Tesi sul tema "Of plates"

Settling basins can be shortened by using a stack of horizontal parallel plates which develop boundary layers in which sedimentation can occur. The purpose of this study is to examine the design parameters for such a system and to apply this approach to a fish rearing channel in which settling length is strictly limited. Flow between parallel rough and smooth plates has been modelled together with sediment concentration profile. Accurate description of boundary layer flow requires the solution of Navier-Stokes equations, and due to the complexity of the equations to be solved for turbulent flow some assumptions are made to relate the Reynolds stresses to turbulent kinetic energy and turbulent energy dissipation rate. The simplified equations are solved using a numerical method which uses the approach given by the TEACH code. The flow parameters obtained from the turbulent flow model are used to obtain the sediment concentration profile within the settling plates. Numerical solution of the sedimentation process is obtained by adopting the general transport equation. The lower plate is assumed to retain sediments reaching the bottom. The design of a sedimentation tank for a fish rearing unit with high velocity of flow has been investigated. The effectiveness of the sedimentation tank depends on the uniformity of flow attained at the inlet, and experiments were conducted to obtain the most suitable geometric system to achieve uniform flow distribution without affecting other performances of the fish rearing unit. The main difficulties to overcome were the heavy circulation present in the sedimentation tank and the clogging of the distributing system by suspended particles. Several distributing systems were investigated, the best is discussed in detail. It was concluded that a stack of horizontal parallel plates can be used in fish rearing systems where space is limited for settling sediments. Flow distribution along the vertical at the entrance to the plates determines the efficiency of the sediment settling process and a suitable geometrical configuration can be constructed to distribute the high velocity flow uniformly across the vertical. Numerical modelling of sediment removal ratio for flow between smooth and rough parallel plates has been calculated. The results show that almost the same pattern of sediment deposition occurs for both the smooth-smooth and rough-smooth plate arrangements.
Applied Science, Faculty of
Civil Engineering, Department of
Graduate

Orientadores: Marcio de Moraes, Luciana Asprino
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Odontologia de Piracicaba
Made available in DSpace on 2018-08-13T02:18:28Z (GMT). No. of bitstreams: 1 Lyrio_MarianaCamiloNegreiros_M.pdf: 2393437 bytes, checksum: f0dfbf68baaeb080347c83445d15e1e9 (MD5) Previous issue date: 2009
Resumo: O propósito neste estudo foi realizar avaliação mecânica e fotoelástica de dois diferentes sistemas de fixação interna rígida (FIR): placas convencionais e placas com sistema de travamento. Para avaliação mecânica foi realizado teste de carregamento linear em réplicas de hemimandíbulas humanas dentadas seccionadas na região de ramo mandibular, representando uma osteotomia sagital, e fixadas com avanço mandibular de 5 mm. No grupo I a fixação foi realizada com placas convencionais e parafusos monocorticais do sistema 2,0mm e no grupo II utilizou-se placas e parafusos monocorticais com sistema de travamento do sistema 2,0 mm. Para análise estatística foram aplicados Anova e teste de Tukey em nível de significância de 5%, os quais demonstraram não haver diferenças entre os grupos I e II nos testes mecânicos. Para os testes fotoelásticos foram confeccionadas hemimandíbulas humanas dentadas em resina fotoelástica, também seccionadas simulando a osteotomia sagital e fixadas com avanço mandibular de 5 mm, com os mesmos grupos utilizados para os testes mecânicos. Em relação à distribuição de tensões, pode-se observar que as mesmas se concentram ao redor dos parafusos, principalmente naqueles próximos à área de osteotomia para ambos os grupos. Dessa forma, pode-se afirmar que os sistemas de fixação utilizando placa e parafusos convencionais ou com sistema de travamento não apresentaram diferenças estatísticas quanto à resistência, e que a maior concentração de forças está nas áreas próximas às osteotomias, consideradas regiões de maior fragilidade após a OSRM.
Abstract: The aim of this study was evaluate the mechanical and photoelastic behavior of two methods of rigid internal fixation (RIF): conventional plates and locking plates. For mechanical tests polyurethane synthetic hemimandible with seccional sagittal ramus split was used, simulating an advancement of 5 mm. The fixation performed on the Group I was a 2.0 mm conventional plates with monocortical screws and fixation used on group II was a 2.0 locking plates with monocortical locking screws. Anova and Tukey tests were applied (P<5) and no statistical differences were noted between the groups. Hemimandibles were made in photoelastic resin with same groups used in mechanical tests and submitted to photoelastical analysis. In relation to tension distribution in photoelastic analysis, the fringes were concentrated around screws, mainly in areas near the osteotomy for both groups. Based in this fact, the conventional and locking fixations systems did not present statistical differences on resistence, and the major forces was concentrated in regions near the osteotomies lines, that considered fragility before sagittal split osteotomy.
Mestrado
Cirurgia e Traumatologia Buco-Maxilo-Faciais
Mestre em Clínica Odontológica

