The improved element-free Galerkin method for elastoplasticity large deformation problems

Abstract

Based on the improved moving least-squares (IMLS) approximation, the improved element-free Galerkin (IEFG) method for elastoplasticity large deformation problems is presented. Compared with the moving least-squares (MLS) approximation, by orthogonalizing the basis function, the IMLS approximation can overcome the disadvantage of ill-conditional or singular equations in the MLS approximation. Compared with the meshless methods based on the MLS approximation, under the similar computational accuracy, the ones using the IMLS approximation have higher computational efficiency. The IMLS approximation is used to form the approximation function, the Galerkin weak form of elastoplasticity large deformation problem is used to form the discretized equation system, and the penalty method is used to apply the displacement boundary conditions, then the formulae of the improved element-free Galerkin (IEFG) method for elastoplasticity large deformation problems are obtained, and Newton-Raphson method is used to obtain the solution of the final equation system. Some numerical examples are given to discuss the influences of the weight function, the scale parameter, the penalty factor, the node distribution and the load step number on the computational precision of the numerical solutions. Considering the relative errors when the cubic, quartic and quintic spline functions are used as weight functions, it is shown that the numerical solution using the cubic spline function has higher computational precision. About the scale parameter of the influence domain and the penalty factor, the numerical results show that d max=3.6 and α =1010× E will obtain the solutions with higher precision. The convergence of the method in this paper is analyzed by considering the influence of the node distribution on the computational precision of the solutions, and it is shown that the method in this paper is convergent. And the influence of the total load step number on the computational precision of the solutions is also discussed. Numerical examples show that the method in this paper is effective, and it has the advantage of improving the computational efficiency of the EFG method.