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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.

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.

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.

This research develops an analytical method for predicting the hydrodynamic force experienced by a long slender solid body of arbitrary cross-sectional shape and body centreline configuration, subjected to an unbounded uniform fluid flow. It is assumed the slenderness parameter, K (the ratio of the body cross-sectional length scale the body length) is small ($ ll 1$), the body centreline radius of curvature is everywhere large (of order body length), the cross-sectional shape varies slowly alone the body length, and the Reynolds number $R sb{e}$, based on the body length is of order unity. / The inner flow solution for an arbitrary cross-section is illustrated by applying the complex variable method for a body with an elliptical cross-section, which is extendable to any cross-sectional shape. / The novelty of this research is the improvement of the approximation of the force per unit length in slender body theory when inertia effects are not negligibly small. (Abstract shortened by UMI.)

The main focus of this thesis is on investigating the minimum size of the Representative Volume Element (RVE) and finite-size scaling of properties of random linear and nonlinear elastic composites. The RVE is a material volume which accurately describes the overall behavior of a heterogeneous solid, and is the core assumption of continuum mechanics theory. If the composite microstructure admits the assumption of spatial homogeneity and ergodicity, the RVE can be attained within a specific accuracy on a finite length-scale. Determining this scale is the key objective of this thesis. / In order to theoretically analyze the scale-dependence of the apparent response of random microstructures, essential and natural boundary conditions which satisfy Hill's averaging theorem in finite deformation elasticity are first considered. It is shown that the application of the partitioning method and variational principles in nonlinear elasticity and thermoelasticity, under the two above-mentioned boundary conditions, leads to the hierarchy of mesoscale bounds on the effective strain- and free-energy functions, respectively. These theoretical derivations lay the ground for the quantitative estimation of the scale-dependence of nonlinear composite responses and their RVE size. / The hierarchies were computed for planar matrix-inclusion composites with the microstructure modeled by a homogeneous Poisson point field. Various nonlinear composites with Ogden-type strain-energy function are considered. The obtained results are compared with those where both matrix and inclusions are described by a neo-Hookean strain-energy function as well as with the results obtained from the linear elasticity theory. The trends toward the RVE are also computed for nonlinear elastic composites subjected to non-isothermal loading. The accuracy of the RVE size estimation is calculated in terms of the discrepancy between responses under essential and natural boundary conditions. Overall, the results show that the trends toward the RVE as well as its minimum size are functions of the deformation, deformation mode, temperature, and the mismatch between material properties of the phases. / The last part of the thesis presents an investigation of the size effect on thermoelastic damping of a micro-/nanobeam resonator. It does not follow the framework described above. The main concern here is the size and the vibration frequency, at which the classical Fourier law of heat conduction is no longer valid, and the finite speed of heat propagation has to be taken into account.

This dissertation is concerned with experimental and analytical studies of the mechanics of interaction where a pneumatic tire is loaded vertically on a supporting ground, i.e., rigid base, clay and sand. / The numerous experiments were conducted under various conditions to characterized the interactions in terms of the experimental results, e.g. axle displacement, contact area, contact pressure, etc. The results of pressure distribution indicate that recognizing a tire as a pneumatic body is crucial in establishing a rational theory for tire-supporting ground interaction problems. The pressure distribution and contact area obtained in the experiments are also utilized in validating an analytical approach (i.e. First Analytical Approach) established in the dissertation. / A hypothetical description of the progress of tire deformation is discussed based on the experimental results. The discussion helps in providing a better understanding of the mechanics of the interaction, and for selecting basic analytical and/or numerical tools in establishing the present analytical methods. / In the analytical work, the two distinct analytical approaches (i.e. First and Second Analytical Approaches) are established under the plane strain condition in predicting contact length and pressure. However, the first analytical approach is emphasized in this dissertation, while the second one is rather a complementary work. / In the first analytical approach, the real contact profile is taken into account, while the existing contact theories (by Hertz, Muskhelishvili, etc.) essentially ignore the real kinematics of contact surfaces on which the pattern of pressure distribution greatly depends. In this first analytical approach, the following steps are taken: (1) transform a tire-supporting ground interaction problem into an equivalent free boundary (-value) problem of the deformed supporting ground; this is done so that the complex factors inherent to pneumatic tires are not directly taken into the analytical formulation; (2) determine the modulus of elasticity of the deformed supporting ground by taking into account the contact profile; (3) find the contact length and pressure by means of the complex variable method. / The contact length and pressure analytically obtained are in close agreement with those obtained through experimentation. An attempt has also been made to solve the sliding interaction problems. / The second analytical approach, which is an iterative technique combining the incremental finite element method and the complex variable method, is established fundamentally to solve an interaction problem between an elastic solid and a nonlinear elastic half-plane. Two different types of interaction problems are solved, i.e. tire-clay and rigid wheel-snowpack interactions. Numerical results on contact length for both problems showed acceptable agreement with the experimental results, while those on sinkage obtained for the rigid wheel did not.

This study considers a number of problems which remain in nonlinear consolidation modelling and prediction, despite the considerable research effort which has already been devoted to the subject. Nonlinear consolidation models refer to those models capable of accounting for material nonlinearity either explicitly, in the formulation of the governing equation, or implicitly in the numerical-solution technique. A nonlinear model can be characterised by its generality, appropriateness for modelling consolidation and prediction-capability. These three characteristics are not consistent; a model's superiority with respect to one characteristic does not imply its overall superiority. This inconsistency between the characteristics is resolved by a proposed model. This model is seen as an improvement over two available and widely used models; the Gibson et al. (1967) and Yong et al. (1983) models. / Nonlinear multiple-layer analysis requires the satisfaction of continuity conditions at the inter-layer boundaries. Existing continuity procedures seek to reduce the problem to a tractable single-layer problem, ignore the interaction between layers and are unsuitable for use with nonlinear models. Procedures, based on the trial-function technique, are proposed which satisfy the continuity conditions and facilitate these analyses. Various procedures are necessary to define the initial consolidation status of a soil depending on whether the field data is complete or incomplete. Procedures which can acknowledge incomplete data by calling for bounded analyses and yet can take full advantage of available data are proposed. / A finite-difference numerical-solution algorithm is developed for use with the proposed non-linear model. This algorithm is efficient, versatile and more suitable for multiple-layer analysis than the Yong et al. (1983) algorithm, on which it is based. / The findings of this study are successfully field validated on the basis of three case histories; the consolidation of highly compressible organic soils underlying two embankments in Poland and subsidence due to groundwater withdrawal in Bangkok, Thailand.