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1.
Summary This study deals with the geometrically nonlinear axisymmetric deflection characteristics of orthotropic thick shallow truncated conical springs. Marguerre type governing equations including the effect of shear deformation have been formulated in terms of normal displacement , shear rotation and stress function . Polynmial approximations are used for these field variables and the discretised equations are obtained using the orthogonal point collocation method. The influence of thickness-to-radius ratio, orthotropic parameter and edge conditions has been investigated. Significant influence of shear deformation on the response is found for moderately thick high-modulus composite clamped caps. Its effect is less pronounced for simply-supported caps.
Nichtlineares Verhalten orthotroper, dicker, flacher Tellerfedern
Übersicht In dieser Arbeit werden die nichtlinearen Kennlinien von orthotropen, dicken, flachen Tellerfedern untersucht. Die dem Problem zugrunde liegenden Gleichungen vom Marguerre-Typ schließen den Effekt der Schubdeformation ein und werden mit Hilfe der Auslenkung , des Schubwinkels und einer Spannungsfunktion formuliert. Diese Größen werden in Potenzreihen entwickelt, und mit dem Kollokationsverfahren ergeben sich diskretisierte Gleichungen. Der Einfluß des Verhältnisses von Dicke zu Radius sowie der Einfluß von Orthotropieparametern und Randbedingungen wird untersucht.
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2.
We prove the existence and uniqueness of entropy solutions of the Neumann problem for the quasilinear parabolic equation uta(u, Du), where a(z,)=f(z,), and f is a convex function of with linear growth as ||||, satisfying other additional assumptions. In particular, this class includes the case where f(z,)=(z)(), >0, and is a convex function with linear growth as ||||.  相似文献   

3.
Summary The viscous properties of calcium carbonate filled polyethylene and polystyrene melts were examined. The relative vircosity r defined in the previous paper gave an asymtptotic value( r)l in the range of the shear stress below 105 dyne/cm2.( r)l of the calcium carbonate filled system was higher than that of the glass beads or glass balloons filled system at the same volume fraction of the filler. Maron-Pierce equation with 0 = 0.44 was able to approximate the( r)l — relationship. However, it was deduced here that the high value of( r)l of calcium carbonyl filled system was due to the apparent increase of and this increase was attributed to the fixed polymer layer formed on the powder particle. By assuming the particle as a sphere with a diameter of 2 µm, the thickness of the fixed polymer layer was estimated as about 0.17 µm. The yield stress estimated from the Casson's plots increased exponentially with.
Zusammenfassung Es wurden die viskosen Eigenschaften von Polyäthylen-und Polystyrol-Schmelzen untersucht, die mit Kalziumkarbonat-Teilchen gefüllt waren. Für die relative Viskosität r, wie sie in einer vorangegangenen Veröffentlichung definiert worden war, ergab sich bei Schubspannungen unterhalb 105 dyn/cm2 ein asymptotischer Wert( r)l. Dieser war bei den mit Kalziumkarbonat gefüllten Schmelzen höher als bei Schmelzen, die bis zur gleichen Volumenkonzentration mit Glaskugeln oder Glasballons gefüllt waren. Die ( r) l -Abhängigkeit ließ sich durch eine Gleichung nachMaron und Pierce mit 0 = 0,44 beschreiben. Es wurde jedoch geschlossen, daß der hohe( r)l-Wert der mit Kalziumkarbonat gefüllten Schmelzen auf eine scheinbare Zunahme von zurückzuführen ist, verursacht durch eine feste Polymerschicht auf der Teilchenoberfläche. Unter Annahme kugelförmiger Teilchen mit einem Durchmesser von 2 µm ließ sich die zugeordnete Schichtdicke zu 0,17 µm abschätzen. Die mittels der Casson-Beziehung geschätzte Fließspannung ergab eine exponentielle-Abhängigkeit.


