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A Comparison Between Two-Dimensional and Three-DimensionalAnalysis, A Review of Horizontal Wood Diaphragms and a Case Study of the Structure Located at 89 Shrewsbury Street, Worcester, MAJohnson, Robert A 30 April 2008 (has links)
A two-dimensional structural analysis design approach has been the universally accepted method for a small structural engineering design firm. The tools to perform the analysis have been paper and pencil, calculators and more recently personal computers with two-dimensional software. With the introduction of three-dimensional software, a major shift is occurring on how small structural engineering firms approach analysis and design. This thesis research reviews the analysis of an existing building utilizing the standard two-dimensional approach, including horizontal diaphragm-action within wood floors. This study also reviews the research performed on horizontal diaphragms and investigates the use of three-dimensional, finite element modeling (RISA-3D) for the analysis of horizontal diaphragms. It is shown that the three-dimensional model can provide results similar to the two-dimensional hand calculations. However, the thickness of the diaphragm elements has to be significantly modified for flexible diaphragm action. The experience described herein is useful for structural engineer interfacing within three-dimensional CAD systems. The thesis concludes with a discussion on the challenges facing small structural engineering firms, including computer based technologies, engineering expertise to develop contract documents and review shop drawings, and outsourcing of design services.
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Symbolic dimensioning in computer-aided designLight, Robert Allan January 1980 (has links)
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 89-90. / by Robert Allan Light. / M.S.
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Contribució a l'estudi de l'efecte del canvi d'escala en l'experimentació en incendis forestalsPérez Ramírez, Yolanda 20 May 2010 (has links)
Any rere any milions d'hectàrees són destruïdes pels incendis forestals, no només a Europa sinó arreu del món, tan sols cal recordar els dramàtics episodis viscuts a Califòrnia i Austràlia recentment. A banda de l'evident impacte mediambiental que això provoca -emissió de gasos d'efecte hivernacle, pèrdua de biodiversitat, acceleració de l'erosió del sòl, etc.- els incendis són també un problema social de primer ordre, que posa en perill a les persones i els seus béns. Davant d'aquesta situació, en les darreres dècades s'ha impulsat fortament la recerca en l'àmbit dels incendis forestals. Tanmateix, l'estudi dels incendis forestals és certament complex per les condicions i l'entorn on aquests es desenvolupen, a banda també del gran nombre de fenòmens -físics, químics i socials- que interaccionen al llarg de diferents escales espacials i temporals, per a donar lloc a l'inici i propagació del foc. És per això que bona part de la recerca sobre el comportament dels incendis forestals ha tingut lloc bàsicament al laboratori, tot i que qüestions com ara com traslladar aquests resultats experimentals als incendis reals, o bé fins a quin punt aquest tipus d'experimentació és útil o què és el que realment es pot extrapolar i què no, no han tingut encara cap resposta clara.L'objectiu d'aquesta tesi ha estat doncs el de contribuir a l'estudi del canvi d'escala en l'experimentació en incendis forestals pel què fa al comportament del foc, mitjançant les tècniques de l'anàlisi dimensional i de semblança. En primer lloc s'ha realitzat una extensa revisió bibliogràfica centrada bàsicament en aquells treballs que havien aplicat d'alguna manera o altra l'anàlisi dimensional i de semblança a l'estudi dels incendis i en particular dels incendis forestals. S'ha vist que no es possible realitzar un escalatge complet d'aquest fenomen i que el més utilitzat ha estat l'escalatge de Froude. A més s'ha detectat que mai abans s'ha aplicat aquest tipus d'anàlisi als models que s'utilitzen normalment avui dia en l'experimentació de laboratori. A continuació s'ha fet doncs una anàlisi exhaustiva de totes les variables que determinen el comportament d'un incendi forestal en els diferents escenaris experimentals (de laboratori i de camp). A partir d'aquestes variables s'ha realitzat una anàlisi dimensional per a estudiar la propagació d'un front de flames -tan bàsic com en condicions de vent i pendent- així com una anàlisi de semblança que ha permès obtenir les lleis d'escala per a les diferents variables que caracteritzen la propagació d'un incendi forestal. S'ha dissenyat i executat un programa experimental al laboratori amb l'objectiu de validar si es complien les lleis d'escala trobades i de determinar-ne el rang de validesa i les possibles causes en cas que no es complissin.Els resultats obtinguts han mostrat que per a fronts de flama bàsics propagant-se sense vent ni pendent, totes les variables analitzades segueixen les lleis d'escala derivades de l'estudi teòric, en el rang de longituds de front de flama abraçat que va dels 25 cm als 3 m. Nogensmenys cal remarcar que paràmetres com la humitat i el tipus de combustible o les característiques de la instal·lació experimental utilitzada poden alterar enormement els resultats si no es