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Artykuły w czasopismach na temat "Compressive non-linearity"

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Hammett, Stephen T., Mark A. Georgeson, Samantha Bedingham i Gillian S. Barbieri-Hesse. "Motion sharpening and contrast: Gain control precedes compressive non-linearity?" Vision Research 43, nr 10 (maj 2003): 1187–99. http://dx.doi.org/10.1016/s0042-6989(03)00071-3.

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Sun, C. T., i A. Wanki Jun. "Compressive strength of unidirectional fiber composites with matrix non-linearity". Composites Science and Technology 52, nr 4 (styczeń 1994): 577–87. http://dx.doi.org/10.1016/0266-3538(94)90041-8.

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Varma, R. Ramgopal, i G. Venkateswazra Rao. "Combined Effects of Geometric and Material Non—linearities on One Dimensional Structural Members". International Journal of Engineering Technology and Sciences 1, nr 1 (26.12.2018): 5–8. http://dx.doi.org/10.15282/ijets.v1i1.1106.

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Combined effects of geometric and material non-linearities on a uniform column subjected to an axial compressive load are presented in the present note. A simple, direct iterative numerical method has been proposed to study the geometric and material non-linear behavior of columns subjected to varying boundary conditions. Introduction of material non-linearity in the large deflection analysis of columns subjected to an axial compressive load reveals a reduction in Euler stress obtained when compared to the effect of geometric non-linear analysis and increase in the same when compared to the eflect of material non-linear analysis. A convergence study has been carried outfor the results obtained from the proposed iterative method to prove the efficacy.
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Korinets, A., i H. Alehossein. "Technical Note On the Initial Non-Linearity of Compressive Stress-Strain Curves for Intact Rock". Rock Mechanics and Rock Engineering 35, nr 4 (1.10.2002): 319–28. http://dx.doi.org/10.1007/s00603-002-0030-4.

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Sakaida, Yoshihisa, Keisuke Tanaka i Shintaro Harada. "Measurement of Residual Stress Distribution of Ground Silicon Nitride by Glancing Incidence X-ray Diffraction Technique". Advances in X-ray Analysis 39 (1995): 331–38. http://dx.doi.org/10.1154/s0376030800022746.

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A new method of X-ray stress measurement was proposed to estimate non-destructively the steep residual stress distribution in the surface layer of ground Si3N4. We assumed an exponential decrement of the residual stress near the ground surface, and derived a formula for the lattice strain as a function of sin2Ψ. In the experiments, the diffraction angles were measured on the ground surface for a widest possible range of sin2ѱ using an Ω-goniometer. In order to measure the diffraction angle at very high sin η values, a scintillation counter was located on the -η side and an incident X-ray beam impinged on the ground surface with a very low angle from the +η side using the glancing incidence X-ray diffraction technique. A strong non-linearity was found in the 20-sin2ѱ diagrams especially at very high ѱ -angles. From the analysis of non-linearity, the stress distribution in the surface layer was determined. Tine residual stress took the maximum compression of 2 GPa at a depth of about 0.5 μm from the surface, and then diminished to zero at about 25 μm in depth. In the close vicinity of the ground surface, the compressive residual stress was relieved because of both the surface roughness and microcracking induced during the grinding process.
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Stine, Wm Wren, i Natalie Khutoryansky. "An Investigation of the Venetian Blind Effect". Seeing and Perceiving 24, nr 3 (2011): 241–92. http://dx.doi.org/10.1163/187847511x580366.

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AbstractWhen a rectangular wave grating is binocularly viewed with a neutral density filter over one eye, an illusory rotation resembling that of a partially opened Venetian blind is perceived (Cibis and Haber, 1951). Using a binary classification task, in the first experiment, the probability of perceiving a rotation in a given direction was measured as a function of a factorial combination of inter-ocular contrast (see Note 1) and luminance ratios. The probability of a rotation in a given direction decreased monotonically with the luminance of the brighter bars when the grating contains a less than unity contrast. This result is inconsistent with (i) the model of the Venetian blind effect proposed by Cibis and Haber (1951), (ii) a mechanism based on irradiation with a compressive non-linearity (von Helmholtz, 1911/1924, pp. 186–193) and (iii) contemporary stereo-energy/cross-correlation models of stereopsis. In the second and third experiments, we tested the prediction that irradiation combined with an early compressive non-linearity in response implies a positive relationship between both the threshold contrast or average luminance disparity to perceive rotation and the magnitude of perceived rotation, and the blur width at the bar's edge. No support was found for the prediction. We propose an intensity difference model of the probability of perceiving a rotation in a given direction as a function of the interocular difference in luminance or contrast.
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Jindal, Sumit Kumar, Ritobrita De, Ajay Kumar i Sanjeev Kumar Raghuwanshi. "Novel MEMS Piezoresistive Sensor with Hair-Pin Structure to Enhance Tensile and Compressive Sensitivity and Correct Non-Linearity". Journal of Electronic Testing 36, nr 4 (16.07.2020): 509–17. http://dx.doi.org/10.1007/s10836-020-05895-0.

