Force and centre of pressure (COP) were measured during a forward skating task on ice using a standard hockey skate and a modified skate with an altered tendon guard and eyelet configuration which allows for increased dorsiflexion and plantarflexion. The objective of this study was to determine if those skate design changes would result in biomechanical changes in the skaters during forward skating. Both left and right skates were instrumented with a calibrated strain gauge force transducer system to measure forces and with an insole system used to measure the COP during the forward skating task. The modified skate showed a reduction of 14.5-24.3 mm in total anterior-posterior COP excursion (p < .05). This suggests that the modified skate changes the biomechanics of the skaters. However, a full body kinematic study might be needed in order to study the exact biomechanical changes. / La force et le centre de poussée (CDP) ont été mesurés pendant le patinage sur glace en ligne droite en utilisant des patins de hockey standards et des patins de hockey modifiés avec un protecteur du tendon d'Achille plus flexible et une configuration différente des oeillets pour lacets permettant une plus grande dorsiflexion et flexion plantaire de la cheville. Le but de cette étude était de déterminer si ces changements de construction de patins ont une influence sur le mouvement biomécanique des patineurs pendant le patinage sur glace en ligne droite. Les patins gauches et droites ont été instrumentés avec un système d'estimation de la force calibré et avec un système de capteurs de pression en dessous de la semelle pour mesurer le CDP. L'utilisation du patin modifié s'est manifestée par une réduction de 14.5 à 24.3 mm du déplacement total du CDP dans la direction antéro-postérieure (p < .05). Celà suggère que l'utilisation du patin modifié a un effet sur la biomécanique des patineurs. Cependant, une étude cinématique du corps au complet serait peut-être nécéssaire afin d'étudier les changements biomécaniques exacts.

The elastic and plastic behaviour of a wide-flange beam with a large extended opening in the web is investigated theoretically and experimentally for various loading conditions. Two different methods are introduced for calculating the elastic stresses at the boundary of the opening for pure bending and for pure shear. [...]

Several aluminum alloy (Alcan 65S-T) struts of thin-walled open section were tested in compression with concentrically applied loads and using hinged-end supports. The tests were carried out on lipped angles of the same cross-section but of varying length. A range of slenderness ratios from 33.6 to 178.9 was covered and lateral deflections, stresses, and rotations of the struts were measured at intervals in all cases. A comparison was drawn between the experimental results and the failure loads predicted by elastic stability theory. The results were found to be in good general agreement with the computed values for the type of section tested.

Formation and breakup of filaments of liquids is of fundamental importance in established and cutting edge technologies such as ink-jet printing, atomization of coolants in electronic systems, and micro-arraying of DNA. Most of the liquids encountered in these processes have macromolecules (e.g., DNA) which make them viscoelastic. The dynamics of such viscoelastic filaments is analyzed in this thesis using state-of-the-art numerical techniques. A transient flow solver, based on the finite element algorithm of Pasquali and Scriven (2002), is developed and used in the computations. Viscoelasticity is modeled using a single macroscopic variable, the conformation tensor, which is computed by solving a generalized constitutive equation (Pasquali 2000). The dynamics of stretching filaments in the low capillary number regime is analyzed using three different weakly strain hardening models. Among thern, Giesekus filaments show the most drastic necking. The dependence of the transient Trouton ratio on the capillary number in this model is demonstrated. Cohesive necking failure due to elastic unloading in the filaments is investigated using both kinematic (Yao et al. 1998) and energy arguments. The thinning in the Giesekus filaments is aided by the elastic unloading, which increases with growing elasticity. The analysis of pinch-off of viscoelastic filaments, to date, relied on simple one-dimensional approximations. In this work, two-dimensional analysis o fpinch-off of FENE-P filaments is conducted for the first time. Scalings of physical variables calculated near pinch-off accord with asymptotic theoretical results. The liquid-gas interface in the neck region of low viscosity FENE-P filaments overturn before breakup when the Ohnesorge number, suitably redefined with the maximum extensional viscosity, is lower than a critical value. A multi-scale algorithm, in which viscoelasticity is modeled using an ensemble of Brownian configuration fields (Hulsen et al. 1997), is developed to solve axisymmetric free surface flows. The new method reproduces filament stretching results with Hookean dumbbells, within statistical error bars, when compared with equivalent macroscopic calculations. Inclusion of hydrodynamic interactions reduces the extension of the dumbbells thereby decreasing the growth of extensional stresses in the filaments.