The prediction of sound and vibration transmission in built-up structures is important for human comfort, health and safety. For structural reasons, engineering structures often incorporate periodic ribbed plates to increase stiffness and stability whilst reducing the weight. However, vibration propagation on periodic ribbed plates is complex due to the existence of stop/pass bands. This thesis is concerned with predicting vibration transmission between isotropic, homogeneous plates and periodic ribbed plates. The objectives are to investigate the use of Statistical Energy Analysis (SEA) and develop and validate advanced SEA (ASEA) using ray tracing to incorporate tunnelling mechanisms. Two approaches were considered for modelling the periodic ribbed plate: either representing it as a single subsystem or representing each bay as a single subsystem in the high-frequency range (above the fundamental local mode of the bay). In the low-frequency range (below the fundamental local mode of the bay) Finite Element Methods (FEM) and laboratory experiments show that the periodic ribbed plate can be adequately modelled in SEA using wave approaches from periodic structure and orthotropic plate theories. In the high-frequency range a significant decrease in energy along successive bays was identified using FEM leading to the conclusion that it is not appropriate to model a periodic plate as a single subsystem. SEA models were therefore investigated that treated each bay as an individual subsystem using wave theory. For different L-junctions formed from an isotropic, homogeneous plate and a periodic ribbed plate, SEA significantly underestimated the response in the bays. Experimental SEA (ESEA) was used to investigate these discrepancies which confirmed the existence of tunnelling mechanisms between physically unconnected subsystems. In contrast to SEA which gave errors up to 60 dB for the furthest bay from the junction, ASEA gave errors less than 6 dB when the mode count for the bay was greater than five. A range of two- and three- plate structures with different periodic ribbed plates or periodic folded plate have been modelled with ASEA. The results all lead to the conclusion that ASEA can successfully incorporate tunnelling mechanisms and provide a significantly more accurate approach to predicting high-frequency vibration transmission across periodic ribbed plates than SEA.

This thesis describes both round-pore microchannel plates (MCPs) used in energetic pho¬ton and particle detectors and their square-pore offspring, micropore optics (MPOs), used to focus x-rays. A Monte Carlo electron raytracing software package is described that is used to predict the energy and angular distribution of electrons (EDOE and ADOE) in a microchannel electron multiplier's output charge cloud, including saturated operation. The model is shown to agree with experimental evidence. The addition of a micromachined electrostatic lens to the end of a microchannel is modelled and found to have no beneficial effects upon the EDOE and ADOE of the channel. The current state of the art planar and slumped 'lobster eye' square-packed MPOs are evaluated. The best focus (5' FWHM) from a large format (61mm x 56mm), small chan¬nel (10μm side length) planar MPO is reported, together with the observation of high energy (~50keV →65keV) x-ray focusing from large (500:1) aspect ratio channels. The alignment of many small lobster eye MPOs to create a large optic for the Lobster-ISS instrument is discussed and the alignment jig constructed for this purpose is used to measure the bias angles of a Lobster specification MPO. The bias angle is found to be 4 ± 1.5'. The concept of the microchannel conic approximation to the Wolter type I and II x- ray lenses is reviewed. A radially-packed twin MPO Wolter approximation is then tested, which while of poor quality, demonstrates true Wolter II imaging with a peak gain greater than unity. Currently proposed (UK) astronomical instruments that employ MPOs are then discussed in the light of the results from the current generation of MPOs.

