Staggered transient analysis procedures for coupled mechanical systems: Formulation

Abstract

Coupled-field dynamic problems in mechanics have been traditionally solved by treating the entire system as one computational entity. More recently, increasing attention has been directed to an alternative approach; partition the governing equations into subsystems, which are treated by subsystem analyzers. The selection of the subsystems may be based on weak-coupling considerations, widely different time response characteristics, isolation of nonlinear effects, or more pragmatic reasons such as the availability of analyzer software. In a staggered solution procedure the solution state of the coupled system is advanced by sequentially executing the subsystem analyzers. Subsystem coupling terms are accounted for by temporal extrapolation techniques.This paper focuses on the formulation and computer implementation of staggered solution procedures for two-field problems governed by semidiscrete second-order coupled differential equations. Such equations find application in the modeling of structure-fluid, structure-soil and structure-structure interaction. Following an introductory description of candidate problems and general solution strategies, direct time integration methods are formulated and applied to the coupled system. Staggered solution procedures are constructed through two alternative approaches which are based upon partitioning at the difference and differential equation level, respectively. Characteristic equations that govern the stability of the resulting implementations are derived, and the selection of stable extrapolators discussed. Finally, possible extensions of staggered solution procedures to coupled-field static and eigenvalue problems are suggested.