An Element-free Galerkin (EFG) scaled boundary method

The scaled boundary method is a semi-analytical method of analysis which can be used in computational mechanics. This method uses a normalised radial coordinate system, introducing shape functions to weaken the governing equations in the circumferential direction and solving the resulting differential equations analytically in the radial direction. This paper presents a new Element-free Galerkin (EFG) scaled boundary method in which the EFG approach is used in the circumferential direction. The proposed model is verified by application to a number of standard problems of elasticity. The numerical solutions show that the new method has higher accuracy (for any particular number of nodes) and better convergence than scaled boundary finite element methods, and an accurate smooth stress field can be obtained directly without the necessity of using a stress recovery procedure.

Research highlights
► An EFG–SBM is developed employing an EFG approach in the circumferential direction.
► In this way the advantages of the SBM and EFG methods are combined.
► Highly accurate and smooth solutions are obtained by the EFG–SBM.
► Comparisons of EFG–SBM with SBFEM and MLPG-SBM are provided.