Nous étudions un rideau visqueux en écoulement vertical. Un injecteur situé en haut du domaine forme un écoulement ouvert composé d'un liquide visqueux homogène qui s'écoule dans un bain et est accéléré dans son mouvement vertical par l'effet de la gravité. Des zones présentant des taux de contrainte compressifs peuvent apparaître au sein de l'écoulement. Le rideau visqueux est alors susceptible de flamber, perdant sa géométrie plane. Le flambage d'une structure fine et visqueuse a précédemment été étudié dans le contexte d'un écoulement de base présentant une direction d'invariance, ici l'état précontraint est purement bidimensionnel. La modélisation théorique de l'écoulement ouvert prend en compte les effets advectifs. Nous introduirons des outils théoriques et numériques que nous appliquons à un problème classique de la mécanique des solides. Nous utilisons ensuite ces mêmes méthodes pour le rideau tombant. Nous obtenons un modèle de plaque visqueuse dont la cinématique mélange des vitesses et un déplacement hors plan. Les termes membranaires sont inspirés de la mécanique des structures fines et obtenus par l'analogie Stokes-Rayleigh, qui transpose aux écoulements visqueux les notions d'étirement et de flexion d'une plaque. Les équations d'équilibre de flambage étant d'ordre élevé, nous aurons recours à une implémentation numérique particulière. Les effets de la capillarité peuvent être pris en compte dans le modèle et seront étudiés. Nous concluons par une approche théorique de la stabilité de l'écoulement. Nous adaptons une méthode d'analyse des écoulements ouverts instables en cisaillement à l'équilibre de flambage du rideau visqueux. / We consider a vertical sheet made up of an homogeneous viscous fluid and falling into a bath. This curtain is formed by an inlet injecting viscous fluid at the top of the domain and creating an open flow. The resulting thin structure is falling under the effect of gravity, and develops regions of compressive stress. These may lead to a mechanical instability as the sheet can buckle under compression, losing its planar geometry and deforming in the out-of-plane direction.In previous studies, buckling of a viscous sheet that leads to surface wrinkles was associated with flows having a direction of invariance. We will be considering a genuinely two-dimensional stress state.We first introduce stability methods on a simple solid mechanics problem, obtaining equations in weak form and using a finite elements solver to obtain its buckled configurations.We will then study both the modelling of the falling curtain as a viscous membrane and its numerical resolution. We will derive a model with kinematics mixing velocities and displacements and use a viscous membrane model. Inspired by the solid mechanics of thin structures it uses the Stokes-Rayleigh analogy to transpose the concepts of stretching and bending stress to viscous flows. Equations for the out-of-plane equilibrium are of high order and require a specific numerical scheme. Capillary effects can be taken into account in the model and we assess their influence.We finally present a stability analysis hoping to improve our analytical understanding of the buckling phenomenon. We adapt a framework developed for the study of open shear flows instabilities to the out-of-plane equilibrium equations.

This thesis introduces two ortho-planar MEMS devices that can be used to position microcomponents: the XZ Micropositioning Mechanism and the XYZ Micromanipulator. The displacement and force relationships are presented. The devices were fabricated using surface micromachining processes and the resulting mechanisms were tested. A compliant XYZ Micromanipulator was also designed to reduce backlash and binding. In addition, several other MEMS positioners were fabricated and tested: the Micropositioning Platform Mechanism (MPM), the Ortho-planar Twisting Micromechanism (OTM), and the Ortho-planar Spring Micromechanism (OSM).

<p>The focus of this study is on evaluating the performance of nine, one-third scale, arching, reinforced masonry (RM) walls subjected to blast loads and three, one-third scale arching, RM walls subjected to out-of-plane static airbag loads. These RM walls were supported on four sides to enforce two-way arching allowing the ability to monitor individual response to varying levels of blast loads and standoff distances. The uniformity of the blast pressure and impulse were ensured by a specifically designed test enclosure, diminishing the wrap-around and clearing effects, allowing valuable data to be documented. The damage levels noted, ranged from Superficial to Blowout compared directly to the CSA S850-12 performance limits. The outcome of this experiment demonstrates the beneficial effect of two-way arching on the flexural behaviour of RM walls under impulsive loading. The use of two-way arching RM walls significantly reduces structural damage and increases out-of-plane resistance, which in turn enhances the overall structural integrity and building preservation. Further, when subjected to blast, two-way arching RM walls considerably reduces debris and their dispersal, thus increasing public safety and minimizing hazard levels. When using the experimental test data results to calibrate finite element models (FEM), more analytical data points can be obtained and therefore getting a larger range of scaled distances and trials. The validation of the LS-DYNA model can be used as an alternative to the costly experimental data, as the information collected concluded that the FEM gave damage patterns and failure modes that were comparable with experimental results. The test data collected provides a better understanding of RM wall response to blast loads and to the ongoing Masonry Blast Performance Database (MBPD) project at McMaster University. The generated MBPD will in turn contribute to masonry design clauses in the future editions of the recently introduced Canadian Standards CSA S850-12 “Design and Assessment of Buildings Subjected to Blast Loads”.</p> / Master of Applied Science (MASc)