controlen adequadament. En el cas dels fronts de flama propagant pendent amunt, els resultats han mostrat que les lleis d'escala de la geometria de flama es compleixen per a tot el rang de pendents estudiat que va de 0 fins a 30°, mentre que en el cas de la llei d'escala de la velocitat de propagació deixa de complir-se per a pendents de 30°. Finalment, en el cas dels fronts de flama propagant en condicions de vent, els resultats han mostrat que per a velocitats del vent superiors a aproximadament 2,5 m/s les lleis d'escala tant de la velocitat de propagació com de la geometria de flama deixen de complir-se.Al final d'aquest treball s'apunten les causes que poden conduir a l'incompliment de les lleis d'escala així com als factors que poden restar validesa als experiments efectuats a escala de laboratori, quan es vol extrapolar els resultats a escales més grans o fins i tot a incendis reals. / Year after year millions of hectares are destroyed by wildland fires, not only in Europe but all over the world; just remember the dramatic episodes recently occurred in California or Australia. Besides the evident environmental impact caused by these fires -emission of greenhouse gases, biodiversity loss, soil erosion, etc- wildland fires represent also a social problem of primary order that threatens human life and their assets.Because of this situation, during the last decades research on wildland fires has been greatly boosted. Nevertheless, the study of forest fires is really complex due to the conditions and the environment in which they develop and to the number of phenomena -physical, chemical and social- that interact all along the different spatial and temporal scales that give rise to the start and development of a fire. That is partly the reason because the study of wildland fire behaviour has mainly been developed in laboratories, but questions like how these experimental results can be translated to real fires?, or is really this kind of experimentation useful?, or what can be extrapolated? These questions have not yet received a clear answer.The goal of this work was to improve the knowledge on the effect of changing the scale in the experimental study of forest fire behaviour, by means of dimensional and similarity analysis. First an extended bibliographic review has been done, centred on those works that had applied in one or another way the dimensional and similarity analysis to the study of fires and more specifically to forest fires. It was observed that it is not possible to undergo a complete scaling of a forest fire and that the most used partial scaling technique was the Froude scaling. Moreover it was detected that this kind of analysis was never before applied to the laboratory models used currently to obtain experimental data on wildland fires. Thus, an exhaustive analysis of all the variables affecting forest fire behaviour has been carried out for the diverse experimental scenario (in the lab and field). From these variables, a complete dimensional analysis has been developed in order to study the spread of a flames front -both in basic conditions and with slop or wind- and a subsequent similarity analysis has provided the scaling laws governing all the variables under study. A complete experimental program has been designed and developed in the laboratory with the aim of validating the scaling laws previously found and to establish the possible causes of any failure of the laws. The results obtained show that in the case of a basic flame front, spreading under no wind and no slope conditions, all the variables analysed followed the scaling laws obtained during the theoretical study for flames front lengths ranging from 25 cm to 3 m. For the tests under slop conditions, the results indicate that the scaling laws corresponding to the flame geometry are verified for all the slopes tested which range from 0 to 30°, while in the case of the rate of spread scaling law is no longer verified for the 30° slope. Finally, in the case of flame fronts spreading under wind conditions, the results show that for wind speed values greater than 2,5 m/s neither of the scaling laws corresponding to the flame geometry and the rate of spread, are verified. It has also been observed that parameters such as moisture content, the type of fuel or the specific design of the experimental device used can have a big influence on the results obtained if they are not adequately controlled.At the end of this work, the main causes leading to the failure of the scaling laws are pointed out together with the factors that can make the laboratory experiments less reliable when trying to extrapolate the results to larger scales or even to real fires.
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Conjunctive Management of Surface Water and Groundwater ResourcesAbu Rumman, Malek 18 April 2005 (has links)
Surface water and groundwater systems consist of interconnected reservoirs, rivers, and confined and unconfined aquifers. The integrated management of such resources faces several challenges:
High dimensionality refers to the requirement of the large number of variables that need to be considered in the description of surface water and groundwater systems. As the number of these variables increases, the computational requirements quickly saturate the capabilities of the existing management methods.