With 7 figures and 1 table  相似文献   

4.
Summary The dynamic-mechanical behaviour of bitumensilica composites is described by a linear biparabolic model. Its mathematical expression allows the calculation of the mean relaxation times () either at different temperatures and given filler contents or for diverse filler contents () at imposed temperatures. At fixed filler concentration and within restricted temperature domains, obeys Arrhenius' law. The activation energies are respectively close to 10 kcal/mole (creep) and 30 kcal/mole (glass-transition). varies exponentially with. The mathematical treatment of the expressions ofE , as a function of temperature and of, leads to a general equation relating the complex modulus to temperature, frequency and filler content. A unique master curve, accounting for the viscoelastic behaviour of the composites, in limited ranges, can thus be constructed.
Zusammenfassung Das dynamisch-mechanische Verhalten von Bitumen-Siliziumdioxyd-Zusammensetzungen kann durch ein lineares biparabolisches Modell beschrieben werden. Sein mathematischer Ausdruck erlaubt die Ausrechnung der mittleren Relaxationszeiten () entweder für verschiedene Temperaturen bei gegebenem Füllstoffgehalt oder für unterschiedliche Siliziumdioxydmengen () bei bekannter Temperatur. Für einen bestimmten Füllstoffgehalt folgt in einem beschränkten Temperaturbereich dem Arrheniusschen Gesetz. Die Aktivierungsenergien betragen näherungsweise 10 kcal/Mol (Fließprozeß) bzw. 30 kcal/Mol (Glasübergang). ändert sich exponentiell mit. Die mathematische Umformung der Ausdrücke fürE und als Funktion der Temperatur und des Parameters ergibt eine allgemeine Gleichung, die den komplexen Modul mit der Temperatur, der Frequenz und dem Füllstoffgehalt verknüpft. Man kann eine einzige Masterkurve bilden, die das viskoelastische Verhalten der Zusammensetzungen zumindest in begrenzten Bereichen beschreibt.

Résumé Le comportement mécanique dynamique des composites à base de bitume et de silice peut être décrit par un modèle biparabolique linéaire. L'expression mathématique permet le calcul des temps moyens () de relaxation d'une part aux différentes températures, à taux de charge donné, et d'autre part pour diverses valeurs des taux de charge (paramètre) à température imposée. A taux de charge donné, et pour des domaines de température restreints, suit la loi d'Arrhénius. Les énergies apparentes d'activation sont respectivement voisines de 10 kcal/mole (processus de fluage) et de 30 kcal/mole (passage à l'état vitreux). Avec, varie exponentiellement. L'évaluation mathématique deE , de en fonction deT et de conduit à une expression générale du module complexe en fonction de la température, de la fréquence et du taux de charge. On peut donc construire une courbe maitresse unique qui décrit entièrement, mais dans des domaines restreints, le comportement viscoélastique des composites.


With 6 figures  相似文献   

5.
Summary This paper deals with the geometrically nonlinear axisymmetric static and transient response of moderately thick cylindrically orthotropic circular plates subjected to uniformly distributed and ring loads. Immovable clamped and simply supported annular plates with and without a rigid plug subjected to static and step function loads have been considered. Shear deformation and rotary inertia have been included. Orthogonal point collocation method and Newmark- scheme have been employed to solve the differential equations expressed in terms of transverse displacement , shear rotation and stress function . The effect of transverse shear has been investigated for isotropic and orthotropic plates. A simple approximate method has also been used to predict the maximum dynamic response to step loads from the results for static loads.
Nichtlineare, axialsymmetrische, statische und dynamische Analyse orthotroper, dicker Kreisringplatten
Übersicht Es wird das geometrisch nichtlineare, axialsymmetrische Verhalten orthotroper Kreisring-platten unter gleichmäßig bzw. ringförmig verteilten Lasten untersucht. Eingespannte und gelenkig gelagerte Platten mit oder ohne starrem Pfropfen unter statischer oder dynamischer Belastung werden behandelt, wobei Schubdeformation und Drehträgheit berücksichtigt werden. Eine Kollokationsmethode und das Newmarksche -Schema werden angewendet, um die Differentialgleichungen für die Durchbiegung , die Verdrehung und die Spannungsfunktion zu lösen.
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6.
Hyperbolic phenomena in a strongly degenerate parabolic equation   总被引:2,自引:0,他引:2  
We consider the equation u t =((u) (u x )) x , where >0 and where is a strictly increasing function with lim s = <. We solve the associated Cauchy problem for an increasing initial function, and discuss to what extent the solution behaves qualitatively like solutions of the first-order conservation law u t = ((u)) x . Equations of this type arise, for example, in the theory of phase transitions where the corresponding free-energy functional has a linear growth rate with respect to the gradient.  相似文献   

