Call number: LD2668 .T4 1966 K78 / Master of Science

published_or_final_version / Mechanical Engineering / Master / Master of Science in Engineering

Finite element formulation based on compatible, assumed displacement fields and the principle of stationary potential energy is applied to analyze edge-stiffened plates. Shear deformation is considered in the formulation of the plate bending and beam bending elements by allowing independent interpolation for displacements and rotations. In addition to bending deformation, plane stress action is superposed on the plate element, while torsion and axial deformation are incorporated in the beam element, so that structural interaction between plate and edge beam elements can be facilitated. By enforcing compatible displacements and rotations across the interface between plate and beam elements, the degrees-of-freedom in one element can be related to the degrees-of-freedom of the adjoining element of a different type. Accordingly, the stiffness matrix and equivalent load vector are transformed to correspond to the common degrees-of-freedom as a result of invariance of the potential energy. By means of the direct stiffness method, the global equilibrium equation is thus established and solved by a frontal solution subroutine. Special features are introduced into the solution subroutine in order to handle varying degrees-of-freedom per node in an element and multiple loading cases. In addition, the speed of input-output transfer between in-core and peripheral storage is optimized. Convergence studies on displacements and stresses show that the current formulation with the program is capable of analyzing shear-flexible structures. The formulation allows convergence of shear-rigid solutions as a limiting case by making use of the selective reduced integration scheme when formulating individual elements. Graphs are presented to aid the design of edge-stiffened plates with two adjacent edges clamped and others cast with intersecting edge beams.

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The idea of creating a material or barrier that attenuates shock and blast waves has long been investigated. Considerable work has been performed on the interactions of shock and blast waves with various materials. The application of permeable solids, porous materials and textiles for the attenuation and reflection of destructive shock waves have been studied extensively. The studies presented herein examine the interaction of shock waves and porous plates in order to ameliorate the hazardous effects of these waves particularly in ducts or channels leading to protected areas or objects. A number of tests were performed in an automated shock tube to determine the effects that a series of directional porous plates had on the initial peak pressure and impulse amelioration experienced by the end wall. Mild steel test specimens, ranging in porosity values from 6.6 % to 41.1 %, were mounted two at a time in the test section of the shock tube. Each plate had directional properties and since four plates were used in the study, a total of forty eight plate configurations were tested. Six pressure transducers were located along the side of the test section and two pressure transducers were located in the end wall of the shock tube in order to measure initial peak pressure and impulse amelioration values experienced by the end wall and to identify the wave interactions involved in the amelioration process. Schlieren photographs were also taken in order to investigate these wave interactions. Tests were run at three different Mach numbers viz. 1.23, 1.35 and 1.42. The separation distances between the plate specimens were varied between 30 mm and 60 mm; however the distance between the downstream plate and the end wall was kept constant at 140mm for all tests. It was found that significant initial peak pressure and impulse amelioration was achievable. The Back & Back plate arrangement produced the greatest initial peak pressure and impulse amelioration with averages values of 73.7 % and 20.45 % respectively. Both the initial peak pressure and impulse amelioration values were found to be dependant on the plate combination porosity. As the porosity of the combination increased, the amelioration values decreased. Complementary plate combinations produced differing results as different wave interactions occur when plate positions were interchanged. The porosity of the combined plates were found to have an overriding influence on the end wall initial peak pressure and impulse amelioration values when compared to the effect that plate arrangement (i.e. geometrical influences) had. For all tests performed in this study, the time period used for the integration of the end wall pressure traces was 9 250 μs. As an acceptable closing time for a blast valve in a shelter’s ventilation system is approximately 4 000 μs, the impulse amelioration values for certain plate combinations were recalculated. It was found that using this time period greater impulse amelioration values were produced as the rate of pressure rise, dp/dt, was initially lower at the beginning of the end wall pressure trace. Therefore, the lowest impulse amelioration value (7.9 %) achieved in this study, would produce significant impulse amelioration (20.3 %) if it were to be used in a shelter’s ventilation system. Impulse amelioration values were found to increase as the separation distance between v plates were increased. The average impulse amelioration value was found to increase approximately 1 % for a 15mm increase in the distance between plates. The amplitude of the entire end wall pressure trace was found to increase as the incident Mach number was increased. This resulted in greater initial peak pressure and impulse experienced by the end wall. The significant attenuation of the incident shock wave obtained during this study is attributed to the system of multiple reflected and transmitted waves that are produced by the presence of the plate specimens in series. This increases the frequency of shock wave and barrier interactions, when compared to just using a single barrier, creating regions of highly unsteady flow, especially in the air space between the plate specimens. Furthermore, the presence of the series of plates also allows for wave resonance to occur which may further attenuate the strength of the incident shock wave. It is suggested that future studies include numerical techniques in order to further investigate the complex wave processes that occur upon interaction with the plate specimens and confirm the major loss mechanisms of the system.

The aim of this thesis is to propose a more general understanding of the influence of the thickness of the plate and of the microstructural and mechanical properties of the material on the resistance to ductile tearing in thin metallic plates. The objective is to attempt unifying different observations made in the literature together with the results of a new extensive experimental campaign. The final goal is to develop predictive simulation tools with a micromechanics-based foundation. In order to reach this objective, a detailed experimental campaign has been performed concerning the fracture behavior of the aluminium alloy 6082, complemented by experiments on a stainless steel A316L and on a set of 14 other materials. In a first modelling effort, we propose very simple closed-form models in order to separate the different contributions to the total work of fracture in thin plates: the work of necking and the work of damage and material separation. The respective contributions are compared and an unique explanation of the different behaviors observed experimentally is proposed. In a second modelling step, we develop a full 3D numerical tool based on cohesive elements for simulating crack propagation in thin ductile plates. Three different methods are proposed to calibrate the parameters of the model in order to reproduce the experimental data and to extrapolate the results to other material properties or geometric conditions. Finally, the parameters of the cohesive zone model are justified using micromechanics-based arguments. / Le but de cette thèse est de proposer un modèle général à base micromécanique permettant de comprendre l’influence de l’épaisseur de la tôle ainsi que de la microstructure et des propriétés mécaniques du matériau sur la résistance à la rupture ductile de plaques minces métalliques. L’objectif est d’essayer d’unifier les différentes observations de la littérature ainsi que les résultats d’une nouvelle campagne expérimentale afin d’aboutir au développement d’outils numériques prédictifs. Pour atteindre cet objectif, nous avons réalisé une campagne d’essais concernant le comportement à la rupture de différents matériaux. Cette campagne a été menée en profondeur sur l’alliage d’aluminium 6082 et de manière moins approfondie sur un acier inoxydable A316L ainsi que sur 14 autres matériaux. Dans un premier temps, nous présentons une série de modèles semi-analytiques simples dont le but est de séparer les différentes contributions au travail de rupture total dans les tôles minces : le travail de striction et le travail d’endommagement du matériau. Ces deux contributions sont ensuite comparées et nous proposons une explication qui reprend les différents comportements observés expérimentalement. Dans un deuxième temps, nous développons un outil numérique 3D complet destiné à simuler la propagation de fissures dans les tôles minces ductiles et qui utilise des éléments cohésifs. Trois méthodes différentes sont proposées pour calibrer les paramètres du modèle de manière à reproduire les données expérimentales et à permettre l’extrapolation des résultats à d’autres matériaux ou d’autres épaisseurs de tôles. Finalement, les paramètres du modèle de zone cohésive sont justifiés grâce à des arguments à fondement micromécanique.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 68-73).

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy