A convenient one-point integration scheme which analytically integrates the element volume and uniform strain modes of first order isoparametric finite elements is presented. The treatment of zero energy modes which arise due to the one-point integration procedure then is addressed. A method for precisely isolating these modes for arbitrary geometry is developed. Two hourglass control schemes, viscous and elastic, are presented and examined. A homogenized element for modeling the dynamics of nuclear fuel pin bundles, which makes use of the one-point integration and hourglass control techniques, is presented. This element incorporates a "thick-plate" bending theory to model the fuel pins, a quasi-Eulerian approach to describe the behavior of the encompassing acoustic fluid, and a mass coupling interaction technique.
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