7.
Equations are obtained for two-dimensional transonic adiabatic (nonisoenergetic and nonisoentropic) vortex flows of an ideal gas, using the natural coordinates (=const is the family of streamlines, and =const is the family of lines orthogonal to them). It is not required that the transonic gas flow be close to a uniform sonic flow (the derivation is given without estimates). Solutions are found for equations describing vortex flows inside a Laval nozzle and near the sonic boundary of a free stream.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–109, September–October, 1973.  相似文献   

8.
Summary A singular integral equation arising in the theory of radiative transfer with polynomial scattering indicatrices is studied in this paper. In the case of a semi-infinite atmosphere, brightness coefficients and auxiliary functions satisfy this equation when the free term is suitably specified. The general solution of the singular equation is given a closed form in terms of its moments n and of the fundamental solution of a homogeneous Hilbert problem. The n's (n 1) are seen to satisfy a set of linear equations, and 0 turns out to be simply related to the subsequent n's.
Sommario In questo articolo viene studiata un'equazione integrale singolare che si presenta nella teoria del trasporto radiativo con indicatrici di scattering polinomiali. I coefficienti di riflessione e trasmissione e le funzioni ausiliarie di un'atmosfera semiinfinita soddisfano questa equazione, con opportune determinazioni del termine noto. La soluzione generale dell'equazione viene espressa in forma chiusa mediante i suoi momenti n e mediante la soluzione fondamentale di un problema omogeneo di Hilbert. Le n (n 1) soddisfano a loro volta un sistema di equazioni lineari, e 0 risulta legato alle successive n da una semplice relazione.


This work was done under the auspices of the CNR Research Groups.  相似文献   

9.
Using approach-withdrawal (AW) as a specific instance of temperament, a theoretical model of temperament as a complex dynamic system is proposed. Developmental contextualism (Lerner, 1998) serves as a guiding theory in determining the structural components of the system and Kauffman's (1993) Boolean models of self-organization are adapted to estimate the parameter functions. In this model P(AW) = f(, ) where P(AW) is the probability density function of an approach or a withdrawal response, ( is a standardized parameter estimate of the biological sensitivity to stimulation, and is a standardized parameter estimate of the contextual response to an approach or withdrawal response. It is theorized that the functions of ( and follow a Hill function of the forms: d /dt = (2/c2 + 2) – K1 d /dt = ( 2/c2 + 2) – K2, where K1, K2, and c are system constants. This results in a double sigmoid function in which at extreme values of and the system stabilizes on a steady state of either approach or withdrawal response patterns. At intermediate parameter values the probability density functions of approach and withdrawal responses are wider. Thus, AW can be modeled as representing two basins of attraction. In addition, considerations are given to the systems sensitivity to initial conditions.  相似文献   

10.
In this paper we consider the asymptotic behavior of solutions of the quasilinear equation of filtration as t. We prove that similar solutions of the equation u t = (u )xx asymptotically represent solutions of the Cauchy problem for the full equation u t = [(u)]xx if (u) is close to u for small u.  相似文献   

11.
We study properties of the topological entropy of the map F: f , C(I), generated by a fixed continuous map f C(I) of an interval of the straight line. In particular, we show that the topological entropy h(F) > 0 if and only if h(f) > 0.Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 180–187, April–June, 2004.  相似文献   