The use of fully grouted reinforced masonry shear walls (RMSWs) has been growing in several areas around the world owing to their relative ease of construction and their in-plane ductile behavior. However, RMSWs possess low out-of-plane ductility which amplifies the vulnerability of such components under blast loading. Furthermore, the long time and high costs of recovery following devastating (deliberate or accidental) explosions have created a need for resilience-based design for risk mitigation, especially considering the different sources of associated uncertainty. As such, this study aims to lay out the foundations of a probabilistic resilience–based blast analysis and design framework. The framework should have the capability of quantifying the overall building post-blast functionality in order to estimate its recovery cost and time, and thus the building resilience following such a demand. The proposed framework will be specifically applied for RMSW buildings incurring blast loads through a profound investigation for the behavior of rectangular RMSWs as being a primary structural element in reinforced masonry buildings. The investigation will subsume an experimental and analytical evaluation for the performance of load-bearing RMSWs with different in-plane ductility levels subjected to out-of-plane quasi-static loading. This will be followed by a numerical investigation of RMSWs to conclude the blast probabilistic performance of RMSWs that can be applied within the proposed probabilistic resilience-based blast framework. The work in this dissertation presents a key step towards adopting resilience based analysis and design in future editions of blast-resistant construction standards and provides the decisionmakers with a complete insight into post-blast building functionality and its recovery. / Thesis / Doctor of Philosophy (PhD)

Thesis (MScEng (Civil Engineering))--Stellenbosch University, 2008. / The Southern African Institute of Steel Construction expressed concern with regard to the unit definition of the effective length factor, K, stipulated for compressive elements of parallel chord trusses in Clause 15 of SANS 10162-1:2005 - Limit state design of hot-rolled steelwork. The simplified method for truss design specified in the code assumes all compression members are pin-connected, which allows for greater design simplicity and reduces the amount of code interpretation required by the designer. In addition to this, Clause 15 requires the additional reduction in resistance of the first web compression members by a factor of 0.85. However, this approach may be considered overly conservative and in current design practice the effective length factor is often reduced to less than 1.0. This research investigates the effective length factor of web compression members in parallel chord trusses, by means of investigative structural analyses of representative trusses using ANGELINE and Prokon analytical programs, and by designing, constructing and testing six representative trusses, using current design practices. A comparative study of a number of different countries’ codified approaches to truss design is also included. The structural analyses revealed that in-plane buckling of the web compression members was the consistent mode of failure, however at a much greater applied load than the design load determined according to SANS 10162-1:2005. Contrary to the expected mode of failure, all six tests performed on the representative trusses exhibited elastic out-of-plane buckling, or strongaxis buckling, of the web compression members, but still at a much greater applied load than the design load. The unexpected out-of-plane buckling of the web members is due to the inplane stiffness of the end connections used. In order to stay true to current design practice, gusset plates and longitudinal welds were used to join the web members to the chords. The stiffness of the gusset plates therefore significantly reduced the effective length of the web compression members in-plane, but did not reduce the effective length out-of-plane. Despite the unanticipated behaviour of the tests performed, certain conclusions can still be drawn from the results. The unit definition of the effective length factor for in-plane buckling of web compression members is too conservative and a K factor of 0.8 is recommended. In addition to this an effective length factor for out-plane-buckling of web compression members of 1.1 is recommended for trusses with welded connections. The necessity of the reduction in resistance of 0.85 of the first web compression members requires further investigation. The most important conclusion to be drawn is that out-of-plane buckling of web compression members can be the dominant failure mode, which is not taken into consideration in current design practice.

