Exact solutions for radial deformations of a functionally graded isotropic and incompressible second-order elastic cylinder

We find closed-form solutions for axisymmetric plane strain deformations of a functionally graded circular cylinder comprised of an isotropic and incompressible second-order elastic material with moduli varying only in the radial direction. Cylinder's inner and outer surfaces are loaded by hydrostatic pressures. These solutions are specialized to cases where only one of the two surfaces is loaded. It is found that for a linear through-the-thickness variation of the elastic moduli, the hoop stress for the first-order solution (or in a cylinder comprised of a linear elastic material) is a constant but that for the second-order solution varies through the thickness. The radial displacement, the radial stress and the hoop stress do not depend upon the second-order elastic constant but the hydrostatic pressure and hence the axial stress depends upon it. When the two elastic moduli vary as the radius raised to the power two or four, the radial and the hoop stresses in an infinite space with a pressurized cylindrical cavity equal the pressure in the cavity. For an affine variation of the elastic moduli, the hoop stress in an internally loaded cylinder made of a linear elastic isotropic and incompressible material at the point is the same as that in a homogeneous cylinder. Here R_in and R_ou equal, respectively, the inner and the outer radius of the undeformed cylinder and R the radial coordinate of a point in the unstressed reference configuration.     

Multiplicity Results for Periodic Solutions to Second-Order Difference Equations

By using the Z _p geometrical index theory, some sufficient conditions on the multiplicity results of periodic solutions to the second-order difference equations

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.     

Glass fibre sizing effect on dynamic mechanical properties of cyanate ester composites I. Single frequency investigations

In order to investigate sizing effect in composite materials, we studied three types of composites, with different sizings. Dynamic mechanical analysis appeared to be a good way to characterize the α relaxation process of composites and their interphases. Results showed that α relaxation temperature shifted to higher temperatures for composites without sizing. Study of sizing extract/resin blend showed too that interphase was a mixture of polyvinyl acetate and cyanate resin. The results allow us to deduce that a plastification effect of resin by sizing could occur, with modification of crosslink density. Moreover, we can think that all resin is affected by sizing and the conversion rate in interphase is not total.     

Generalized second-order characterizations of convex functions

We introduce a second-order upper Dini-directional derivative and obtain a second-order characterization for a continuously Gâteaux differentiable function to be a convex function.This research was done under the supervision of Dr. V. Jeyakumar whose helpful guidance and valuable suggestions are much appreciated. The author is thankful to the referee for providing a simplication of the original proof of Theorem 2.1.     

Mathematical approach for the dynamic testing technique

In dealing with phenomena which show a linear response such as viscoelastic or dielectric properties, measurements are carried out by observing the relationship between the stimulus applied to the sample and the response from the sample. Since the Fourier analysis technique is effective in obtaining this relationship, two types of circuitries based on Fourier analysis have been created. Both DMA and dielectric measurement were used to evaluate these circuitries. Results were satisfactory, especially with respect to tanδ precision.

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Zusammenfassung Bei der Arbeit mit Erscheinungen, die wie z.B. viskoelastische oder dielektrische Eigenschaften eine lineare Reaktion zeigen, wurden Messungen durch Beobachtung der Beziehung zwischen der auf die Probe angewendeten Aktion und der von der Probe gezeigten Reaktion durchgeführt. Da die Fourier-Analyse eine effektive Technik zur Ermittlung dieser Beziehung ist, wurden auf der Grundlage der Fourier-Analyse zwei Typen von Schemen geschaffen. Sowohl DMA als auch dielektrische Messungen wurden zur Entwicklung dieser Schemen verwendet. Did Resultate waren zufriedenstellend, insbesondere mit Hinblick auf die Genauigkeit von tanδ.

     

Spectral multiplicity of some stochastic processes

In this paper we consider the connection between the canonical and the weak-canonical representations for the given second-order stochastic process in a separable Hilbert space and we extend a well-known theorem of H. Cramer concerning sufficient conditions for a process to be of multiplicity one.

     

Three Point Boundary Value Problems on Time Scales

This work formulates existence theorems for solutions to three-point boundary value problems on time scales. The ideas are based on a relationship between the three point boundary conditions, lower and upper solutions and topological degree theory.     

On the rheology of a dilute suspension of rigid spheres in a weakly viscoelastic matrix fluid

The complete solution for the pressure and the velocity field up to O(De) of a dilute suspension of neutrally buoyant, non-Brownian rigid spheres suspended in an unbounded, weakly viscoelastic matrix fluid, where is the solid volume fraction and De is the Deborah number of the matrix fluid, is presented. The spheres are subjected to an arbitrary linear velocity profile at infinity. The analytical solution is used for the prediction of the bulk stress, and specifically for the calculation of the first and the second normal stress differences in simple shear and uniaxial elongational flows. A comparison of the results with available values reported in the literature is also offered. The final expressions for the bulk normal stress differences in shear and uniaxial elongational flow fully agree with those reported earlier by Greco et al., J. Non-Newton. Fluid Mech., 147 (2007) 1–10.