Extension of infinite elements and absorbing boundary conditions to eigenanalysis of submerged structures
Dr. Jeffrey Cipolla, ABAQUS, Inc.

Abstract:
Infinite elements are distinct from alternative methods for exterior problems in that, like a finite element, they describe a small sub-region of the problem domain, and use locally supported shape functions to derive a method of weighted residuals statement thereon. Until recently, eigenanalysis was not possible using infinite elements.
A single formulation of acoustic infinite element compatible with implicit dynamics, time-harmonic acoustics, far-field extrapolation, explicit dynamics, and eigenanalysis is described. First steps in the development are the adoption of a basis corresponding to spherical radiating harmonics, the Bettess geometric map, and the Astley-Leis weighted residual formulation. A modified means to compute the element integrals, and a modification of the spherical harmonic basis, improve numerical conditioning of the element and stability of the formulation. The trivial frequency dependence of the Astley-Leis formulation, critical for its application to transient problems, also enables a formulation for eigenanalysis, which will be discussed. Absorbing boundary conditions, which can be considered equivalent to low (first or zeroth) order infinite elements, are shown also to have the trivial polynomial frequency dependence required for eigenanalysis. Some computational examples are shown.

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