A more stable scheme for BEM/FEM coupling applied to two-dimensional elastodynamics

Abstract

A linear θ method is used in this paper in order to improve the stability of the time domain BEM/FEM coupling formulation. To make possible the coupling of BEM approaches that employ the standard linear θ method with FEM algorithms that employ the Newmark scheme, the former has to be modified. In the standard linear θ method, the response is initially computed at the time ( n+ θ) Δt and subsequently the response at the time ( n+1) Δt is obtained. In the modified version, integral equations are written at the time ( n+ θ) Δt and then modified so that unknowns at the time ( n+1) Δt are introduced back in the BEM system of equations. Thus it becomes possible to write BEM/FEM coupling compatibility conditions at the time ( n+1) Δt. In this way, the θ scheme, which is more stable than the standard BEM formulation, is implicitly considered. The stability improvement achieved by the formulation presented here, when applied to two-dimensional elastodynamics, is illustrated by two numerical examples. The effect of varying θ on the stability of the numerical responses is also studied in this paper.