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Fagan, M. J., S. Julian, D. J. Siddall i A. M. Mohsen. "Patient-specific spine models. Part 1: Finite element analysis of the lumbar intervertebral disc—a material sensitivity study". Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 216, nr 5 (1.05.2002): 299–314. http://dx.doi.org/10.1243/09544110260216577.

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If patient-specific finite element models of the spine could be developed, they would offer enormous opportunities in the diagnosis and management of back problems. Several generic models have been developed in the past, but there has been very little detailed examination of the sensitivity of these models' characteristics to the input parameters. This relationship must be thoroughly understood if representative patient-specific models are to be realized and used with confidence. In particular, the performance of the intervertebral discs are central to any spine model and need detailed investigation first. A generic non-linear model of an intervertebral disc was developed and subjected to compressive, flexion and torsional loading regimes. The effects of both material and geometric non-linearities were investigated for the three loading schemes and the results compared with experimental data. The basic material properties of the fibres, annulus and nucleus were then varied and the effects on the stiffness, annulus bulge and annulus stresses analysed. The results showed that the non-linear geometry assumption had a significant effect on the compression characteristics, whereas the non-linear material option did not. In contrast, the material non-linearity was more important for the flexural and torsional loading schemes. Thus, the inclusion of non-linear material and geometry analysis options in finite element models of intervertebral discs is necessary to predict in vivo load-deflection characteristics accurately. When the influence of the material properties was examined in detail, it was found that the fibre properties did not have a significant effect on the compressive stiffness of the disc but did affect the flexural and torsional stiffnesses by up to ±20 per cent. All loading modes were sensitive to the annulus properties with stiffnesses varying by up to ±16 per cent. The model also revealed that for a particular compressive deformation or flexural or torsional rotation, the disc bulge was not sensitive to any of the material properties over the range of properties considered. The annulus stresses did differ significantly as the material properties were varied (up to 70 per cent under a compressive load and 60 per cent during disc flexion).
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Balevičius, Robertas, i Eugedijus Dulinskas. "ON THE PREDICTION OF NON‐LINEAR CREEP STRAINS". JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 16, nr 3 (30.09.2010): 382–86. http://dx.doi.org/10.3846/jcem.2010.43.

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In the short term, the Euorocode‐based techniques will be implemented as the main design specifications for structural engineers from the member‐states of the European Union instead of the national standards. Therefore, it is of primary importance draw attention to the observed inaccuracies, particularly, in predicting non‐linear creep strains according to EC‐2. The analysis performed was mainly focused on an inconsistency elimination observed in the original EC‐2 approach, when transition from the linear to non‐linear creep laws for a constant compressive stress is required. A recent CEN corrigendum eliminating the observed inconsistency was also discussed in detail. In this context, similar techniques which were reported in the literature for predicting the creep non‐linearity function were analysed to account for the results obtained. It was particularly demonstrated that the recent CEN amendment results in an extremely enhanced creep strain for low strength concrete. A comparison of the creep non‐linearity functions with experimental test results was also considered. Santrauka Artimiausiu metu nacionalines normas pakeis Europos normos, kurios taps privalomu normatyviniu dokumentu Europos Sajungos šaliu statybos inžinieriams. Todel labai svarbu konstatuoti ir patikslinti jose pastebetus netikslumus. Straipsnyje akcentuojamas normu EC2 metodikoje pastebetas valkšnumo deformaciju nesutapimas, kai reikalingas perejimas iš tiesiniu valkšnumo deformaciju prie netiesiniu. Pateikiama žinomu metodu ir eksperimentiniu tyrimu rezultatu lyginamoji analize, autoriu siūlymai bei detaliai nagrinejamas neseniai išleistas CEN komiteto taisymas. Atlikus analize nustatyta, kad CEN korektūra lemia nepaprastai dideles mažo stiprumo betonu netiesinio valkšnumo deformacijas.
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Pastor-Artigues, Ma-Magdalena, Francesc Roure-Fernández, Xavier Ayneto-Gubert, Jordi Bonada-Bo, Elsa Pérez-Guindal i Irene Buj-Corral. "Elastic Asymmetry of PLA Material in FDM-Printed Parts: Considerations Concerning Experimental Characterisation for Use in Numerical Simulations". Materials 13, nr 1 (18.12.2019): 15. http://dx.doi.org/10.3390/ma13010015.

