recent years for solving partial differential equations.Compared with the traditional finite element method,the structure of the trial function does not require a mesh,only the node information is required,and the calculation accuracy is high.It has become one of the research hotspots in the field of computational mechanics,and it is also the trend of scientific and engineering computing development.The meshless local Petrov-Galerkin method is one of the most widely studied meshless methods.The most important feature is that no matter whether it is constructing approximation function or numerical integration,no mesh is needed.It is a true meshless method.In this paper,the meshless local Petrov-Galerkin method has many problems such as too many points,large amount of calculation,and easy generation of ill-conditioned equations.In this paper,The complex variable moving least squares method is introduced into the meshless local Petrov-Galerkin method to establish the complex variable meshless local Petrov-Galerkin method.The method is applied to the bending problem of the kirchhoff plate and the bending problem of the ground substrate.The specific research contents are as follows:The complex variable meshless local Petrov-Galerkin method is applied to the bending problem of the Kirchhoff plate.The complex variable meshless local Petrov-Galerkin method for Kirchhoff plate bending problem is established and the corresponding discrete equations are derived.The complex variable meshless local Petrov-Galerkin method is applied to the bending problem of the ground substrate.The complex variable meshless local Petrov-Galerkin method for elastic substrate is established and the corresponding discrete equations are derived.In order to verify the validity of the complex variable meshless local Petrov-Galerkin method,the corresponding MATLAB program is written for the above algorithm,and the effectiveness of the proposed method is verified by several numerical examples.