Este trabalho apresenta uma teoria de barras não-linear geometricamente exata, com multi-parâmetros para a representação geral de deslocamentos no plano da seção transversal (distorção) e também fora do plano da seção (empenamento). A formulação apresentada constitui-se em uma extensão de trabalhos anteriores, [1] a [6], [8] e [9], no sentido de que a hipótese de seção rígida (Timoshenko) e a função de empenamento elástico de Saint-Venant foram removidos. Essa abordagem define os esforços internos energeticamente conjugados, atuantes na seção transversal, em função de deformações e tensões generalizadas, baseadas no conceito de vetor diretor da seção transversal. Além da importância prática, o uso do vetor diretor simplifica a formulação das equações de equilíbrio e a imposição das condições de contorno, tanto na forma fraca quanto na forma forte do equilíbrio. Além disso, facilita a obtenção da matriz de rigidez tangente, resultando sempre simétrica pra materiais hiper-elásticos e carregamento externo conservativo, mesmo em situações distantes da condição de equilíbrio. Permite também a introdução de graus de liberdade independentes para descrever tanto os deslocamentos no plano quanto fora do plano da seção transversal. Equações constitutivas tri-dimensionais adequadas para problemas com grandes deslocamentos e grandes deformações podem ser implementadas sem a ocorrência de enrijecimentos espúrios. A formulação é absolutamente geral e sua extensão para materiais inelásticos, em particular materiais elasto-plásticos, é imediata uma vez qua a integração de tensões com carregamentos incrementais está disponível. Rotações finitas são tratadas através da expressão de Euler-Rodrigues em uma abordagem puramente Lagrangeana. Assume-se o eixo reto como configuração de referência da barra, porém, barras inicialmente curvas também podem ser consideradas como configurações de referência deformadas, sem tensões iniciais, obtidas a partir de configurações inicialmente retas [11]. É importante ressaltar que a teoria apresentada permite uma modelagem consistente e precisa de distorções da seção transversal, típicas de perfis metálicos esbeltos dobrados a frio. Acredita-se que esta seja uma das principais contribuições dessa formulação como opção ao uso de modelos de cascas. / The main purpose of this work is to present a fully nonlinear geometrically-exact multi-parameter rod model that incorporates general in-plane cross-sectional changes as well as general out-of-plane cross-sectional warping. The formulation constitutes an extension of the earlier works presented in [1] to [6], [8] and [9], in the sense that the restrictions to a rigid cross-section and to a Saint-Venant-like elastic warping are now removed from the theory. Our approach defines energetically conjugated cross-sectional resultants in terms of generalized stresses and strains, based on the concept of a cross-section director. Besides their practical importance, the use of cross-sectional resultants simplifies the derivation of equilibrium equations and the enforcement of boundary conditions, in either weak or strong senses. In addition, the corresponding tangent bilinear weak form is obtained in a more expedient way, rendering always symmetric for hyperelastic materials and conservative loadings (even far from equilibrium states). Definition of a cross-section director plays a central role in the present model. Accordingly, it allows the introduction of independent degrees-of-freedom to describe both the in-plane cross-sectional changes and the out-of-plane warping. Fully three-dimensional finite strain constitutive equations can therefore be employed with no spurious stiffening. The ideas are general and extension to inelastic rods, in particular to those of elastoplastic materials, is straightforward once a stress integration scheme within a time step is at hand. Finite rotations are treated here by the Euler-Rodrigues formula in a pure Lagrangean framework. We assume a straight reference configuration for the rod axis, but initially curved rods can also be considered if regarded as a stress-free deformed state from the straight position (see [11]). The use of convective non-Cartesian coordinate systems is this way avoided and only components on orthogonal frames are employed. Moreover, initial curvatures that are completely independent of the isoparametric concept are possible to be attained, which can be used even in (for example) straight finite elements. Altogether, the present assumptions allow a consistent basis for the proper representation of profile (distortional) deformations, which are typical of coldformed thin-walled rod structures. We believe this is one of the main features of our formulation, as the use of more complex shell models in order to capture such phenomena becomes unnecessary.

