Three-dimensional acceleration waves are studied for a large class of materials which includes nonlinear elastic materials, finite linear viscoelastic materials, elastic-plastic materials, hypo-elastic materials, and materials with fading memory. Thermodynamic effects are not included. The material is allowed to be inhomogeneous, anisotropic and undergoing an arbitrary motion ahead of the wave. The purpose of this study is to show how the singular surface theory of continuum mechanics can be used to investigate the effect of material motions ahead of the wave on the growth of the wave amplitude. Results are expressed in terms of the Cauchy stress tensor and the geometry of the wave in the current configuration, and also in terms of the Piola-Kirchoff stress tensor and the geometry of the wave in the reference configuration. The general formulae are applied to plane waves in laminated elastic plates and cylindrical waves in laminated cylindrical shells.

Non-ideal behavior of condensed explosives with metal particle additives has been observed experimentally. In general, adding metal particles to a homogeneous explosive leads to a reduction in the detonation velocity and pressure, depending on the charge diameter, the concentration of the additive, and the particle size. To investigate these phenomena, detonation propagation in liquid and aluminized liquid explosives has been studied theoretically by including source terms in the 1-D conservation equations for mass, momentum and energy. To predict the steady state detonation parameters and the detailed structure of the detonation, the generalized C-J condition has been used to obtain a unique solution from the spectrum of possible solutions to the differential equations. / The eigenvalue detonation solution is first determined for a weakly confined, cylindrical liquid explosive charge. The steady-state analysis assuming an Arrhenius reaction rate predicts the detonation failure diameter which depends on the curvature of the detonation wave, wall friction, and heat loss to the wall. The calculated detonation velocity deficit for liquid nitromethane (NM) is less than 2.1 % near the failure diameter. The predicted failure diameter for liquid NM varies from 15--18 mm for activation energy E*, ranging from 30--40 kcal/mol. These results agree well with the experimental data. A second form for the reaction rate law is also considered (i.e., the so-called "simple" law in which the reaction rate is not dependent on temperature). In this case, the detonation failure is not correctly predicted, and hence this rate law is not appropriate for liquid NM. / Detonation propagation in an aluminized liquid explosive involves complex exothermic and endothermic processes. A two-phase flow model is proposed to take into account the non-equilibrium processes which determine the differences in velocity and temperature between the liquid explosive detonation products and solid particles. The onset of reaction of the Al particles in the detonation zone is set based on a simple ignition criterion. / The calculations show that micron-sized Al particles are chemically inert whereas nanoscale particles may react within the detonation zone. For an explosive with nanoscale additives, the reaction heat of the particles in the detonation zone, if any, contributes to an increase in the detonation temperature. The large detonation velocity deficit for an aluminized liquid explosive is primarily due to momentum losses to the particles, with heat losses playing a relatively minor role, unless the particles are very small. The calculations also reproduce the measured effects of particle size and concentration on detonation velocity. From Chariton's theory of failure diameter, the comparison of the measured failure diameter to the prediction of the detonation zone timescales by the two-phase model with an Arrhenius reaction rate law suggests that the addition of solid particles alters the chemical kinetics of the liquid explosive. A so-called "hot spot" reaction rate law is proposed. With this new reaction rate law, the model predicts the effects of particle size and concentration on the detonation velocity and the detonation zone timescale, in general agreement with the experimental observations.

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Deformation will occur for the flexible structures undergoing large rigid-body motion such as the opening of an umbrella, which poses a problem falling into the category of dynamics of deformable bodies, an intersected area between structural dynamics and rigid-body dynamics. Based on the Euler-Bernoulli beam theory, an FE model is developed to simulate the process of deployment of an umbrella under a zero gravity circumstance in which the structural FEA is adopted to define the displacement field of beam elements. The position of an arbitrary point on a body is located by a set of generalized coordinates of the system, including rigid and elastic sets characterizing rigid-body motion and deformation for the components, respectively. After formulating the kinetic energy, potential energy and generalized forces of the system, the governing equations of motion with different holonomic constraint conditions corresponding to the stages of the deployment are then derived by invoking Lagrange's equations with multipliers. As for the validation of this model, a rigid FE model and a continuum rigid-body model are also derived. The numeric process reveals that significant periodic vibration is induced on the leaf at full deployment if an initial velocity is applied on the sleeve of the modeled umbrella and the deformation of the members causes the retard of the deployment. Comparison of the results shows good agreement between 3-element and 6-element models, and the deformable models are validated by the rigid-body ones. Although the formulation is based on the holonomic 2-body model, it is also applicable to a more complicated nonholonomic system.

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The viscous, incompressible and laminar flow around bluff bodies is analysed via a random vortex method using a hybrid (Eulerian-Lagrangian) scheme. The Navier-Stokes equations, written in the form of vorticity equations, are split into nonlinear convection and linear diffusion parts according to a fractional step method. Vorticity is modelled by discrete point vortices. Vortices are created on the surface to satisfy the zero tangential velocity boundary condition. Random walks are applied to the vortices to simulate the diffusion equation. Vortices are then convected in an inviscid calculation in the Lagrangian scheme to simulate the convection equation. The velocity of each vortex is calculated using the Clould-in-Cell method. / The random vortex method is developed to simulate the flow around a circular cylinder with a splitter plate. A conformal transformation is used to map the cylinder with a splitter plate to a unit circular cylinder. The force coefficients and Strouhal number are presented for various lengths of the splitter plate and are in good agreement with experiments. / The random vortex method has also been developed for the flow around a circular cylinder vibrating transverse to the flow in a channel. The results are presented for various values of Reynolds number, forcing frequency and vibration amplitudes. The effect of blockage on the drag coefficient is presented. The drag coefficient and vortex shedding frequency are shown to compare favourably with experimental results. The flow around a vibrating cylinder with a splitter plate is also simulated. The results are presented for various values of forcing frequency and lengths of the splitter plate. / The flow around multiple stationary cylinders is also simulated. Also, results are presented for the flow around two cylinders, one of which is forced to oscillate in a transverse direction. The numerical results of Strouhal number are in reasonable agreement with experiments.

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