The Improved Element-Free Galerkin Method For Elastoplasticity And Viscoelastic Large Deformation Problems

With the development of engineering technology,engineering fields has higher and higher requirements for the accuracy and efficiency of numerical computation,because the computations based on small deformation assumption and linear elasticity theory can't satisfy the requirements of engineering practice.For the meshless method,because it constructs trial function based on nodes,it does not need to generate the elements of mesh,and can avoid mesh distortion and other problems.Therefore,meshless method has certain advantages in dealing with nonlinear problems.Element-free Galerkin(EFG)method is one of meshless methods used and researched most widely.The EFG method may appear some problems,such as low computational efficiency and forming singular matrix easily.To solve these problems,in this dissertation,based on the improved moving least-squares(IMLS)approximation,the improved element-free Galerkin(IEFG)method is presented for three-dimensional elastoplasticity and two-dimensional viscoelastic large deformation problems.For three-dimensional elastoplasticity problems,the IMLS approximation is used to obtain the shape function,the Galerkin weak form of elastoplasticity problems is used to form the discretized equation system,and using the penalty method to impose the displacement boundary conditions,the IEFG method for three-dimensional elastoplasticity problems is presented,and the corresponding formulae are given.In order to further improved computational efficiency,the method of pre-stored shape function is used.Compared with the EFG method,the IEFG method in this paper can obtain greater computational efficiency.For two-dimensional viscoelasticity large deformation problems,the IMLS approximation is used to obtain the shape function,the Galerkin weak form of viscoelasticity large deformation problems is used to form the discretized equation system,the penalty method is used to impose the displacement boundary conditions,and the Newton-Raphson iteration procedure is selected,the three-parameters model is used under creep condition,then the IEFG method of two-dimensional viscoelastic large deformation problems based on the total Lagrange formulation is presented.Compared with the EFG method,the computational efficiency of the IEFG method is higher.In this dissertation,the MATLAB codes of the IEFG method for three-dimensional elastoplasticity and two-dimensional viscoelastic large deformation problems are written respectively.From analyzing numerical examples,the validity and efficiency of the IEFG method in this dissertation are shown.