STABILIZING THE RETARDED POTENTIAL METHOD FOR TRANSIENT FLUID-STRUCTURE INTERACTION PROBLEMS

The Retarded Potential (RP) method, which is a boundary element techni que and non-local in both space and time, is employed to discretize th e fluid domain for the analysis of transient fluid-structure interacti on problems. The retarded potential analysis program RPFS is coupled t o the ABAQUS non-linear finite element code to form ABAQUS/RPFS. The s tandard RP is inherently unstable for time steps below a critical time step that is equal to the maximum distance in the fluid divided by th e wave speed. A technique referred to as the Figueiredo method is used to convert the standard RP differential-delay equations for the fluid to simply delay equations, which are more stable. The Figueiredo appr oach extends the stability range of the standard RP by a factor of app roximately 10-20, but this time step is still not small enough to be u seful for analysis. Digital signal processing methods are used to furt her stabilize the response of the fluid by removing the oscillating hi gh-frequency noise in the time histories of the solution without intro ducing phase shifting or any significant damping. Stability of the cou pled system is achieved by not extrapolating the structural accelerati ons. ABAQUS/RPFS is applied to both a rigid and elastic sphere subject ed to a plane wave, and the results using the full time histories requ ired are completely stable and quite accurate. With this procedure, th e retarded potential method may yet prove to be a valuable analysis to ol for transient fluid-structure interaction problems. (C) 1997 John W iley & Sons, Ltd.