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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.)

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Interaction between rigid and flexible track-grouser systems with a clay soil is examined in order to obtain a better understanding of the manner in which energy is transferred and dissipated in the bearing soil substrate. Analytical framework is developed for the establishment of the kind of mechanisms involved in this interaction with a view to obtaining a rational prediction of track-soil performance. / The method of visioplasticity is used to determine the specific participants contributing to the expenditure of energy at different soil levels beneath a simple representative multiple grouser element. Subsoil reponse behaviour and dissipated energy components are investigated for different grouser shapes, spacings, displacements, and flexibility boundary conditions. / A predictive model is established for the off-road track performance prediction based on the principle of energy conservation for the entire track/grouser-soil system. This energetic model provides successful predictions which are in good agreement with the experimentally measured performance of a full track model at various degrees of slip.

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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.

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