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The objective of this research is to characterise the material poly lactic acid (PLA), printed by fused deposition modelling (FDM) technology, under three loading conditions—tension, compression and bending—in order to get data that will allow to simulate structural components. In the absence of specific standards for materials manufactured in FDM technology, characterisation is carried out based on ASTM International standards D638, D695 and D790, respectively. Samples manufactured with the same printing parameters have been built and tested; and the tensile, compressive and flexural properties have been determined. The influences of the cross-sectional shape and the specimen length on the strength and elastic modulus of compression are addressed. By analysing the mechanical properties obtained in this way, the conclusion is that they are different, are not coherent with each other, and do not reflect the bimodular nature (different behaviour of material in tension and compression) of this material. A finite element (FE) model is used to verify these differences, including geometric non-linearity, to realistically reproduce conditions during physical tests. The main conclusion is that the test methods currently used do not guarantee a coherent set of mechanical properties useful for numerical simulation, which highlights the need to define new characterisation methods better adapted to the behaviour of FDM-printed PLA.
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Rozprawy doktorskie na temat "Compressive non-linearity"

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Haque, Serajul. "Perceptual features for speech recognition". University of Western Australia. School of Electrical, Electronic and Computer Engineering, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0187.

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Automatic speech recognition (ASR) is one of the most important research areas in the field of speech technology and research. It is also known as the recognition of speech by a machine or, by some artificial intelligence. However, in spite of focused research in this field for the past several decades, robust speech recognition with high reliability has not been achieved as it degrades in presence of speaker variabilities, channel mismatch condi- tions, and in noisy environments. The superb ability of the human auditory system has motivated researchers to include features of human perception in the speech recognition process. This dissertation investigates the roles of perceptual features of human hearing in automatic speech recognition in clean and noisy environments. Methods of simplified synaptic adaptation and two-tone suppression by companding are introduced by temporal processing of speech using a zero-crossing algorithm. It is observed that a high frequency enhancement technique such as synaptic adaptation performs better in stationary Gaussian white noise, whereas a low frequency enhancement technique such as the two-tone sup- pression performs better in non-Gaussian non-stationary noise types. The effects of static compression on ASR parametrization are investigated as observed in the psychoacoustic input/output (I/O) perception curves. A method of frequency dependent asymmetric compression technique, that is, higher compression in the higher frequency regions than the lower frequency regions, is proposed. By asymmetric compression, degradation of the spectral contrast of the low frequency formants due to the added compression is avoided. A novel feature extraction method for ASR based on the auditory processing in the cochlear nucleus is presented. The processings for synchrony detection, average discharge (mean rate) processing and the two tone suppression are segregated and processed separately at the feature extraction level according to the differential processing scheme as observed in the AVCN, PVCN and the DCN, respectively, of the cochlear nucleus. It is further observed that improved ASR performances can be achieved by separating the synchrony detection from the synaptic processing. A time-frequency perceptual spectral subtraction method based on several psychoacoustic properties of human audition is developed and evaluated by an ASR front-end. An auditory masking threshold is determined based on these psychoacoustic e?ects. It is observed that in speech recognition applications, spec- tral subtraction utilizing psychoacoustics may be used for improved performance in noisy conditions. The performance may be further improved if masking of noise by the tonal components is augmented by spectral subtraction in the masked region.
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Saneecharaun, Jeet T. "Development of a current to pressure (I/P) converter. System analysis of a current to pressure (I/P) converter through physical modelling and experimental investigation, leading to a design for improved linearity and temperature independence". Thesis, University of Bradford, 2014. http://hdl.handle.net/10454/7823.

