Study Of Consistent High Order Element-free Galerkin Method Forthin Plate Bending Analysis

Thin plates,as an important class of engineering components,are widely used in many industries such as aerospace engineering,civil engineering,marine engineering,mechanical engineering and chemical engineering,etc,e.g.the bridge deck in civil engineering.Therefore,developing efficient and accurate numerical methods for thin plates based on the bending theory is of great significance to the accurate strength analysis of thin plates and even to their safe operation in engineering.Different from the general solid problem whose governing equation is a second-order partial differential equation,the governing equation of the thin-plate bending theory is a fourth-order partial differential equation,which requires the C~1 continuity of approximation functions.As a result,the ordinary finite element method which possesses only C~0 continuity cannot be directly applied to bending thin plates,hence special and complex thin plate elements are required.Different from the finite element method,the approximate function of the element-free galerkin(EFG)method possesses high order continuity and EFG can be directly applied to the bending analysis of thin plates.This thesis is devoted to the study and development of an efficient and accurate element-free galerkin method for the analysis of bending thin plates in small deflection.The main work is as follows:(1)Detailed derivation of the formulation of the moving least square approximation is conducted and the algorithm to compute nodal shape functions of third order approximation is established.The governing equation and boundary conditions of thin-plate bending in small deflection is formulated,and the corresponding Galerkin weak form is established.By further application of the element-free galerkin method for spatial discretization,the final discretized equation is obtained.(2)The nodal shape functions of the EFG method are rational functions,the ordinary integration methods such as the Gauss integration and Hammer integration cannot accurately evaluate the weak form.Aiming at this issue,a consistent integration method using background quadrilateral elements based on the Hu-Washizu three-field mixed variational principle is proposed in this thesis.(3)A FORTRAN code of the element-free galerkin method for thin-plate bending analysis is constructed in this thesis.The code includes the standard Gauss integration method and the proposed consistent integration method.(4)Detailed numerical investigation of the developed consistent integration method and the computer code is conducted in this thesis by three examples:circular plate,square plate and porous circular plate.Numerical results show that,in comparison with the standard EFG method,the proposed consistent EFG method remarkably improves the computational accuracy and efficiency.In addition,the method of this thesis also possesses good feasibility to bending of thin plates with complex geometries.