On effective implicit time integration in analysis of fluid–structure problems

Abstract

During recent years a considerable amount of research effort has been spent on the analysis of fluid-structure systems. An important feature of these analyses is in many cases the use of implicit-explicit time integration of the dynamic response:l’* the response of the fluid is integrated using an explicit method (central difference technique) and the response of the structure is integrated with an implicit technique (e.g. the Newmark method). The principal advantage of such time integration of the dynamic response is that no stiffness matrix need be calculated for the fluid and a relatively large time step can be employed in the incremental analysis. Various schemes for performing the explicit-implicit integration have been proposed, and these were analysed for their stability and accuracy characteristic^.'*^ These combined time integration techniques are not restricted in their use to the analysis of fluid-structure systems, but can be employed for the analysis of systems with ‘stiff and flexible domains’ in general. The objective in this short paper is to point out that an effective solution of fluid-structure systems (and ‘stiff and flexible domains’ in general) can frequently also be calculated using an implicit time integration for the complete structural model with a lumped mass idealization and the recently proposed BFGS m e t h ~ d . ~ ” In the analysis procedure used, the response is calculated with implicit time integration for the fluid and the structure without setting up a stiffness matrix of the fluid, and by satisfying the dynamic equilibrium equations using the BFGS iterations.