This report describe the wear of the protruding areas on the sides of the grate plates in the grate-kiln process in the hematite pellet production in LKAB, Kiruna. The steel plates are exposed to a hostile environment with heat cycles and corrosive atmosphere. An evaluation of the plates was made in co-operation with LKAB Metlab in Luleå and LKAB mechanical workshop in Kiruna. Instruments used are stereomicroscope, LOM, SEM, Spectroscope, Vickers Hardness and a surface nish meter. Results show the protruding areas of the plates are exposed to a tribochemical wear, where tops of the rough areas are torn down. A coating test is carried out at Tribolab, LTU in Luleå, using an SRV. Samples with a wear and corrosion resistant coating called Diamalloy 4276 abrade against eachother at high temperature and pressure. The coating do help to resist wear, but the environment of the test is to unrealistic to say by certain that it will help in the grate. A FEM-model in COMSOL Multiphysics 4.4 is made to calculate thermal stresses between coating and metal, the result show stresses up to 1 GPa will occur, this can be explain by the big dierence in thermal expansion coefficients of the materials. It will probably create cracks in the coating surface. Two solutions are presented, a coating is not recommended. The tribochemical wear is decreased by using a better surface nish. Therefore one can either machine the areas by drilling or milling, or one can change the casting method. Today sand casting is used, by using shell casting or precision casting, for example Shaw process, the surface nish is better over the whole plate, which also is better for corrosion resistance since less initiation points exist.
Denna rapport presenterar en undersökning av slitaget på sidorna av grateplattor som används i gratekilnprocessen i hematitpelletstillverkningen på LKAB i Kiruna, även lösningar presenteras. Plattorna benner sig i en svår miljö med termiska cykler och korrosiva substanser. Utvärderingen av slitaget gjordes i samarbete med LKAB Metlab i Luleå och LKAB mekaniska verkstad i Kiruna. Utrustning som användes var Stereomikroskop, LOM, SEM, Spektroskop, Vickers hårdhetsmätare och ytnhetsmätare. Resultatet visar att sidorna av plattorna utsetts för ett tribokemiskt slitage där toppar av den grova utan slits ner. Ett ytbeläggningstest utfördes på Tribolab, LTU i Luleå, med en SRV. Prover med en beläggning har gnidits mot varandra under tryck och hög temperatur och jämförts med prover utan beläggning som utsattes för samma test. Ytbeläggningen som används står främst emot korrosion, men även slitage, den kallas Diamalloy 4276. Resultatet visar att beläggningen skyddar bra mot slitage, men miljön under testet var för orealistiskt för att med säkerhet kunna säga att det kommer hjälpa i graten. En FEM-modell gjordes med hjälp av COMSOL Multiphysics 4.4 för att beräkna de termiska spänningarna som uppstår mellan ytbeläggningen och metallen. Resultatet visar att spänningar på upp till 1 GPa kommer uppstå, detta kan förklaras med den stora skillnaden i termisk utvidgningskoecient mellan de två materialen. De höga spänningarna kan skapa sprickor i ytan. Två lösningar presenteras, en ytbeläggning rekommenderas inte i dagsläget. Det tribokemiska slitaget kan motverkas genom att förbättra ytnheten. Detta kan antingen utföras genom att bearbeta ytan, med fräsning eller slipning, eller att man byter gjutningsmetod. Idag används manuell formtillverkning, om man istället skulle använda skalformsgjutning eller precisionsgjutning, till exempel Shawprocessen, skulle man få en bättre ytnhet över hela plattan. Detta leder även till bättre korrosionsbeständighet då färre initieringspunkter nns.

This study developed an automated approach to understand plume and plate boundary interactions over time, investigating how flat slab and porphyry development are linked to formation mechanisms of major eastern Pacific Large Igneous Provinces (LIPs). Our method allows us to detail how the Shatsky-Hess conjugate collided with North America from 85 Ma, with the subducting front corresponding to porphyry development and matching divisions between shallow and flat slab areas. Our new formation model for the Enigma Ridge, conjugate to the Tuamotu Plateau, resolves problems for development of the Peruvian Flat Slab and the Nazca ridge, with porphyry deposits formed at the eastern tip or sides of the Enigma Ridge. We infer development of the metallogenically significant Juan Felix LIP by identifying the importance of overprinting relationships between plume trails and the potential effect of slow spreading on LIP size and note that it corresponds to the Altiplano Flat Slab, with related deposits forming between 44 Ma and 31 Ma. While deposits mainly form at the front of the flat slab or along its margins, deposits form to the north and south of the San Felix and Juan Fernandez plume trails between 36 Ma to 29 Ma. We provide an explanation for a previously unexplained set of deposits in SAM (64 to 51 Ma age), relating them to the collision of a San Felix-MOR interaction. We investigated the controversy over whether plumes may affect tectonic and metallogenic development at subduction zones or are instead suppressed or destroyed by descending flow and find that while plumes do survive relatively close interaction with a subduction zone, if they cross that zone then it takes tens of millions of years to re-establish themselves or they do not survive the interaction. Plumes identified in the geological record by non-tomographic methods, such as the Manus plume, may have either died or become temporarily suppressed by crossing a subduction zone.