Uncertainty relates to the imprecise nature of many system inputs and parameters, including reservoir and tributary inflows, precipitation, evaporation, aquifer parameters (e.g., hydraulic conductivity and storage coefficient), and various boundary and initial conditions. Uncertainty complicates very significantly the development and application of efficient management models.
Nonlinearity is intrinsic to some physical processes and also enters through various facility and operational constraints on reservoir storages, releases, and aquifer drawdown and pumping. Nonlinearities compound the previous difficulties.
Multiple objectives pertain to the process of optimizing the use of the integrated surface and groundwater resources to meet various water demands, generate sufficient energy, maintain adequate instream flows, and protect the environment and the ecosystems. Multi-objective decision models and processes continue to challenge professional practice.
This research draws on several disciplines including groundwater flow modeling, hydrology and water resources systems, uncertainty analysis, estimation theory, stochastic optimization of dynamical systems, and policy assessment. A summary of the research contributions made in this work follows:
1.High dimensionality issues related to groundwater aquifers system have been mitigated by the use of transfer functions and their representation by state space approximations.
2.Aquifer response under uncertainty of inputs and aquifer parameters is addressed by a new statistical procedure that is applicable to regions of relatively few measurements and incorporates management reliability considerations.
3.The conjunctive management problem is formulated in a generally applicable way, taking into consideration all relevant uncertainties and system objectives. This problem is solved via an efficient stochastic optimization method that overcomes dimensionality limitations.
4.The methods developed in this Thesis are applied to the Jordanian water resources system, demonstrating their value for operational planning and management.
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Constitutive modeling of viscoelastic behavior of bituminous materialsMotamed, Arash 10 March 2014 (has links)
Asphalt mixtures are complex composites that comprise aggregate, asphalt binder, and air. Several research studies have shown that the mechanical behavior of the asphalt mixture is strongly influenced by the matrix, i.e. the asphalt binder. Therefore, accurate constitutive models for the asphalt binders are critical to ensure accurate performance predictions at a material and structural level. However, researchers who use computational methods to model the micromechanics of asphalt mixtures typically assume that (i) asphalt binders behave linearly in shear, and (ii) either bulk modulus or Poisson’s ratio of asphalt binders is not time dependent. This research develops an approach to measure and model the shear and bulk behavior of asphalt binders at intermediate temperatures. First, this research presents the findings from a systematic investigation into the nature of the linear and nonlinear response of asphalt binders subjected to shear using a Dynamic Shear Rheometer (DSR). The DSR test results showed that under certain conditions a compressive normal force was generated in an axially constrained specimen subjected to cyclic torque histories. This normal force could not be solely attributed to the Poynting effect and was also related to the tendency of the asphalt binder to dilate when subjected to shear loads. The generated normal force changed the state of stress and interacted with the shear behavior of asphalt binder. This effect was considered to be an “interaction nonlinearity” or “three dimensional effect”. A constitutive model was identified to accommodate this effect. The model was successfully validated for several different loading histories. Finally, this study investigated the time-dependence of the bulk modulus of asphalt binders. To this end, poker-chip geometries with high aspect ratios were used. The boundary value problem for the poker-chip geometry under step displacement loading was solved to determine the bulk modulus and Poisson’s ratio of asphalt binders as a function of time. The findings from this research not only improve the understanding of asphaltic materials behavior, but also provide tools required to accurately predict pavement performance. / text
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TESTING SMALL-SCALE AND FULL-SCALE LIQUID-TO-AIR MEMBRANE ENERGY EXCHANGERS (LAMEEs)2014 February 1900 (has links)
A liquid-to-air membrane energy exchanger (LAMEE) is a novel flat-plate membrane-based energy exchanger where heat and moisture transfer between air and solution streams occurs through a semi-permeable membrane. The LAMEE consists of many air and solution flow channels, each separated by a membrane. A small-scale single-panel LAMEE consists of a single pair of neighboring air and solution channels. This PhD thesis focuses on developing, testing and modeling the small-scale single-panel LAMEE, and investigating the similarity between the small-scale LAMEE and a full-scale LAMEE. This PhD thesis presents a methodology to investigate similarity between small-scale and full-scale energy exchangers.
