Dynamic soil-structure interaction analysis of layered unbounded media via a coupled finite element/boundary element/scaled boundary finite element model

Abstract

SUMMARYIn this paper, a coupled model based on finite element method (FEM), boundary element method (BEM) and scaled boundary FEM (SBFEM) (also referred to as the consistent infinitesimal finite element cell method) for dynamic response of 2D structures resting on layered soil media is presented. The SBFEM proposed by Wolf and Song (Finite-element Modelling of Unbounded Media. Wiley: England, 1996) and BEM are used for modelling the dynamic response of the unbounded media (far-field). The standard FEM is used for modelling the finite region (near-field) and the structure.In SBFEM, which is a semi-analytical technique, the radiation condition at infinity is satisfied exactly without requiring the fundamental solution. This method, also eliminates the need for the discretization of interfaces between different layers. In both SBFEM and BEM, the spatial dimension is decreased by one. The objective of the development of this coupled model is to combine advantages of above-mentioned three numerical models to solve various soil-structure interaction (SSI) problems efficiently and effectively. These three methods are coupled (FE-BE-SBFEM) via substructuring method, and a computer programme is developed for the harmonic analyses of SSI systems. The coupled model is established in such a way that, depending upon the problem and far-field properties, one can choose BEM and/or SBFEM in modelling related far-field region(s). Thus, BEM and/or SBFEM can be used efficiently in modelling the far-field. The proposed model is applied to investigate dynamic response of rigid and elastic structures resting on layered soil media. To assess the proposed SSI model, several problems existing in the literature are chosen and analysed. The results of the proposed model agree with the results presented in the literature for the chosen problems. The advantages of the model are demonstrated through these comparisons.

A boundary condition in Padé series for frequency‐domain solution of wave propagation in unbounded domains

“…Anisotropic materials are handled without additional computational efforts. This method has been applied successfully to the dynamic analysis of unbounded domains in both frequency and time domains [9,41,[44][45][46][47][48][49][50]. It is extended in Bazyar and Song [51] to calculate the dynamic stiffness matrix of non-homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates.…”

“…The results for the dynamic stiffness coefficients are shown in Figure 9 as dotted lines. This technique has been verified extensively by other numerical methods [42,44,[46][47][48]51]. Its results are used as reference solutions as no analytical solution for this problem is available.…”

The Scaled Boundary Finite Element Method for the Efficient Modelling of Linear Elastic Fracture

“…Further, a non-linear heat transfer problem was solved using the homotopy analysis method (HAM) [22]. Also, hybrid methods such as coupling with meshless methods [23], boundary element method (BEM) [24] and the finite element method (FEM) [25] have been developed. Furthermore, SBFEM has been used as crack tip enrichment in XFEM [26].…”

A frequency-domain approach for modelling transient elastodynamics using scaled boundary finite element method

“…This has been demonstrated by a few recent studies. For example, the dynamic soil-structure interaction was modelled by Zhang et al [18] using the SBFEM, by Yan et al [19], and Ekevid and Wiberg [20] using coupled FEM-SBFEM methods, and by Genes and Kocak [21] using a FEM-BEM-SBFEM coupling method. What's more, the analytical stress field explicitly represents stress singularities at crack tips, which allows accurate stress intensity factors to be computed directly from the definition.…”