A time domain coupled boundary element-finite element method for the dynamic response of structures

This paper presents a coupled finite element-boundary eleme nt 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 calcu lated with a boundary element formulation in the frequency domain. It is transformed to a forc e-displacement relationship in the time domain and combined with a direct time integration sche me 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 be haviour and the dynamic interaction between the soil and the structure are fully accounted for. INTRODUCTION Repeated dynamic excitations in the built environment as ca u ed by heavy traffic and pile driving may result in structural damage, which is relat d o the constitutive behaviour of building materials and foundation soils under cycli c loading. Recently, a numerical model for the prediction of traffic ind uced structural vibrations that fully accounts for the dynamic soil-structure in teraction has been developed and validated [11]. The model is limited to linear structura l behaviour as the analysis is performed in the frequency domain. In the case of structur al damage, however, the non-linear constitutive behaviour requires a direct time i nt gration procedure. This paper presents a coupled finite element-boundary eleme nt approach in the time domain for the calculation of the structural response d u to dynamic excitations as arising from traffic or pile driving. The structure is modell ed 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 t he structure are accounted for. Coupled finite element-boundary element calculations in th e time domain are classified into hybrid domain [13] and time domain approache s [2, 5, 8]. In the hybrid domain approach, the dynamic soil flexibility in the frequen cy domain is transformed to a force-displacement relationship in the time domain. The b oundary element method in the time domain directly results in this force-displacemen t r lationship and is classified as a time domain approach. In the present study, a hybrid domain method is elaborated an d 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 excit d by an incident wave field are elaborated (figure 1). Two substructures are defined. The first is the generalised structureΩb, which can have non-linear characteristics and possibly co ntains a nonlinear or non-homogeneous part of the soil. The second subst ructure is the linear elastic unbounded soil domainΩ s . Due to the semi-infinite extent of the soil domain, radiation conditions have to be satisfied. The substructure s a coupled through the boundaryΣbs between the generalised structure and the soil.