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

Document Type : Research Article

Authors

1 K.N. Toosi University of Technology, Tehran, Iran

2 Tarbiat Modares University, Tehran, Iran

3 Arak University, Arak, Iran

Abstract

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.

Keywords

References

1.    Chopra, A.K. and Gupta, S. (1982) Hydrodynamic and foundation interaction effects in frequency response functions for concrete gravity dams. Earthquake Engineering and Structural Dynamics, 10(1), 89-106.
2.    Lofti, V., Roesset, J.M., and Tassoulas, J.L. (1987) A technique for the analysis of the response of dams to earthquakes. Earthquake Engineering and Structural Dynamics, 15(4), 463-490.
3.    Medina, F. and Domínguez, J. (1989) Boundary elements for the analysis of the seismic response of dams including dam-water-foundation interaction effects. I. Engineering Analysis with Boundary Elements, 6(3), 152-157.
4.    Domínguez, J. and Medina, F. (1989) Boundary elements for the analysis of the seismic response of dams including dam-water-foundation interaction effects. II. Engineering Analysis with Boundary Elements, 6(3), 158-163.
5.    Yazdchi, M., Khalili, N., and Valliappan, S. (1999) Dynamic soil-structure interaction analysis via coupled finite-element-boundary-element method. Soil Dynamics and Earthquake Engineering, 18, 499-517.
6.    Wolf, J.P. (2003) The Scaled Boundary Finite Element Method. John Wiley & Sons Inc.
7.    Khodakarami, M.I. (2012) A Method of Scaled Boundary-Finite Element with Diagonal Coefficient Matrices for Solving Continuum Mechanics Problems. Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Ph.D.) in Civil Engineering, Department of Earthquake Engineering, Faculty of Civil and Environmental Engineering, Tarbiat Modares University (in Persian).
8.    Khodakarami, M.I. and Khaji, N. (2014) Wave propagation in semi-infinite media with topographi-cal irregularities using decoupled equations method. Soil Dynamics and Earthquake Engineering, 65, 102-112.
9.    Khaji, N. and Khodakarami, M.I. (2011) A new semi-analytical method with diagonal coefficient matrices for potential problems. Engineering Analysis with Boundary Elements, 35(6), 845-854.
10.    Khodakarami, M.I. and Khaji, N. (2011) Analysis of elastostatic problems using a semi-analytical method with diagonal coefficient matrices. Engineering Analysis with Boundary Elements, 35(12), 1288-1296.
11.    Khaji, N. and Khodakarami, M.I. (2012) A semi-analytical method with a system of decoupled ordinary differential equations for three-dimen-sional elastostatic problems. International Journal of Solids and Structures, 49(18), 2528-2546.
12.    Khodakarami, M.I., Khaji, N., and Ahmadi, M.T. (2012) Modeling transient elastodynamic problems using a novel semi-analytical method yielding decoupled partial differential equations. Computer Methods in Applied Mechanics and Engineering, 213-216, 183-195.
13.    Khaji, N. and Mirzajani, M. (2013) Frequency domain analysis of elastic bounded domains using a new semi-analytical method. Acta Mechanica, 224(7), 1555-1570.
14.    Mirzajani, M., Khaji, N., and Khodakarami, M.I. (2016) A new global nonreflecting boundary condition with diagonal coefficient matrices for analysis of unbounded media. Applied Mathematical Modelling, 40(4), 2845-2874.
15.    Khaji, N. and Yazdani, M. (2016) Determination of stress intensity factors of 2D fracture mechanics problems through a new semi-analytical method. Fatigue and Fracture of Engineering Materials and Structures, 39(4), 467-478.
16.    Yazdani, M., Khaji, N., and Khodakarami, M.I. (2016) Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate. Acta Mechanica, 227(12), 3529-3547.
17.    Yazdani, M. and Khaji, N. (2018) Development of     a new semianalytical approach for 2D analysis of crack propagation problems. Fatigue and Fracture of Engineering Materials and Structures, 41(6), 1344-1363.
Bulletin of Earthquake Science and Engineering
Volume 7, Issue 3 - Serial Number 24
November 2020
Pages 83-96

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History

  • Receive Date: 07 February 2019
  • Accept Date: 05 December 2019

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