12.
We propose a new method for the solution of stochastic unsaturated flow problems in randomly heterogeneous soils which avoids linearizing the governing flow equations or the soil constitutive relations, and places no theoretical limit on the variance of constitutive parameters. The proposed method applies to a broad class of soils with flow properties that scale according to a linearly separable model provided the dimensionless pressure head has a near-Gaussian distribution. Upon treating as a multivariate Gaussian function, we obtain a closed system of coupled nonlinear differential equations for the first and second moments of pressure head. We apply this Gaussian closure to steady-state unsaturated flow through a randomly stratified soil with hydraulic conductivity that varies exponentially with where =(1/) is dimensional pressure head and is a random field with given statistical properties. In one-dimensional media, we obtain good agreement between Gaussian closure and Monte Carlo results for the mean and variance of over a wide range of parameters provided that the spatial variability of is small. We then provide an outline of how the technique can be extended to two- and three-dimensional flow domains. Our solution provides considerable insight into the analytical behavior of the stochastic flow problem.  相似文献   

13.
This paper deals with the stress distribution in a homogeneous isotropic elastic hemisphere embedded in a semi-infinite homogeneous isotropic elastic medium when a rigid circular disc is clamped to the plane face of the hemisphere and the stresses are caused by the rotation of the disc through an angle . The problem is reduced to the solution of a Fredholm integral equation of the second kind in the auxiliary function (t). An analytical expression for the torque T required to rotate the die through an angle is obtained in terms of (t). The Fredholm integral equation is solved numerically, and the numerical values of T are graphed.This work has been supported by the National Research Council of Canada through NRC-Research Grant No. A4177.  相似文献   

14.
An engineering method is proposed for calculating the friction and heat transfer through a boundary layer in which a nonuniform distribution of the velocity, total enthalpy, and static enthalpy is specified across the streamlines at the initial section x0. Such problems arise in the vortical interaction of the boundary layer with the high-entropy layer on slender blunt bodies, with sudden change of the boundary conditions for an already developed boundary layer (temperature jump, surface discontinuity), and in wake flow past a body, etc.Notation x, y longitudinal and transverse coordinates - u,, H, h gas velocity, stream function, total and static enthalpy - p,,, pressure, density, viscosity, Prandtl number - , q friction and thermal flux at the body surface - r(x), (x) body surface shape and boundary layer thickness - V, M freestream velocity and Mach number - u(0)(x0,), H(0)(x0,), h(0)(x0,) parameter distributions at initial section - u(0)(x,), h(0)(x,), h(0)(x,) profiles of quantities in outer flow in absence of friction and heat transfer at the surface of the body The indices v=0, 1 relate to plane and axisymmetric flows - , w, b, relate to quantities at the outer edge of the inner boundary layer, at the body surface in viscid and nonviscous flows, and in the freestream, respectively. The author wishes to thank O. I. Gubanov, V. A. Kaprov, I. N. Murzinov, and A. N, Rumynskii for discussions and assistance in this study.  相似文献   

15.
Predicted and measured water-retention values,(), were compared for repacked, stratified core samples consisting of either a sand with a stone-bearing layer or a sand with a clay loam layer in various spatial orientations. Stratified core samples were packed in submersible pressure outflow cells, then water-retention measurements were performed between matric potentials,, of 0 to -100 kPa. Predictions of() were based on a simple volume-averaging model using estimates of the relative fraction and() values of each textural component within a stratified sample. In general, predicted() curves resembled measured curves well, except at higher saturations in a sample consisting of a clay loam layer over a sand layer. In this case, the model averaged the air-entry of both materials, while the air-entry of the sample was controlled by the clay loam in contact with the cell's air-pressure inlet. In situ, avenues for air-entry generally exist around clay layers, so that the model should adequately predict air-entry for stratified formations regardless of spatial orientation of fine versus coarse layers. Agreement between measured and predicted volumetric water contents,, was variable though encouraging, with mean differences between measured and predicted values in the range of 10%. Differences in of this magnitude are expected due to variability in pore structure between samples, and do not indicate inherent problems with the volume averaging model. This suggets that explicit modeling of stratified formations through detailed characterization of the stratigraphy has the potential of yielding accurate() values. However, hydraulic-equilibration times were distinctly different for each variation in spatial orientation of textural layering, indicating that transient behavior during drainage in stratified formations is highly sensitive to the stratigraphic sequence of textural components, as well as the volume fraction of each textural component in a formation. This indicates that prolonged residence times of water, nutrients, and pollutants are likely within finer-textured layers, when conditions have resulted in drainage of underlying coarser-textured strata.  相似文献   

