Study Of Efficient Meshfree Methods For Large Deformation Analysis

With the development of engineering technologies and the increasing demand for high accuracy,the assumption of small deformation has been difficult to meet the needs of practical engineering applications.The research on the problems of large deformation is becoming more and more urgent.As a typical meshfree method,the element-free Galerkin(EFG)method does not depend on meshes to construct approximation functions and it has apparent advantage in alleviating the numerical difficulties of mesh distortion.Therefore,large deformation analysis has been one of the most important fields to apply the EFG method.In this paper,the EFG method is employed to solve two dimensional elastoplastic large deformation problems and three-dimensional hyperelastic large deformation problems.In the framework of the updated Lagrangian method,the tangent stiffness matrix including geometrical and physical nonlinearities is established by the linearization of the weak form of the governing equation.Hyperelastic and hypo-elastoplastic materials are considered.The tangent modulus and the corresponding algorithm to update the stress are described.Taking full advantage of the merit that the EFG method is convenient to construct high order approximation functions,second order moving least-squares approximation of the displacement is employed.The consistent integration methods,which are recently developed for small deformation analysis,is employed to numerically evaluate the stiffness matrix.They are the Quadratically Consistent 3-point(QC3)integration scheme for 2D problems and the Quadratically Consistent 4-point(QC4)integration scheme for 3D problems,respectively.QC3 and QC4 are able to exactly pass the linear and quadratic patch tests and thus possess the merit of high efficiency and high accuracy.Extension of these two methods from small deformation analysis to elastoplastic large deformation analysis is the major contribution of this thesis.Programming of the FORTRAN code to implement the theory and algorithms mentioned above for two-dimensional elastoplastic large deformation analysis and three-dimensional geometric large deformation analysis has been done in this thesis.Some typical numerical examples such as cantilever beams,shallow arches,necking of aluminum rods are employed to validate the developed algorithms and codes.Numerical results show that the meshfree method using the QC3 integration scheme is able to accurately solve the hyperelastic and hypo-elastoplastic large deformation problems.Furthermore,in comparison with the linear finite element method,the proposed method possesses higher computational accuracy;in comparison with the standard EFG method using Gauss integration,the method possesses higher computational efficiency.With regard to the three-dimensional hyperelastic large deformation problems,the EFG method using the QC4 integration scheme shows higher accuracy than the linear finite element method.Furthermore,it substantially reduces the number of integration points required by the three-dimensional EFG method.Therefore,the methods presented in this thesis remarkably improve the computational efficiency of meshfree analysis of large deformation problems.