This dissertation considers a general concept of nonconservative measures of dynamic system performance via a consistent approach in terms of signal and system norms and suggests an appropriate iterative procedure for reduction of conservatism in the design of active structural control systems. This reduction is accomplished by introducing two modified variants of the H$\sb2$-norm leading to less conservative system performance criteria than the conventional H$\sb2$-norm-based performance indices. These modifications make both the stochastic and the deterministic control design specifications less conservative and, at the same time, retain all the benefits of the standard H$\sb2$-norm. In view of model uncertainties, the standard H$\sb2$-method alone (as, virtually, all existing control strategies) may lead to arbitrarily small stability margins. On the contrary, the modern H$\sb\infty$-control method can handle the robust stability problem but cannot guarantee an admissible nominal performance. In the context of robustly stable control design, the dissertation considers the general mixed H$\sb2$/H$\sb\infty$-control problem that is stated as a reduction of the H$\sb2$-norm of one transfer function under a constraint in terms of the H$\sb\infty$-norm of another transfer function. As a solution for this problem, the dissertation introduces a new H$\sb2$/H$\sb\infty$ nested control synthesis which combines the advantages of the both standard control methods. An important practical application of the nested control synthesis to active structural control design, such as control for an optimal H$\sb2$-norm-based performance with guaranteed robust stability, is considered. An iterative algorithm which incorporates a less conservative H$\sb2$-norm-based performance measure into the nested synthesis is introduced. The H$\sb2$/H$\sb\infty$ nested synthesis employs the idea of Youla parametrization of all H$\sb2$-suboptimal controllers. The state-space formulae of a parametrized controller can be obtained in terms of the solutions of two modified Riccati equations. In the new formulation the explicit state-space formulae of the full parametrization are specially derived for the most general case when the traditionally accepted simplifying assumptions are relaxed.

The permanent deformation of a rigid perfectly-plastic beam subjected to a time-dependent line load is calculated. The beam has finite length, and the load is applied transversely in the middle of the span. At the initial time, the load is zero; thereafter, it increases linearly, reaches a maximum value, and then decreases linearly to zero. For sufficiently large values of the applied load, there is a plastic hinge moving along the beam. The system of nonlinear ordinary differential equations that governs the motion of the hinge is solved numerically. After the plastic deformation has taken place, the beam appears as a bent curve that translates in the direction of the applied load. Formulas for the permanent deformation of the beam are obtained, and curves are presented to illustrate the results.

A numerical study of natural convection in cavities under the effects of thermocapillarity and gravity modulation is conducted in this research. Three different algorithms which are first-order explicit, second-order Taylor-Galerkin and semi-implicit schemes based on the projection finite element method (FEM) are developed. Each algorithm presents its own characteristics and advantages. By considering the problem characteristics and computational efficiency, the semi-implicit method is a better choice for this research. In this thesis, the physical investigation of cavity natural convection with augmenting or counteracting effects is divided into four parts. At first, the cavity flow with buoyancy force and thermocapillary effect is studied for different Marangoni numbers and aspect ratios. Next, the Benard convection with gravity modulation effects in normal gravity and zero-g gravity is investigated. The natural convection flow exhibits dramatically different flow structure under the influence of different modulation directions and frequencies. In addition, the natural convection with combined thermocapillarity and gravity modulation is explored for different modulation directions, frequencies and Marangoni numbers. Finally, the cavity natural convection flow with a deformable free surface is analyzed for different Grashof numbers and Marangoni numbers. Results of this research show that the surface tension provides a strong influence in the natural convection flow in both normal gravity and microgravity states. Particularly, the low aspect ratio and microgravity environments favor the development of thermocapillary-driven flow. On the other hand, the existence of gravity modulation makes the flow field different from the constant gravity state by applying different modulation directions and frequencies. The simultaneous presence of thermocapillarity and g-jitter creates a dramatically different flow pattern when compared to the results had without thermocapillary effect. When a deformable free surface is considered, the flow field and heat transfer rate at the corners of free surface are changed due to the deformation of free surface shape.