A single-panel energy exchanger test (SPEET) facility is developed and built to measure the performance of the small-scale single-panel LAMEE under different test conditions. Also, the small-scale LAMEE is numerically modeled by solving coupled heat and mass transfer equations for the air, solution and membrane of the LAMEE. The effects of membrane vapor diffusion resistance and enhanced air side convective heat transfer coefficient are numerically investigated. The numerical model of the small-scale LAMEE is validated with the experimental data for summer test conditions, and effectiveness values agree within ±4% in most cases. Moreover, the effects of different heat and mass transfer directions, and salt solution types and concentrations are experimentally and numerically investigated. The results show that the LAMEE effectiveness is strongly affected by the heat and mass transfer directions but negligibly affected by salt solution type and concentration.
The solution-side effectiveness for liquid-to-air membrane energy exchangers is introduced in this thesis for the first time. The results show that the solution-side effectiveness should be used to evaluate the sensible and total effectiveness of LAMEE regenerators. Finally, the similarity between the small-scale and full-scale LAMEEs is investigated experimentally and numerically. The results show that the small-scale LAMEE effectiveness results can be used to predict the performance of a full-scale LAMEE within ±2% to ±4% in most cases.
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A Study of the Cutting Performance in Abrasive Waterjet Contouring of Alumina Ceramics and Associated Jet Dynamic CharacteristicsLiu, Hua January 2004 (has links)
Abrasive waterjet (AWJ) cutting is one of the most recently developed nontraditional manufacturing technologies. It has been increasingly used in industry owing to its various distinct advantages over the other cutting technologies. However, many aspects of this technology require to be fully understood in order to increase its capability and cutting performance as well as to optimize the cutting process. This thesis contains an extensive literature review on the investigations of the various aspects in AWJ machining. It shows that while considerable work has been carried out, very little reported research has been found on the AWJ contouring process although it is a common AWJ cutting application. Because of the very nature of the AWJ cutting process, the changing nozzle traverse direction involved in AWJ contouring results in kerf geometrical or shape errors. A thorough understanding of the AWJ contouring process is essential for the reduction or elimination of these shape errors. It also shows that a lack of understanding of the AWJ hydrodynamic characteristics has limited the development of cutting performance models that are required for process control and optimization. Accordingly, a detailed experimental investigation is presented in this thesis to study the various cutting performance measures in AWJ contouring of an 87% alumina ceramic over a wide range of process parameters. For a comparison purpose, the study also considers AWJ straight-slit cutting. The effects of process parameters on the major cutting performance measures in AWJ contouring have been comprehensively discussed and plausible trends are amply analysed. It finds that the taper angles on the two kerf walls are in different magnitudes in AWJ contouring. The kerf taper on the outer kerf wall increases with the arc radius (or profile curvature), while that on the inner kerf wall decreases. Moreover, the depth of cut increases with an increase in arc radius and approaches the maximum in straight cutting for a given combination of parameters. The other process variables affect the AWJ contouring process in a way similar to that in straight cutting. The analysis has provided a guideline for the selection of process parameters in the AWJ contouring of alumina ceramics. In order to predict the cutting performance in process planning and ultimately optimize the cutting process, mathematical models for the major cutting performance measures in both straight-slit cutting and contouring are developed using a dimensional analysis technique. The models are then verified by assessing both qualitatively and quantitatively the model predictions with respect to the corresponding experimental data. It shows that the models can adequately predict the cutting performance measures and form the essential basis for developing strategies for selecting the optimum process parameters in AWJ cutting. To achieve an in-depth understanding of the jet dynamic characteristics such as the velocity and pressure distributions inside a jet, a Computational Fluid Dynamics (CFD) simulation is carried out using a Fluent6 flow solver and the simulation results are validated by an experimental investigation. The water and particle velocities in the jet are obtained under different input and boundary conditions to provide an insight into the jet characteristics and a good understanding of the kerf formation process in AWJ cutting. Various plausible trends and characteristics of the water and particle velocities are analysed and discussed, which provides the essential knowledge for optimizing the jet performance through optimizing the jetting and abrasive parameters. Mathematical models for the water and particle velocity distributions in an AWJ are finally developed and verified by comparing the predicted jet characteristics with the corresponding CFD simulation data. It shows that the jet characteristics models can yield good predictions for both water and particle velocity distributions in an AWJ. The successful development of these jet dynamic characteristics models is an essential step towards developing more comprehensive mathematical cutting performance models for AWJ cutting and eventually developing the optimization strategies for the effective and efficient use of this advanced manufacturing technology.