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Current-to-pressure (I/P) converters are pneumatic devices which provide precise control of pressure in various industries – for example these devices are often used in valve positioner systems (typically found in the oil and gas industry) and tensioning systems (typically used in the packaging industry). With an increasing demand for such devices to operate in harsh environments all by delivering acceptable performance means that Current-to-pressure converters need to be carefully designed such that environmental factors have no or minimal effects on its performance. This work presents an investigation of the principles of operation of an existing I/P converter through mathematical modelling. A simulation model has been created and which allows prediction of performance of the I/P converter. This tool has been used to identify areas of poor performances through theoretical analysis and consequently led to optimisation of certain areas of the I/P converter through a design change to deliver improved performances, for instance the average percentage shift in gain at 1mA input signal (over the temperature range of -40°C to 85°C) on the new I/P converter is 2.13% compared to the average gain of 4.24% on the existing I/P converter, which represents an improvement of almost two fold. Experimental tests on prototypes have been carried out and tests results showed that improved linearity and temperature sensitivity can be expected from the new design.
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Streszczenia konferencji na temat "Compressive non-linearity"

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Yoosef-Ghodsi, Nader, Istemi Ozkan i Qishi Chen. "Comparison of Compressive Strain Limit Equations". W 2014 10th International Pipeline Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/ipc2014-33182.

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Buried pipelines subjected to non-continuous ground movement such as frost heave, thaw settlement, slope instability and seismic movement experience high compressive strains that can cause local buckling (or wrinkling). In the context of strain-based design, excessive local buckling deformation that may cause loss of serviceability, or even pressure containment in some cases, is managed by limiting the strain demand below the strain limit. The determination of compressive strain limit is typically performed by full-scale structural testing or nonlinear finite element analysis that takes into account material and geometric non-linearity associated with the inelastic buckling of cylindrical shells. Before performing testing and numerical analysis (or when such options do not exist), empirical equations are used to estimate the strain limit. In this paper a number of representative equations were evaluated by comparing strain limit predictions to full-scale test results. Work prior to this study has identified the importance of key variables that have the greatest impact on the local buckling behaviour. Examples of these variables include the diameter-to-thickness ratio (D/t), internal pressure and shape of the stress strain curve. The evaluation presented here focused on how existing equations address these key variables, and the performance of the equations with respect to key variables and in different ranges.
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Billon, F., G. Batmale i B. Drevon. "Improvement of Leak Tightness Analysis of Bolted Closure Systems in Pressure Equipment". W ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78538.

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The aim of this work is to study the Leak Tightness of the closure systems of nuclear pressure equipment during all situations including in-service operating, emergency and accidental conditions. The analysis is performed using a complete 3-dimensional finite element model of the closure system including : the studs, the gasket, the contacts between the gasket and their seating surfaces (contact elements), the nuts, the cover, the part of the shell on which the opening is located and the tightening preload of the studs. It comprises 2 main phases: (a) Using the 3D model, with non linear internal parameters converted in appropriate linear that allows performing linear analyses, we select, with respect to leaktightness, the most critical thermal and pressure transient among a large amount of transient. This selected transient presents the weakest compressing force between the gasket and its seating surfaces, which is the selection criterion. (b) Then, using the 3D model we perform a full non-linear analysis of the selected transient, taking into account the non linearity of the contacts as well as the non linearity of the gaskets and the tightening preload of the studs. Thus for this transient, we obtain the history of the compressive forces on the gasket and particularly the history of the metal-metal contact for the gaskets multi-ring type (metallic-graphite-metallic) and we can check if compressive forces remain effective. An important consequence is the re-calculation of the tightening preload applied to the studs if the intensity of the metal-metal contact is not sufficient.
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Gandhi, Umesh, Stephane Roussel, K. Furusu i T. Nakagawa. "Application of Finite Strip Method in Vehicle Design: Part 2 of 2—Post Buckling Analysis of Thin Walled Structures". W ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63553.

