Dynamic Analysis of Soil-Structure Interaction Using the Spectral Element Method

Abstract

The spectral element method is used to solve soil-structure interaction (SSI) problems. The system sol-structure is presented as a beam on elastic Winkler foundation. The Spectral Element Method is a frequency domain method based on the Fast Fourier Transform (FFT).The spectral formulation requires that the governing system of equations of motion be solved in the frequency domain and utilizes the Fast Fourier Transform (FFT) to transform the time domain responses to the frequency domain and vice versa. The shape functions and dynamic stiffness matrix of the spectral element are frequency dependent. At first the general formulation of the method is outlined. The formulation of the dynamic stiffness matrices of structures such as rods, Euler-Bernoulli and Timoshenko beams are presented. The spectral formulation of elastically supported beams and beams on Winkler foundation are developed. The second part deals with application of the method to several examples. The main advantage of the proposed method is extremely high precision with few numbers of elements in comparison to the conventional method (FEM).