The load-deformation curve is obtained for a thin tube crushed between two parallel, rigid plates. It is found that the influence of geometry changes after initial yield results in increased load-carrying capacity. In addition, the effects on the yield condition due to direct stress and shear are quantitatively discussed.

This paper describes the theoretical formulation and computational implementation of a method for treating hull cavitation in underwater-shock problems. In addition, the method can be applied to the analysis of submerged structures that contain internal fluid volumes. In the present implementation, the doubly asymptotic approximation (DAA) serves to simulate a radiation boundary that is located away from the fluid-structure surface at a distance sufficient to contain any cavitating region. The enclosed fluid is discretized with volume finite elements that are based upon a displacement-potential formulation. An explicit time-integration algorithm is used to advance the solution in the fluid-volume region, implicit algorithms are used for the structure and DAA boundary, and a staggered solution procedure has been developed to treat the interface condition. Results for two example problems obtained with the present implementation show close agreement with those obtained by other methods.

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SUMMARYComputational techniques for the treatment of fluid-structure interaction effects by discrete boundary integral methods are examined. Attention is focused on the computation of the added mass matrix by finite element methods for a structure submerged in an infinite, inviscid, incomljressible fluid. A general computational procedure is presented that is based upon a variational approach involving the assumption of constant source strength over each surface element. This is followed by an analysis of the discretization error for a spherical body that is then used to develop a hierarchy of computational schemes. These schemes are then evaluated numerically in terms of 'fluid boundary modes' for a submerged spherical surface. One scheme has been found to be surprisingly accurate in relation to its computational demands. INTRODUCllONIn recent years, growing interest has been shown in the forced response analysis &'submerged complex structures (see, e.g. Reference 1). During this same period, substantial progress has been made in the continuing development of discrete element (finite element, finite difference) methods of structural analysis, which make possible very sophisticated forced response analyses of complex structures in vucuo. A key element in the extension of this capability to submerged structures is the development of techniques for the treatment of the fluid-structure interaction that are compatible with discrete element structural analysis methods. This paper deals with the finite element analysis of the fluid-structure interaction in situations where fluid viscosity effects are negligible and where the dominant frequency components characterizing the motion of the structure are low-frequency in nature. The latter condition refers to cases in which A: r << A; , where A,r is a characteristic structural wavelength for the motion of the structure's surface and A,, = c/f is a characteristic acoustic wavelength for that motion; in this last expression, f is a characteristic frequency of the motion and c is the speed of sound in the fluid. When these conditions are satisfied, which occurs in a great number of practical situations, the fluid can be treated in the inviscid, incompressible limit.*The governing equation for an inviscid, incompressible fluid of infinite extent that is set into motion by the movement of a body submerged in it is simply Laplace's e q~a t i o n .~ The solution of this equation is readily effected with discrete boundary integral techniques through the construction of a finite element mesh over the surface of the submerged body.4 The end result of this procedure is an added mass matrix that accounts for the entrainment of fluid caused by the rigid-body and/or deformational motion of the body.5 The appropriate combination of the added mass matrix with the in vucuo structural mass matrix accounts for the effects of the * Research Scientist. t Staff Scientist.