The preferential orientation for the initiation or extension of a crack is the one which gives the maximum strain energy reduction for a given crack length. This criterion is based on the concept of maximum energy release rate, and makes no assumptions on the configuration, the homogeneity, the stress condition on the crack faces, or the material response. Consequently it is valid under the usual engineering conditions as well as under compression and high confining pressures such as obtain inside the Earth; in the latter case it replaces the empirical and approximate Coulomb-Mohr criterion. The mathematical formulation of the criterion is approached by way of constrained optimization, and the solution is proven to exist uniquely. The numerical implementation is based on a finite element scheme. An iterative method is employed to handle the material and geometric non-linearity. Test cases agree with laboratory and field data.

Mixed finite element discritizations for problems arising in flow in porous medium applications are considered. We first study second order elliptic equations which model single phase flow. We consider the recently introduced expanded mixed method. Combined with global mapping techniques, the method is suitable for full conductivity tensors and general geometry domains. In the case of the lowest order Raviart-Thomas space, quadrature rules reduce the method to cell-centered finite differences, making it very efficient computationally. We consider problems with discontinuous coefficients on multiblock domains. To obtain accurate approximations, we enhance the scheme by introducing Lagrange multiplier pressures along subdomain boundaries and coefficient discontinuities. This modification comes at no extra computational cost, if the method is implemented in parallel, using non-overlapping domain decomposition algorithms. Moreover, for regular solutions, it provides optimal convergence and discrete superconvergence for both pressure and velocity. We next consider the standard mixed finite element method on non-matching grids. We introduce mortar pressures along the non-matching interfaces. The mortar space is chosen to have higher approximability than the normal trace of the velocity spaces. The method is shown to be optimally convergent for all variables. Superconvergence for the subdomain pressures and, if the tensor coefficient is diagonal, for the velocities and the mortar pressures is also proven. We also consider the expanded mixed method on general geometry multiblock domains with non-matching grids. We analyze the resulting finite difference scheme and show superconvergence for all variables. Efficiency is not sacrificed by adding the mortar pressures. The computational complexity is shown to be comparable to the one on matching grids. Numerical results are presented, that verify the theory. We finally consider the mixed finite element discretizations for the nonlinear multi-phase flow system. The system is reformulated as a pressure and a saturation equation. The methods described above are directly applied to the elliptic or parabolic pressure equation. We present an analysis of a mixed method on non-matching grids for the saturation equation of degenerate parabolic type.

The dynamic response of stiffness degrading models subjected to random excitations is investigated. Monte Carlo simulation is performed to determine the effect on the response of various system parameters and to provide results for testing the applicability of approximate analytical techniques. The principal focus is on the single degree of freedom Clough model for reinforced concrete structures with white excitations lasting eight nominal periods of the structure. A heuristic equivalent linearization method is proposed to estimate the response of degrading structures through approximate analysis. The equivalent linear stiffness and damping at any time are computed from certain weighted averages of the secant stiffness and the hysteretic energy dissipation associated with limiting hysteresis loops corresponding to the maximum amplitude at that time. The drift component of the displacement is not treated explicitly, but is approximately accounted for by assigning appropriate weighting functions in this scheme. The equivalent linear coefficients are expressed as functions of some measure of the maximum response statistics and are modified at specified increments of time. The problem of predicting such maximum response statistics is also investigated for the simpler process representing the nonstationary response of linear structures. An approximate method is developed and compared with two existing approximate methods. The new method is found to yield reasonably accurate estimates of the mean and the variance of the response maximum with significant improvements in computational efficiency as compared to simulation. The applicability of a closure approach for finding the response of degrading models is also investigated. A modified Gaussian closure procedure is shown to yield good approximations for two simpler problems which embody some aspects of the Clough model: the maximum value problem for linear systems, and the random response of bilinear hysteretic structures. For the Clough model also, this technique has been applied successfully.