Este trabalho apresenta uma teoria de barras não-linear geometricamente exata, com multi-parâmetros para a representação geral de deslocamentos no plano da seção transversal (distorção) e também fora do plano da seção (empenamento). A formulação apresentada constitui-se em uma extensão de trabalhos anteriores, [1] a [6], [8] e [9], no sentido de que a hipótese de seção rígida (Timoshenko) e a função de empenamento elástico de Saint-Venant foram removidos. Essa abordagem define os esforços internos energeticamente conjugados, atuantes na seção transversal, em função de deformações e tensões generalizadas, baseadas no conceito de vetor diretor da seção transversal. Além da importância prática, o uso do vetor diretor simplifica a formulação das equações de equilíbrio e a imposição das condições de contorno, tanto na forma fraca quanto na forma forte do equilíbrio. Além disso, facilita a obtenção da matriz de rigidez tangente, resultando sempre simétrica pra materiais hiper-elásticos e carregamento externo conservativo, mesmo em situações distantes da condição de equilíbrio. Permite também a introdução de graus de liberdade independentes para descrever tanto os deslocamentos no plano quanto fora do plano da seção transversal. Equações constitutivas tri-dimensionais adequadas para problemas com grandes deslocamentos e grandes deformações podem ser implementadas sem a ocorrência de enrijecimentos espúrios. A formulação é absolutamente geral e sua extensão para materiais inelásticos, em particular materiais elasto-plásticos, é imediata uma vez qua a integração de tensões com carregamentos incrementais está disponível. Rotações finitas são tratadas através da expressão de Euler-Rodrigues em uma abordagem puramente Lagrangeana. Assume-se o eixo reto como configuração de referência da barra, porém, barras inicialmente curvas também podem ser consideradas como configurações de referência deformadas, sem tensões iniciais, obtidas a partir de configurações inicialmente retas [11]. É importante ressaltar que a teoria apresentada permite uma modelagem consistente e precisa de distorções da seção transversal, típicas de perfis metálicos esbeltos dobrados a frio. Acredita-se que esta seja uma das principais contribuições dessa formulação como opção ao uso de modelos de cascas. / The main purpose of this work is to present a fully nonlinear geometrically-exact multi-parameter rod model that incorporates general in-plane cross-sectional changes as well as general out-of-plane cross-sectional warping. The formulation constitutes an extension of the earlier works presented in [1] to [6], [8] and [9], in the sense that the restrictions to a rigid cross-section and to a Saint-Venant-like elastic warping are now removed from the theory. Our approach defines energetically conjugated cross-sectional resultants in terms of generalized stresses and strains, based on the concept of a cross-section director. Besides their practical importance, the use of cross-sectional resultants simplifies the derivation of equilibrium equations and the enforcement of boundary conditions, in either weak or strong senses. In addition, the corresponding tangent bilinear weak form is obtained in a more expedient way, rendering always symmetric for hyperelastic materials and conservative loadings (even far from equilibrium states). Definition of a cross-section director plays a central role in the present model. Accordingly, it allows the introduction of independent degrees-of-freedom to describe both the in-plane cross-sectional changes and the out-of-plane warping. Fully three-dimensional finite strain constitutive equations can therefore be employed with no spurious stiffening. The ideas are general and extension to inelastic rods, in particular to those of elastoplastic materials, is straightforward once a stress integration scheme within a time step is at hand. Finite rotations are treated here by the Euler-Rodrigues formula in a pure Lagrangean framework. We assume a straight reference configuration for the rod axis, but initially curved rods can also be considered if regarded as a stress-free deformed state from the straight position (see [11]). The use of convective non-Cartesian coordinate systems is this way avoided and only components on orthogonal frames are employed. Moreover, initial curvatures that are completely independent of the isoparametric concept are possible to be attained, which can be used even in (for example) straight finite elements. Altogether, the present assumptions allow a consistent basis for the proper representation of profile (distortional) deformations, which are typical of coldformed thin-walled rod structures. We believe this is one of the main features of our formulation, as the use of more complex shell models in order to capture such phenomena becomes unnecessary.

The Bistable Aerial Platform (BAP) has been developed in order to further enlarge the repertoire of devices available at the microscale. This novel device functions as a switch in that its platform can lock in two positions, up or down. Herein, it will be examined and explained, but a true understanding of its workings requires a better understanding of its compliant constituent parts. The Helico-Kinematic Platform (HKP), which serves as an actuator for the BAP, is currently under investigation by another researcher and will be merely touched upon here. The focus, therefore, will rest on the analysis of the Quadrantal Bistable Mechanism (QBM), the principle component of the BAP. A preliminary pseudo-rigid-body model, an aid for the understanding of compliant mechanisms, will also be examined for the QBM. The models developed for these two devices, the HKP and QBM, can later be combined to form a full model of the Bistable Aerial Platform.

The advancement in manufacturing technologies to produce high-performing engineered wood products (EWP) has allowed wood to be utilized beyond the traditional low-rise light-frame structures and to become a viable material option for much larger structures. Although glued-laminated timber (glulam) is included as a material option in the current blast code (CSA, 2012), its response to blast loading is not yet well documented. An experimental program investigating the behaviour of seventy glulam beams and columns was developed with focus on establishing the dynamic characteristics of glulam beams and columns with and without the effect of FRP reinforcement. A shock tube capable of simulating high strain rates similar to those experienced during blast was used. Thirty-eight beams with three different cross-sections were tested statically and dynamically to establish the high strain rate effects (dynamic increase factor). Six columns were also tested dynamically with axial load levels ranging from 15 to 75 % of the columns’ compression design capacity. Different retrofit configurations varying from simple tension reinforcement to U-shaped tension reinforcement with confinement using both unidirectional and bi-directional FRP were investigated on a total of twenty-six beams. A procedure capturing the strain-rate effects, variable axial load and FRP, was developed and found to be capable of predicting the flexural behaviour of the beams up to maximum resistance with reasonable accuracy when compared to experimentally obtained static and dynamic resistance curves. Implications on the design of both retrofitted and unretrofitted specimens are also discussed.

No description available.