An interpolating element-free Galerkin scaled boundary method applied to structural dynamic analysis

Abstract

• An efficient semi-analytical method, namely the IEFG-SBM is developed for structural dynamic analysis. • The proposed method unifies the advantages of the SBM and the IEFG method. • The IIMLS method is superior to the MLS approximation because its shape function has the delta function property . • The IIMLS method is also superior to the IMLS method because the weight function involved is nonsingular. • The improved continued fraction solution can represent the inertial effect at high frequencies with no internal mesh. An efficient semi-analytical method, namely the interpolating element-free Galerkin scaled boundary method (IEFG-SBM) is developed for structural dynamic analysis in this paper, which is based on boundary scattered nodes with no need of element connectivity. Since the shape functions of the improved interpolating moving least-squares (IIMLS) method satisfy the delta function property, the essential boundary conditions, as a result, can be enforced accurately without any additional efforts. Based on the improved continued fraction, the dynamic properties of a bounded domain are expressed by the high order static stiffness and mass matrices. This continued fraction solution is computationally more robust and the transient response can be obtained directly in the time domain using standard procedures in structural dynamics. It is testified from the computational results that the present method for structural dynamic analysis is quite easy to be implemented with high accuracy.