Due to high specific strength and stiffness as well as outstanding energy-absorption characteristics, sandwich structures are extensively used in aircraft, aerospace, automobile, and marine industries. With the objective of finding lightweight blast-resistant sandwich structures for protecting infrastructure, we have found, for a fixed areal mass density, one- or two-core doubly-curved sandwich shell's (plate's) geometries and materials and fiber angles of unidirectional fiber-reinforced face sheets for it to have the maximum first failure load under quasistatic (blast) loads. The analyses employ a third-order shear and normal deformable plate/shell theory (TSNDT), the finite element method (FEM), a stress recovery scheme (SRS), the Tsai-Wu failure criterion and the Nest-Site selection (NeSS) optimization algorithm, and assume the materials to be linearly elastic. For a sandwich shell under the spatially varying static pressure on the top surface, the optimal non-symmetric one-core (two-core) design improves the first failure load by approximately 33% (27%) and 50% (36%) from the corresponding optimal symmetric design with clamped and simply-supported edges, respectively. For a sandwich plate under blast loads, it is found that the optimal one-core design is symmetric about the mid-surface with thick face sheets, and the optimal two-core design has a thin middle face sheet and thick top and bottom face sheets. Furthermore, the transverse shear stresses (in-plane transverse axial stresses) primarily cause the first failure in a core (face sheet). For the computed optimal design under a blast load, we also determined the collapse load by using the progressive failure analysis that degrades all elasticities of the failed material point to very small values. The collapse load of the clamped (simply-supported) sandwich structure is approximately 15%–30% (0%–17%) higher than its first failure load. Incompressible materials such as rubbers, polymers, and soft tissues that can only undergo volume preserving deformations have numerous applications in engineering and biomedical fields. Their vibration characteristics are important for using them as wave reflectors at interfaces with a fiber-reinforced sheet. In this work we have numerically analyzed free vibrations of plates made of a linearly elastic incompressible rubber-like material (Poison's ratio = 0.5) by using a TSNDT for incompressible materials and the mixed FEM. The displacements at nodes of a 9-noded quadrilateral element and the hydrostatic pressure at four interior nodes are taken as unknowns. Computed results are found to match well with the corresponding either analytical or numerical ones obtained with the commercial FE software Abaqus and the 3-dimensional linear elasticity theory. The analysis discerns plate's in-plane vibration modes. It is found that a simply supported plate admits more in-plane modes than the corresponding clamped and clamped-free plates.
Doctor of Philosophy
A simple example of a sandwich structure is a chocolate ice cream bar with the chocolate layer replaced by a stiff plate. Another example is the packaging material used to protect electronics during shipping and handling. The intent is to find the composition and the thickness of the "chocolate layer" so that the ice cream bar will not shatter when dropped on the floor. The objective is met by enforcing the chocolate layer with carbon fibers and then finding fiber materials, their alignment, ice cream or core material, and its thickness to resist anticipated loads with a prescribed level of certainty. Thus, a sandwich structure is usually composed of a soft thick core (e.g., foam) bonded to two relatively stiff thin skins (e.g., made of steel, fiber-reinforced composite) called face sheets. They are lightweight, stiff, and effective in absorbing mechanical energy. Consequently, they are often used in aircraft, aerospace, automobile, and marine industries. The load that causes a point in a structure to fail is called its first failure load, and the load that causes it to either crush or crumble is called the ultimate load. Here, for a fixed areal mass density (mass per unit surface area), we maximize the first failure load of a sandwich shell (plate) under static (dynamic) loads by determining its geometric dimensions, materials and fiber angles in the face sheets, and the number (one or two) of cores. It is found that, for a non-uniformly distributed static pressure applied on the central region of a sandwich shell's top surface, an optimal design that has different materials for the top and the bottom face sheets improves the first failure load by nearly 30%-50% from that of the optimally designed structure with identical face sheets. For the structure optimally designed for the first failure blast load, the ultimate failure load with all of its edges clamped (simply supported) is about 15%-30% (0%-17%) higher than its first failure load. This work should help engineers reduce weight of sandwich structures without sacrificing their integrity and save on materials and cost. Rubberlike materials, polymers, and soft tissues are incompressible since their volume remains constant when they are deformed. Plates made of incompressible materials have a wide range of applications in everyday life, e.g., we hear because of vibrations of the ear drum. Thus, accurately predicting their dynamic behavior is important. A first step usually is determining natural frequencies, i.e., the number of cycles of oscillations per second (e.g., a human heart beats at about 1 cycle/sec) completed by the structure in the absence of any externally applied force. Here, we numerically find natural frequencies and mode shapes of rubber-like material rectangular plates with different supporting conditions at the edges. We employ a plate theory that reduces a 3-dimensional (3-D) problem to a 2-D one and the finite element method. The problem is challenging because the incompressibility constraint requires finding the hydrostatic pressure as a part of the problem solution. We show that the methodology developed here provides results that match well with the corresponding either analytical or numerical solutions of the 3-D linear elasticity equations. The methodology is applicable to analyzing the dynamic response of composite structures with layers of incompressible materials embedded in it.

