An Interpolating Element-free Galerkin Scaled Boundary Method For Elastodynamics

The interpolating element-free Galerkin scaled boundary method(IEFG-SBM)is a semi-analytical numerical method in the frame of improved interpolating moving least-squares(IIMLS)method,which combines the advantages of both element-free Galerkin method and the scaled boundary method.In the IEFG-SBM,only the information of discretized nodes on the boundary of the computational domain is required and thus the problem dimension is reduced by one,which greatly simplifies the computational cost.In addition,the solution in the radial direction is obtained analytically and thus high computational accuracy is ensured.The improved interpolating moving least-squares method,which is based on nonsingular weight functions,can avoid the calculation inconvenience caused by the singularity of the weight functions in the interpolating moving least-squares method by Lancaster.In addition,the shape function of the improved interpolating moving least-squares method can satisfy the Kronecker delta function property and thus the essential boundary conditions can be imposed directly as in the traditional finite element method.Moreover,the improved interpolating moving least-squares method has fewer undetermined coefficients in the trial function than that in the conventional moving least-squares approximation,which can improve the calculation accuracy and efficiency.Based on the improved continued-fraction method,the interpolation element-free Galerkin scaled boundary method is firstly proposed to solve elastodynamic problem in this paper.In addition,the corresponding MATLAB program has been developed.At last,a lot of numerical examples are presented to verify the effectiveness and accuracy of the proposed method for elastodynamic problems.