Twelfth International Congress on Sound and Vibration A TIME DOMAIN COUPLED BOUNDARY ELEMENT-FINITE ELEMENT METHOD FOR THE DYNAMIC RESPONSE OF STRUCTURES

This paper presents a coupled finite element-boundary element approach in the time domain for the calculation of the dynamic response of structures due to dynamic excitations as arising from traffic or pile driving. The dynamic soil flexibility is calculated with a boundary element formulation in the frequency domain. It is transformed to a force-displacement relationship in the time domain and combined with a direct time integration scheme for the finite element model of the structure. The method is applied to the calculation of the response of a structure due to traffic induced vibrations, where non-linear material behaviour and the dynamic interaction between the soil and the structure are fully accounted for. INTRODUCTION Repeated dynamic excitations in the built environment as caused by heavy traffic and pile driving may result in structural damage, which is related to the constitutive behaviour of building materials and foundation soils under cyclic loading. Recently, a numerical model for the prediction of traffic induced structural vibrations that fully accounts for the dynamic soil-structure interaction has been developed and validated [11]. The model is limited to linear structural behaviour as the analysis is performed in the frequency domain. In the case of structural damage, however, the non-linear constitutive behaviour requires a direct time integration procedure. This paper presents a coupled finite element-boundary element approach in the time domain for the calculation of the structural response due to dynamic excitations as arising from traffic or pile driving. The structure is modelled with finite elements while the soil domain is modelled with boundary elements. Both the non-linear constitutive behaviour and the dynamic interaction between the soil and the structure are accounted for. Coupled finite element-boundary element calculations in the time domain are classified into hybrid domain [13] and time domain approaches [2, 5, 8]. In the hybrid domain approach, the dynamic soil flexibility in the frequency domain is transformed to a force-displacement relationship in the time domain. The boundary element method in the time domain directly results in this force-displacement relationship and is classified as a time domain approach. In the present study, a hybrid domain method is elaborated and applied to the calculation of the response of a two-story masonry building excited by an incident wave field due to the passage of a truck on a traffic plateau. THE EQUATIONS OF MOTION OF THE BUILDING-SOIL SYSTEM In this section, the equations of motion of a structure excited by an incident wave field are elaborated (figure 1). Two substructures are defined. The first is the generalised structure Ωb, which can have non-linear characteristics and possibly contains a nonlinear or non-homogeneous part of the soil. The second substructure is the linear elastic unbounded soil domain Ω s . Due to the semi-infinite extent of the soil domain, radiation conditions have to be satisfied. The substructures are coupled through the boundary Σbs between the generalised structure and the soil.