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Modelling the cutting process and cutting performance in abrasive waterjet machining with controlled nozzle oscillationXu, Shunli January 2006 (has links)
Abrasive waterjet (AWJ) cutting is one of the most recently developed manufacturing technologies. It is superior to many other cutting techniques in processing various materials, particularly in processing difficult-to-cut materials. This technology is being increasingly used in various industries. However, its cutting capability in terms of the depth of jet penetration and kerf quality is the major obstruction limiting its further applications. More work is required to fully understand the cutting process and cutting mechanism, and to optimise cutting performance. This thesis presents a comprehensive study on the controlled nozzle oscillation technique aiming at increasing the cutting performance in AWJ machining. In order to understand the current state and development in AWJ cutting, an extensive literature review is carried out. It has found that the reported studies on controlled nozzle oscillation cutting are primarily about the use of large oscillation angles of 10 degrees or more. Nozzle oscillation in the cutting plane with such large oscillation angles results in theoretical geometrical errors on the component profile in contouring. No published attempt has been found on the study of oscillation cutting under small angles although it is a common application in practice. Particularly, there is no reported research on the integration of nozzle oscillation technique into AWJ multipass cutting, which is expected to significantly enhance the cutting performance. An experimental investigation is first undertaken to study the major cutting performance measures in AWJ single pass cutting of an 87% alumina ceramic with controlled nozzle oscillation at small angles. The trends and characteristics of cutting performance quantities with respect to the process parameters as well as the science behind which nozzle oscillation affects the cutting performance have been analysed. It has been shown that as with oscillation cutting at large angles, oscillation at small angles can have an equally significant impact on the cutting performance. When the optimum cutting parameters are used for both nozzle oscillation and normal cutting, the former can statistically increase the depth of cut by 23% and smooth depth of cut by 30.8%, and reduce kerf surface roughness by 11.7% and kerf taper by 54%. It has also been found that if the cutting parameters are not selected properly, nozzle oscillation can reduce some major cutting performance measures. In order to correctly select the process parameters and to optimise the cutting process, the mathematical models for major cutting performance measures have then been developed. The predictive models for the depth of cut in both normal cutting and oscillation cutting are developed by using a dimensional analysis technique. Mathematical models for other major cutting performance measures are also developed with the aid of empirical approach. These mathematical models are verified both qualitatively and quantitatively based on the experimental data. The assessment reveals that the developed models conform well to the experimental results and can provide an effective means for the optimum selection of process variables in AWJ cutting with nozzle oscillation. A further experimental investigation of AWJ cutting of alumina ceramics is carried out in order to study the application of AWJ oscillation technique in multipass cutting. While high nozzle traverse speed with multipass can achieve overall better cutting performance than low traverse speed with single pass in the same elapsed time, it has been found that the different combination of nozzle traverse speed with the number of passes significantly affects cutting process. Optimum combination of nozzle traverse speed with the number of passes is determined to achieve maximum depth of cut. It has also demonstrated that the multipass cutting with low nozzle traverse speed in the first pass and a comparatively high traverse speed for the following passes is a sensible choice for a small kerf taper requirement. When nozzle oscillation is incorporated into multipass cutting, it can greatly increase the depth of cut and reduce kerf taper. The predictive models for the depth of cut in both multipass normal cutting and multipass oscillation cutting are finally developed. With the help of dimensional analysis, the models of the incremental cutting depth for individual pass are derived based on the developed depth of cut models for single pass cutting. The models of depth of cut for a multipass cutting operation are then established by the sum of the incremental cutting depth from each pass. A numerical analysis has verified the models and demonstrated the adequacy of the models' predictions. The models provide an essential basis for the development of optimization strategies for the effective use of the AWJ cutting technology when the multipass cutting technique is used with controlled nozzle oscillation.