16.
Illinois coal was ground and wet-sieved to prepare three powder stocks whose particle-size distributions were characterized. Three suspending fluids were used (glycerin, bromonaphthalene, Aroclor), with viscosities s that differed by a factor of 100 and with very different chemistries, but whose densities matched that of the coal. Suspensions were prepared under vacuum, with coal volume fractions that ranged up to 0.46. Viscosities were measured in a cone-and-plate over a shear rate range 10–3–102 s–1. Reduced viscosity r = /s is correlated in the high-shear limit ( ) with/ M, where M is the maximum packing fraction for the high-shear microstructure, to reveal the roles of size distribution and suspending fluid character. A new model that invokes the stress-dependence of M is found to correlate r well under non-Newtonian conditions with simultaneous prediction of yield stress at sufficiently high; a critical result is that stress and not governs the microstructure and rheology. Numerous experimental anomalies provide insight into suspension behavior.  相似文献   

17.
The purpose is to extend the existence result of vortex solutions to semilinear elliptic equations for a large class of nonlinearities. M. I. Weinstein used variational techniques to show the existence of nodal solutions for the specific nonlinear term f(¦¦)=(1–¦¦2). An ordinary differential equation phase space setting is used to show the unique transverse intersection of unstable and stable manifolds which contain the solutions satisfying the necessary boundary conditions under certain assumptions on the nonlinearity.  相似文献   

18.
We present an elementary proof of an important result of Y. Brenier [Br1, Br2], namely, that vector fields in d satisfying a nondegeneracy condition admit the polar factorization (*) u(x)=(s(x)), where is a convex function and s is a measure-preserving mapping. Brenier solves a minimization problem using Monge-Kantorovich theory; whereas we turn our attention to a dual problem, whose Euler-Lagrange equation turns out to be (*).  相似文献   

19.
Stress-optical measurements are used to quantitatively determine the third-normal stress difference (N 3 = N 1 + N 2) in three entangled polymer melts during small amplitude (<15%) oscillatory shear over a wide dynamic range. The results are presented in terms of the three material functions that describe N 3 in oscillatory shear: the real and imaginary parts of its complex amplitude 3 * = 3 - i 3 , and its displacement 3 d . The results confirm that these functions are related to the dynamic modulus by 2 3 * ()=(1-)[G *())– G *(2)] and 2 3 d ()=(1- )G() as predicted by many constitutive equations, where = –N 2/N 1. The value of (1-) is found to be 0.69±0.07 for poly(ethylene-propylene) and 0.76±0.07 for polyisoprene. This corresponds to –N 2/N 1 = 0.31 and 0.24±0.07, close to the prediction of the reptation model when the independent alignment approximation is used, i.e., –N 2/N 1 = 2/7 – 0.28.  相似文献   

20.
A method by which the transport of anisotropic radiative multiple scattering can be predicted is developed in this paper. A one-dimensional integral intensity model and a three-dimensional diffusion intensity model are both constructed. The former provides a closed-form solution, while the latter involves successive approximation and Gauss's quadrature. On the basis of these methods, the reflection and transmission of solar radiation in a homogeneous cloud layer are computed. The results differ from those for isotropic and Rayleigh scattering assumptions and illustrate the effects on transmission and reflectivity of optical thickness, wavelength, incidence angle, and albedo of single scattering.Nomenclature D + transmitted diffusion radiation intensity [W/cm2 sr · m] - D reflected diffusion radiation intensity [W/cm2 sr · m] - I pencil of radiation or specific intensity [W/cm2 sr · m] - I 0 solar irradiance [W/cm2] - K extinction cross-section or total cross-section, + - s (u, ), unit scattered radiation vector - s 0 (u 0, 0), unit incident radiation vector - t optical thickness - u cosine of the viewing angle, , which is measured from the vertical - u 0 cosine of the angle of incident, 0, which is measured from the vertical - absorption cross-section - scattering function - absorption coefficient - scattering angle, s · s 0 - scattering cross-section - scattered azimuthal angle - 0 incident azimuthal angle - a sphere - a solid angle - 0 albedo of single scattering,   相似文献   

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