Dans cette thèse on étudie la géométrie systolique des variétés de Bieberbach. La \emph{systole} d'une variété riemannienne compacte et non simplement connexe $(M^n,g)$ est l'infimum des longueurs des courbes fermées non contractiles; le \emph{rapport systolique} est le quotient $(\mathrm{systole})^n/\mathrm{volume}$. Un résultat fondamental de Gromov assure que si $M^n$ est essentielle, il existe une constante $c(M)$ strictement positive telle que, pour toute métrique $g$ sur $M^n$: $Vol(M,g) \geq c(M) Sys(M,g)^n$. Les surfaces compactes autres que $S^2$ sont essentielles, et le théorème de Gromov est une généralisation profonde des mêmes résultats pour le tore $T^2$ (C. Loewner), pour le plan projectif (M. Pu) et pour la bouteille de Klein (C. Bavard). Pour ces variétés la constante $c(M)$ est bien connu mais en dimension supérieure, on ne connait pratiquement rien en dehors de l'existence de cette constante. Nous nous intéressons aux variétés de Bieberbach de dimension 3, c'est à dire aux variétés compactes de dimension 3 qui portent une métrique riemannienne plate, qui ne sont pas des tores et démontrons que les métriques plates ne sont pas optimales pour le rapport systolique.

This paper presents the investigation of the nonlinear eigenvalue problem describing free vibrations of plates with elastically attached masses. We study properties of eigenvalues and eigenfunctions and prove the existence theorem. Theoretical results are illustrated by numerical experiments.

Classical methods for solving plate buckling problems involve using different forms of solution on case by case basis. In place of this approach, This thesis presents a novel single form equation and the parameters required to account for the interaction of geometry, boundary conditions and different forms of edge load distribution. The thesis also presents more results for different combination of plate edge boundary conditions than can be found in most design manuals such as the ESDD. The method presented is titled 'Parametric Buckling Analysis (PBA),. It combines a number of concepts in a heuristic manner to achieve the single form solution proposed. Among the concepts is an extension of the Euler column buckling boundary condition coefficients to represent various possible plate edge boundary conditions. The geometry parameter introduced reflects the combined effect of plate aspect ratio and the number of buckle waves. The load parameter introduces a regularising factor that allows the effect of different load distribution forms to be included in the equation. The method is tested on flat plates of different rectangular, triangular, evolutive trapezoidal shapes and on slightly curved plates with cylindrical geometries. Eighteen (18) different combinations of free, simple and clamped edges boundary conditions were considered. Uniform and linearly varying edge stress loading conditions were also considered. The results obtained arc compared with those obtained using analytical and finite element analysis. Excellent agreement is obtained in most cases. Possible causes of discrepancies are highlighted in the other cases. The PBA method is useful and will save time in the pre-sizing buckling design analysis of structures especially in the aerospace industry. This stage is usually followed by detailed analysis using finite clement or other numerical techniques. When programmed PBA should prove easier to use by desigoel1' than existing manuals such as the ESDU because of its unified formula approach.

