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Model degrees-of-freedom reduction and frequency windowing via interpolation are combined for application to acoustic finite element analysis problems. Projection operators are employed for the model reduction or condensation process. Interpolation is then introduced over a user defined frequency window, which can have real and imaginary boundaries and be quite large. Hermitian interpolation functions (which require derivative information) as well as standard Lagrangian functions, which can be linear, quadratic or cubic, have been used to construct the windows. For one-dimensional windows, the location of interior evaluation points can be varied to increase accuracy. Results are excellent for example problems, even for large d.o.f. reduction and large frequency windows containing numerous resonances (eigenvalues). The reduced models within the windows appear to indicate accurately the location of the resonances.

The Retarded Potential (RP) method, which is a boundary element technique and non-local in both space and time, is employed to discretize the fluid domain for the analysis of transient fluid–structure interaction problems. The retarded potential analysis program RPFS is coupled to the ABAQUS non-linear finite 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 fluid divided by the 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 approach extends the stability range of the standard RP by a factor of approximately 10–20, 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 fluid by removing the oscillating high-frequency noise in the time histories of the solution without introducing phase shifting or any significant 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 fluid–structure interaction problems. © 1997 John Wiley & Sons, Ltd.

In this work, the stress-point approach, which was developed to address tension instability and improve accuracy in Smoothed Particle Hydrodynamics (SPH) methods, is further extended and applied for one-dimensional (1-D) problems. Details of the implementation of the stress-point method are also given. A stability analysis reveals a reduction in the critical time step by a factor of 1/√2 when the stress points are located at the extremes of the SPH particle. An elementary damage law is also introduced into the 1-D formulation. Application to a 1-D impact problem indicates far less oscillation in the pressure at the interface for coarse meshes than with the standard SPH formulation. Damage predictions and backface velocity histories for a bar appear to be quite reasonable as well. In general, applications to elastic and inelastic 1-D problems are very encouraging. The stress-point approach produces stable and accurate results. © 1997 by John Wiley & Sons, Ltd.