An Interpolating Element-Free Galerkin Scaled Boundary Method For Elastic And Piezoelectric Cracks

The interpolating element-free Galerkin scaled boundary method(IEFG-SBM)is a boundary meshless method based on improved interpolating moving least-squares(IIMLS),which combines the element-free Galerkin method and the scaled boundary method.When applied to the analysis of elastic and piezoelectric cracks,this method allows the stress and electric displacement intensity factors to be calculated directly from their definitions and only the boundary of the computational domain requires to be discretized by the element-free Galerkin method.However,in contrast to the boundary element method,no fundamental solution is required.The solution in the radial direction is analytical,so the simulation precision of this method is relatively high.The shape function of the improved interpolating moving least-squares method satisfies 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 not only can overcome the difficulties caused by the singularity of the weight function in the interpolating moving least-squares method by Lancaster,but also has fewer undetermined coefficients in the trial function than that in the conventional moving least-squares approximation.The main contents are summarized as below:(1)The interpolating element-free Galerkin scaled boundary method baesd on improved interpolating moving least-squares for elastic cracks is presented,the relevant calculation formulas are derived.Several typical examples are calculated by Matlab programs to verify the high validity and efficiency of the method.(2)Baed on the study of elasticity,the interpolating element-free Galerkin scaled boundary method is applied to the fracture behavior of the piezoelectric materials,and the corresponding formulas and Matlab programs are obtained,so then the validity of the method is further verified.(3)In order to obtain higher validity and the flexibility of mesh division,dividing the stucture into two independent zones.Then a novel method is developed that couples the element-free Galerkin scaled boundary element method and finite element method(FEM)for crack propagation modelling.At last,the method is applied to the fracture problems of elastic and piezoelectric materials,and the accuracy and effectiveness of the method are verified by numerical examples.