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High fidelity open rotor noise predictionThomas, Paul Huw January 2017 (has links)
As improving the performance of turbofan designs becomes increasingly difficult, manufacturers are looking to new technologies for the next generation of jet engines. An 'open rotor' replaces the fan of the turbofan with a set of external rotors. This has the potential to offer a significant improvement in propulsive efficiency, but the design for low noise is a key challenge. Hence, high fidelity noise prediction methods are needed to accurately predict and compare the noise of different designs. This thesis focuses on one set of methods based on the Ffowcs Williams-Hawkings (\fwh) equation. This equation is considered to be the most realistic description of aeroacoustic noise generation, as it is a direct rearrangement of the Navier-Stokes equations. The \fwh\ equation is difficult to solve for realistic test cases such as an open rotor, and is susceptible to several types of error. This thesis categorises these errors as ``input'', ``neglection'' and ``discretisation'' errors. Discretisation errors arise from the need to integrate a discretised source field for the total noise, neglection errors result from needing to ignore part of the source field for practical reasons, and input errors relate to any errors caused by inaccurate input to the solver. The fundamental motivation of this thesis is to advance the understanding of neglection and discretisation errors and how they can be mitigated, in order to develop best practice solvers and methodologies for application to open rotors. Dimensional analysis is combined with analytical flow solutions to develop a process for isolating and quantifying discretisation errors. This process is used to study a wide range of solver methodologies and select a best practice solver methodology for open rotor noise prediction. This first-of-a-kind study produces a solver methodology that reduces discretisation errors by an order of magnitude compared to an industry standard solver. Previous research into neglection errors has shown that avoiding density perturbations in acoustic source terms can be beneficial. This thesis uses a generic aeroacoustic analogy to provide a new, physically intuitive method of incorporating a surface discontinuity that enables density perturbations to be avoided in a far more elegant manner than previous research. The above method improvements are investigated using a modern open rotor rig test case. The results demonstrate that discretisation and neglection errors can be severe in realistic cases and the potential of the method improvements to significantly mitigate them.
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Análise estrutural de enrijecedores à flexão de geometria complexa utilizados em operações offshore. / Structural analysis of bending stiffeners with complex geometries utilized in offshore operations.José Roberto de Souza 26 August 2008 (has links)
Os enrijecedores à flexão ou bending stiffeners contemplados neste trabalho são componentes estruturais auxiliares utilizados em linhas flexíveis em suas conexões com unidades flutuantes em sistemas de produção de petróleo offshore. A configuração destes acessórios deve conferir à instalação uma variação gradual da rigidez à flexão próximo ao ponto de fixação da linha flexível à unidade flutuante, diminuindo sua curvatura e suavizando o campo de tensões, evitando assim que a linha ultrapasse a curvatura máxima estabelecida em projeto. Na análise estrutural destes acessórios, diversas simplificações geométricas são consideradas e, em geral, os modelos propostos partem de uma geometria cônica simples. Na prática, entretanto, é comum a existência de unidades que envolvem até quatro diferentes seções. Este trabalho apresenta uma análise estrutural estática destes componentes complexos por meio de um modelo linear elástico, analiticamente formulado, que resulta em uma equação diferencial não-linear de segunda ordem com coeficientes variáveis. O problema matemático de valor de contorno é então solucionado numericamente com um código desenvolvido em Matlab®, usando uma função interna baseada no método de colocação em oposição ao método de tiros, freqüentemente usado em trabalhos anteriores. Finalmente, soluções previamente obtidas por outros autores com modelos analítico-numéricos e com elementos finitos são utilizadas para validar as soluções aqui obtidas, seguidas de uma análise paramétrica da geometria complexa de novos enrijecedores à flexão, além de breve discussão sobre análise dimensional e questões normativas relacionadas ao projeto destes acessórios. / The bending stiffeners discussed in this work are ancillary structural components installed on flexible lines at their connections with floating units in offshore oil production systems. The configuration of these accessories must provide the installation with a gradual variation of the bending stiffness near the lines attaching point, smoothing the curvature and the stress field of the compliant structure therein fixed, thus avoiding exceeding its designed structural bending limit. In the structural analysis of these accessories, several geometric simplifications are considered and, in general, the proposed models start from a simple conic geometry. In practice, however, bending stiffeners geometries are not so simple. Indeed, units consisting of four different sections are common. This work presents a parametric static structural analysis of these complex components by means of an analytically formulated linear elastic model, which results in a second order non-linear differential equation with variable coefficients. The ensuing mathematical boundary value problem is then solved numerically with a code developed in Matlab®, using an internal function based on the collocation method as opposed to the shooting method, frequently used in previous works. Finally, solutions obtained previously by other authors, with analytical-numerical and finite element models, are used to validate the solutions obtained herein, followed by a parametric analysis of the complex geometry of new bending stiffeners, besides brief related dimensional analysis and normative discussions.
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