In this paper, we examine a method on how to model and produce Chladni Figures. We walk through how a thin metal plate, when vibrating at certain frequencies, can create various interest patterns. First we discuss the equation for the vertical force exerted on the plate, then we derive a PDE to solve for the nodal lines (lines that remain fixed, while the rest of the plate is oscillating). And, discuss how to create and model these figures, through a finite difference method. There have been several experiments on Chladni Figures, using some sort of vibrating membrane or plate and then either through the use of a speaker or a violin bow, produce frequencies in order to resonate with the membrane. These eigenvalue solutions can been physically observed by putting sand on the plate and vibrating it. We will approximate theses figures, calculate the convergence of the approximation, and relate the generated figures to figures produced in experiments.

Perforated plates are quite often used as a means of engineering noise control to reduce the sound radiated by structures. However, there appears to be a lack of representative models to determine the sound radiation from a perforated plate. The aim of this thesis is to develop such a model that can be used to give quantitative guidance corresponding to the design and effectiveness of this noise control measure. Following an assessment of various models for the radiation efficiency of an unbaffled plate, Laulagnet’s model is implemented. Results are calculated and compared with those for baffled plates. From this, simple empirical formulae are developed and give a very good agreement with the analytical result. Laulagnet’s model is then modified to include the effect of perforation in terms of a continuously distributed surface impedance to represent the holes. This produces a model for the sound radiation from a perforated unbaffled plate. It is found that the radiation efficiency reduces as the perforation ratio increases or as the hole size reduces. An approximate formula for the effect of perforation is proposed which shows a good agreement with the analytical calculation up to half the critical frequency. This could be used for an engineering application to predict the noise reduction due to perforation. The calculation for guided-guided boundary conditions shows that the radiation efficiency of an unbaffled plate is not sensitive to the edge conditions. It is also shown that perforation changes the plate bending stiffness and mass and hence increases the plate vibration. The situation is also considered in which a perforated unbaffled plate is located close to a reflecting rigid surface. This is established by modifying the Green’s function in the perforated unbaffled model to include an imaginary source to represent the reflected sound. The result shows that the presence of the rigid surface reduces the radiation efficiency at low frequencies. The limitation of the assumption of a continuous acoustic impedance is investigated using a model of discrete sources. The perforated plate is discretised into elementary sources representing the plate and also the holes. It is found that the uniform surface impedance is only valid if the hole distance is less than an acoustic wavelength for a vibrating rectangular piston and less than half an acoustic wavelength for a rectangular plate in bending vibration. Otherwise, the array of holes is no longer effective to reduce the sound radiation. Experimental validation is conducted using a reciprocity technique. A good agreement is achieved between the measured results and the theoretical calculation for both the unbaffled perforated plate and the perforated plate near a rigid surface.

This thesis deals with reliability analysis of laminated composite plates subjected to transverse lateral pressure loads. Input parameters to strengths of the plates such as applied transverse lateral pressure loads, elastic moduli, geometric and ultimate strength values of the plates are treated as basic design variables, and specific probability distributions are applied to them to take into account the variability nature of these basic design variables. Based on the statistical information on the basic design variables, these variables are pseudo-randomly generated in accordance with the corresponding probability distributions by using statistical sampling techniques. Generated random values of the basic design variables corresponding to the applied loads, elastic moduli and geometric values are substituted into various laminated plate theories which can accommodate different lamination schemes and boundary conditions to assess the probabilistic strengths of the plates. The limit state equations are developed by using maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, Hoffman and Azzi-Tsai-Hill failure criteria. Calculated probabilistic plate strengths and generated random values of the ultimate strength basic design variables of the plates are substituted into the developed limit state equations to define the failure or survival state of the plates. In solving the limit state equations, structural reliability techniques are adopted and evolved appropriately for the reliability analysis of the plates. Developed reliability analysing algorithms are applied to laminated plates from experiment to check its validity. Finally, the EUROCOMP Design Code is compared with the developed reliability analysis procedures by applying the both approaches to the strengths of laminated plates.

In the simulation of deformations of plates it is well known that we have to use a special treatment of the thickness dependence. Therewith we achieve a reduction of dimension from 3D to 2D. For linear elasticity and small deformations several techniques are well established to handle the reduction of dimension and achieve acceptable numerical results. In the case of large deformations of plates with non-linear material behaviour there exist different problems. For example the analytical integration over the thickness of the plate is not possible due to the non-linearities arising from the material law and the large deformations themselves. There are several possibilities to introduce a hypothesis for the treatment of the plate thickness from the strong Kirchhoff assumption on one hand up to some hierarchical approaches on the other hand.