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Thin walled parts of high strength steel, under compressive loads are likely to buckle locally, and then depending on geometry and material properties the section may continue to carry additional load. For the post buckling conditions the deformations are large but finite. Therefore we need to consider geometrical non linearity in the calculations. In this paper we are extending the linear finite strip element formulation to include geometrical non linearity. Method to derive secant and tangent stiffness matrix for non linear finite strip element is developed and then the element formulation is verified for inplane and center load on a plate using Newton Raphson solver. The new non linear finite strip element can be useful in estimating maximum load capacity (including post buckling) of thin walled structures from 2D data.
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Peral Moreno, Alonso, Francisco Javier Marquina Zárraga, Francisco José Prieto Santos i Francisco Javier Gómez Sánchez. "Experimental Validation of a Non-Linear Buckling Method on a Rear Engine Mount Support Structure". W ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-25114.

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Traditionally buckling analyses in engine structures have been performed using analytical solutions from validated bibliographical reference (e.g. Bruhn). This method requires a certain margin of safety due to the idealization of the real complex geometries into the more simple validated set of cases. As computational power increased, linear Euler buckling based on finite element solutions has become accessible. This second approach also requires of a certain margin of safety due to not considering material and geometrical non-linear effects. This paper presents the development of an accurate non-linear finite element prediction of the buckling characteristics of a rear engine mount support structure. The method includes both material and geometrical non-linearity. This analytical prediction method has been validated by a series of material coupon and sub-component compressive experimental rig tests. The work presented in this paper will be completed in the future with validation from a full component test and with a method to account for manufacturing tolerances.
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Webber, Kyle G., i Christopher S. Lynch. "Analysis of the Non-Linear Behavior of ECLIPSE Actuators". W ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81057.

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This work discusses the development and characterization of rectangular shaped Epoxy Composite Laminated Piezoelectric Stress-Enhanced actuators (ECLIPSE). ECLIPSE actuators are unimorph type d31 actuators that are manufactured with a lead zirconate titanate (PZT) plate sandwiched between unidirectional Kevlar 49/epoxy composite layers with dissimilar coefficients of thermal expansion in orthogonal directions. Cooling the actuator from an elevated curing temperature resulted in a residual stress gradient through the actuator, a compressive stress on the brittle piezoelectric plate, and a large out-of-plane deformation. Extended classical lamination theory (ECLT) is used to model the residual stress state and curvature of the actuator. The model results are compared to the classical lamination theory. The ECLT was developed by Hyer to explain the non-linear behavior of unsymmetric cross-ply laminates [1-3]. Three actuator layups were fabricated and characterized: [90/PZT/90/0], [90/90/PZT/90/0/0], and [90/90/90/PZT/90/0/0/0]. It is shown that geometric non-linearity is important to consider when modeling ECLIPSE actuators.
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Butlin, Tore, i Alain Batailly. "Anti-Optimisation Applied to the Analysis of Rotor/Stator Interaction". W ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94633.

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There is a drive towards minimising operating clearances within turbomachines in order to limit reverse leakage flows and hence improve their efficiency. This increases the likelihood of contact occurring between the blade and the casing, which can give rise to high amplitude vibration. Modelling this interaction represents a significant computational challenge. The non-linear contact precludes the use of well-established linear methods, and is also subject to uncertainties: the contact law is imprecisely known and the exact geometry of imperfections that trigger contact may be unknown. In this paper a novel approach is presented that aims to account for the uncertainties associated with the non-linearity in a non-probabilistic way. The worst case is sought, by framing the system as a constrained anti-optimisation problem. The target to be maximised represents a metric of the output of interest. The degrees of freedom of the anti-optimisation are the non-linear input forces (considered as external loads), and the constraints are designed to capture what is thought to be known about the non-linear contact law and geometry. A realistic three-dimensional model of a turbine blade is used to explore the approach, with contact considered at the leading and trailing edge. The blade dynamics are described in terms of a linear transfer function matrix and the target metric of interest is chosen to be the peak displacement of the contact points. The non-linearity is taken to result from an offset shaft, giving a sinusoidal clearance variation. The blade is driven at constant frequency and the scope of the study is limited to finding bounds on periodic solutions. A variety of constraint conditions are explored that describe aspects of the non-linearity. For example, only compressive forces are permitted (no tension from the contact), and the displacement must not exceed the clearance. The method yields encouraging initial results: constraints can be identified that give efficient estimates of the upper bound response of the system as a function of drive frequency. The results are compared with a benchmark time-domain simulation and are found to correctly over-predict the response without being overly conservative. Broad trends are also in agreement with the benchmark solution. The proposed method appears to be a promising approach for efficiently accounting for uncertainties associated with the non-linearity and thus improving blade design.
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Zaouter, Yoann, Eric Cormier, Pierre Rigail, Clemens Hönninger i Eric Mottay. "High average power, low non-linearity Ytterbium fiber amplifier using spectral compression". W ICALEO® 2006: 25th International Congress on Laser Materials Processing and Laser Microfabrication. Laser Institute of America, 2006. http://dx.doi.org/10.2351/1.5060765.

