Dynamic Analysis of Soil-Structure Interaction Using Decoupled Scaled Boundary Finite Element Method

Structures are subjected to different loadings during their lifetime. Most of these loads are time dependent and change over the time. Therefore, it is important to evaluate structures under dynamic loads. On the other hand, dynamic response of structures is affected by several factors that results in many complexities to structural analysis. Thus, numerical methods are used for seismic analysis of structures. In this article, a new semi analytical method with high efficiency is developed for soil-structure interaction (SSI) analysis, which is called decoupled scaled boundary finite element method (DSBFEM). This method has analytical solution in radial direction and uses a specific shape functions as the interpolation function in the circumferential direction. In addition, the boundaries of the problem are discretized by specific new non-isoparametric elements. In these elements, new special shape functions as well as higher-order Chebyshev mapping functions are implemented. For the shape functions, Kronecker Delta property is satisfied for displacement function, simultaneously. Moreover, the first derivatives of shape functions are assigned to zero at any given control point. In fact, to model the geometry of the problems, we consider a local coordinate origin (LCO) for transportation of the geometric characteristics of global coordinate and local coordinate. Consequently, using a form of weighted residual method and implementing Clenshaw-Curtis numerical integration, coefficient matrices of the system of equations are converted into diagonal ones, which leads to a set of decoupled partial differential equations for solving the whole system. This means that the governing partial differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. Due to the soil flexibility effect on structural responses, in this paper, SSI problem has been investigated considering different values of modulus of elasticity for soil domain. To achieve this, two different LCOs have been used to discretize the soil domain and the structure domain. Thus, a three-step algorithm is proposed, which consists of: (1) considering an initial stress on the interaction boundary, (2) analysis of soil domain, and (3) analysis of structure domain. Therefore, after the initial assumption of stress on the interaction boundary, the soil domain will be completely analyzed by two-stage traction redistribution and the results on interaction boundary will be used as boundary conditions of structure domain. It should be noted that in the proposed algorithm, only one-stage traction redistribution will be used to analyze the structure domain. Finally, validity and accuracy of DSBFEM are fully demonstrated through some benchmark examples with different values of modulus of elasticity for the soil domain, and the results are compared with Finite Element Method (FEM). The results indicate that the proposed method has high accuracy and flexibility to consider the SSI effect, determine the resonant frequency and the maximum displacement amplitude of the structure. In addition, the number of elements used in the DSBFEM is much less than the FEM, which will lead to a reduction in computational costs.