The strength and behavior of gusset plates in buckling is evaluated herein based on data from the experimental investigations conducted by other researchers and the analytical work presented herein. A set of design guidelines has been recommended through the review of the current practice. Representative single and double brace gusset plates normally adopted for connections with compressive bracing/diagonal members in braced frames and trusses, were modeled and analyzed using linear and nonlinear finite element methods to determine the buckling loads. The buckling analysis data along with the test data indicated the occurrence of inelastic buckling of the gusset plates. Current design practice and a set of formulas for determination of gusset plate thickness have been reviewed. A set of guidelines has been recommended for the design and evaluating gusset plate buckling loads.

Bibliography: leaves 94-96.
This primarily experimental investigation describes a series of experiments on fully-clamped circular plates, rectangular beams and stiffened circular plates. These test specimens were subjected to a uniformly distributed impulse. The impulse was provided by plastic explosive. This was arranged in such a way that a uniformly distributed impulse was imparted to the test specimens. The impulse was measured by means of a ballistic pendulum to which the test specimens were attached. The final mid-point deflections of the plates and beams were measured. The plate and beam results were compared to previous experimental work. A non-dimensional number for plates was modified to include an experimental mass scaling factor due to the ballistic pendulum mass. A non-dimensional number for rectangular beams was developed, including a similar experimental mass scaling factor. Comparing the beam and plate results from this study with those of previous work, using the respective non-dimensional numbers, showed good correlation. The results for the stiffened plates are compared with the plate results.

The present thesis describes research on quasi-static and low velocity perforation of rolled aluminium plates, where the main objective has been to gain a better knowledge of the physical processes taking place during this type of structural problem. The objective has been met by a combination of laboratory tests, material modelling and non-linear finite element simulations.

The thesis is organized in a synopsis, giving a brief introduction to the problem and summarising the main findings and conclusions, in addition to four independent papers.

Paper I presents an experimental technique for measuring the deformations the plate undergoes during impact and perforation. This information can be used to validate numerical models and to increase the understanding of how energy is absorbed by the plate.

Paper II presents an experimental and numerical investigation on the quasi-static perforation of AA5083-H116 aluminium plates. In the tests, square plates were mounted in a circular frame and penetrated by a cylindrical punch. A full factorial design was used to investigate the effects of varying plate thickness, boundary conditions, punch diameter and nose shape. Based on the obtained results, both the main and interaction effects on the maximum force, displacement at fracture and energy absorption until perforation were determined. The perforation process was then computer analysed using the nonlinear finite element code LS-DYNA. Simulations with axisymmetric elements, brick elements and shell elements were conducted. Slightly modified versions of the Johnson-Cook constitutive relation and fracture criterion were used to model the material behaviour. It was shown that the FEM models were able to predict the trends observed in experiments.

Paper III evaluates methods for determination of the anisotropic properties of polycrystalline metallic materials. Four calibration methods were evaluated for the linear transformation-based anisotropic yield function YLD2004-18p (Barlat et al., 2005) and the aluminium alloy AA5083-H116. The different parameter identifications are based on least squares fits to combinations of uniaxial tensile tests in seven directions with respect to the rolling direction, compression (upsetting) tests in the normal direction and stress states found using the full-constraint (FC) Taylor model for 690 evenly distributed strain paths. An elastic-plastic constitutive model based on YLD2004-18p has been implemented in a non-linear finite element code and used in finite element simulations of plane-strain tension tests, shear tests and upsetting tests. The experimental results as well as the Taylor model predictions can be satisfactorily reproduced by the considered yield function. However, the lacking ability of the Taylor model to quantitatively reproduce the experiments calls for more advanced texture models.

Paper IV presents an experimental and numerical investigation on low velocity perforation of AA5083-H116 aluminium plates. In the tests, square plates were mounted in a circular frame and penetrated by a cylindrical blunt-nosed projectile. The perforation process was then computer analysed using the nonlinear finite element code LS-DYNA, in order to investigate the effects of anisotropy, dynamic strain aging and thermal softening in low velocity impacts on the present aluminium alloy. Dynamic strain aging has been shown to influence both the predicted force level and fracture, while thermal softening only influences the fracture prediction. No effect of plastic anisotropy was observed.