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Mori, Yasuhito. "Non-linearity of Polyethylene Hugoniot up to 1 GPa and Its Interpretation by Grüneisen Parameter Estimation". W SHOCK COMPRESSION OF CONDENSED MATTER - 2003: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter. AIP, 2004. http://dx.doi.org/10.1063/1.1780194.

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Briones, Alejandro M., Nathan Thomas i Brent A. Rankin. "Effects of Combustor Enclosure Flow Path on Combustor Design". W ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14127.

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Abstract A design optimization procedure was implemented to resize the holes of a combustor liner for practical applications. A combustor geometry evaluated without an enclosure was to be reformulated within an enclosure. The objective functions of the combustor with enclosure involved targeting the flow splits of the combustor without enclosure. Latin Hypercube Sampling (LHS) design of experiments (DOE) was utilized to obtain at least a pure quadratic response surface (RS). These were computed using Genetic Aggregate (GA). These RS were, in turn, evaluated by a multiple objective genetic algorithm (MOGA) optimizer. The focus of this study was a small-scale cavity-stabilized combustor. Steady, compressible three-dimensional simulations are performed using a multi-phase Realizable k-ε Reynolds-averaged Navier-Stokes (RANS) approach. Combustion-turbulence interaction is modeled with flamelet progress variable (FPV) and β-presumed probability density function (PDF). There are eleven input and output parameters corresponding to the combustor hole sizes and associated mass flow rates. The RS obtained with GA were principally of the Kriging kind (with constant and linear trends and damped sinusoid and Gaussian kernels). A combustor hole mass flow rate was mainly determined by its hole size but was also influenced by the other holes. The combustor flow split non-linearity shows that increasing a hole size increases its mass flow rate, but simultaneously decreases another hole flow rate. This was also verified by sensitivity analysis. Due to this non-linearity, matching flow splits between geometry without and with enclosure is challenging and may not be possible for some situations. Thus, it is concluded that optimization of the combustor geometry without the enclosure is not the best route. Rather, it would be better for the geometry to be optimized with the enclosure included in order to account for flow separation and non-linear influence of the combustor holes on the flow field.
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Borboni, Alberto, Diego De Santis i Rodolfo Faglia. "Large Deflection of a Non-Linear, Elastic, Asymmetric Ludwick Cantilever Beam". W ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24257.

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The investigated cantilever beam is characterized by a constant rectangular cross-section and is subjected to a concentrated vertical constant load at the free end. The same beam is made by an elastic non-linear asymmetric Ludwick type material with different behavior in tension and compression. Namely the constitutive law of the proposed material is characterized by two different elastic moduli and two different strain exponential coefficients. The aim of this study is to describe the deformation of the beam neutral surface and particularly the horizontal and vertical displacements of the free end cross-section. The analysis of large deflection is based on the Euler-Bernoulli bending beam theory, for which cross-sections, after the deformation, remain plain and perpendicular to the neutral surface; furthermore their shape and area do not change. On the stress viewpoint, the shear stress effect and the axial force effect are considered negligible in comparison with the bending effect. The mechanical model deduced from the identified hypotheses includes two kind of non-linearity: the first due to the material and the latter due to large deformations. The mathematical problem associated with the mechanical model, i.e. to compute the bending deformations, consists in solving a non-linear algebraic system and a non-liner second order ordinary differential equation. Thus a numerical algorithm is developed and some examples of specific results are shown in this paper. Precisely, the proposed problem is a generalization of similar cases in literature, consequently numerical comparisons are performed with these previous works, i.e. assuming linear elastic materials or assuming symmetric Ludwick type material with same behavior in tension and compression like aluminum alloy and annealed copper. After verifying a proper agreeing with the literature, in order to investigate the effect of the different material behavior on the horizontal and vertical displacements of the free end cross-section, numerical results are obtained for different values of elastic moduli and strain exponential coefficients. The arising conclusions are coherent with the assumed hypotheses and with similar works in literature.
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