STABILIZING THE RETARDED POTENTIAL METHOD FOR TRANSIENT FLUIDÐSTRUCTURE INTERACTION PROBLEMS

The Retarded Potential (RP) method, which is a boundary element technique and non-local in both space and time, is employed to discretize the ßuid domain for the analysis of transient ßuidÐstructure interaction problems. The retarded potential analysis program RPFS is coupled to the ABAQUS non-linear Þnite element code to form ABAQUS/RPFS. The standard RP is inherently unstable for time steps below a critical time step that is equal to the maximum distance in the ßuid divided by the wave speed. A technique referred to as the Figueiredo method is used to convert the standard RP di¤erential-delay equations for the ßuid to simply delay equations, which are more stable. The Figueiredo approach extends the stability range of the standard RP by a factor of approximately 10Ð20, but this time step is still not small enough to be useful for analysis. Digital signal processing methods are used to further stablize the response of the ßuid by removing the oscillating high-frequency noise in the time histories of the solution without introducing phase shifting or any signiÞcant damping. Stability of the coupled system is achieved by not extrapolating the structural accelerations. ABAQUS/RPFS is applied to both a rigid and elastic sphere subjected to a plane wave, and the results using the full time histories required are completely stable and quite accurate. With this procedure, the retarded potential method may yet prove to be a valuable analysis tool for transient ßuidÐstructure interaction problems.