Ballistic testing is a vital part of the armor design. However, it is impossible to test every condition and it is necessary to limit the number of tests to cut huge costs. With the intro- duction of hydrocodes and high performance computers
there is an increasing interest on simulation studies to cutoff these aforementioned costs. This study deals with the numerical modeling of ballistic impact phenomena, regarding the ballistic penetration of hardened steel plates by 7.62 mm AP (Armor Piercing) projectile. Penetration processes of AP projectiles are reviewed. Then, a survey on analytical models is given. After the introduction of fun- damentals of numerical analysis, an intensive numerical study is conducted in 2D and 3D. Johnson Cook strength models for the four different heat treatments of AISI 4340 steel were constructed based on the dynamic material data taken from the literature. It was found that 2D numerical simulations gave plausible results in terms of residual projectile velocities, con- sidering the literature review. Then, 3D numerical simulations were performed based on the material properties that were selected in 2D studies. Good agreement was obtained between the numerical and test results in terms of residual projectile velocities and ballistic limit thick- nesses. It was seen that the ballistic protection efficiency of the armor plates increases with the increasing hardness, in the examined range. This study is a part of T¨
ubitak project 106M211 of MAG.

This research is concerned with analytical modelling of the effects of cracks in structural plates and panels within aerospace systems such as aeroplane fuselage, wing, and tail-plane structures, and, as such, is part of a larger body of research into damage detection methodologies in such systems. This study is based on generating a so-called reduced order analytical model of the behaviour of the plate panel, within which a crack with some arbitrary characteristics is present, and which is subjected to a force that causes it to vibrate. In practice such a scenario is potentially extremely dangerous as it can lead to failure, with obvious consequences. The equation that is obtained is in the form of the classical Duffing equation, in this case, the coefficients within the equation contain information about the geometrical and mass properties of the plate, the loading and boundary conditions, and the geometry, location, and potentially the orientation of the crack. This equation has been known for just over a century and has in the last few decades received very considerable attention from both the analytical dynamics community and also from the dynamical systems researchers, in particular the work of Ueda, Thompson, in the 1970s and 1980s, and Thomsen in the 1990s and beyond. An approximate analytical solution is obtained by means of the perturbation method of multiple scales. This powerful method was popularized in the 1970s by Ali H.Nayfeh, and discussed in his famous books, ‘Perturbation Methods’ (1974) and ‘Nonlinear Oscillations’ (1979, with D.T.Mook), and also by J.Murdock (1990), and M.P.Cartmell et al. (2003) and has been shown to be immensely useful for a wide range of nonlinear vibration problems. In this work it is shown that different boundary conditions can be admitted for the plate and that the modal natural frequencies are sensitive to the crack geometry. Bifurcatory behaviour of the cracked plate has then been examined numerically, for a range of parameters. The model has been tested against experimental work and against a Finite Element model, with good corroboration from both. In all events, this is a significant new result in the field and one that if implemented within a larger damage detection strategy, could be of considerable practical use.

In this thesis we report on a system of colloidal plates and spheres developed to model the key particles found in paint and other industrial formulations. From theories of mixtures of particles of different shapes and sizes one would expect entropic phase sep- aration to occur at sufficiently high volume fractions, due to the gains in free volume. An aqueous system consisting of synthetic nano-gibbsite Al(OHh plates and alumina coated silica nano-spheres were sterically stabilized with a commercial stabiliser in wa- ter to create near-hard particle interactions. The stabilizer was chosen, by using in the first instance an NMR spin-spin relaxation technique. This gave a pseudo-adsorption isotherm. This technique was complemented with electrophoresis and elemental anal- ysis. The addition of the stabilizer to the suspension of plates modified the kinetics of the isotropic-nematic phase formation, with larger domains forming than in a surfac- tant free system. Colloidal plate-sphere mixtures were investigated using small-angle neutron scattering (SANS), optical microscopy (polarising and differential interference contrast). In SANS,' for dilute suspensions using contrast matching, the addition of colloidal plates to colloidal spheres showed an increase in density fluctuations of the spheres, which agreed well with theoretical predictions. The birefringence of the sys- tems was also observed in order to study the isotropic-nematic (I-N) transition. On adding spheres, the I-N transition occurs at a lower platelet concentration. The impact of the plate __ ~(Ls