On second order asymptotic solutions of axial symmetrical problems ofr>0 thin uniform circular toroidal shells with a large parametera 2/R0h

According to the classical shell theory based on the Love-Kirchhoff assumptions, the basic differential equations for the axial symmetrical problems of r>0 thin uniform circular toroidal shells in bending are derived, and the second order asymptotic solutions are given for r>0 thin uniform circular toroidal shells with a large parameter a²/R₀h. In the resent paper, the second order asymptotic solutions of the edge problems far from the apex of toroidal shells are given, too. Their errors are within the margins allowed in the classical theory based on the Love-Kirchhoff assumptions.     

The axial symmetrical edge problems for thin-walled shells of revolution

In this paper, the uniformly valid asymptotic solutions for the axial symmetrical edge problems of thin-walled shells of revolution in bending are given.     

The general solution on nonlinear axial symmetrical deformation of nonhomogeneous cylindrical shells

In this paper, the general solution on nonlinear axial symmetrical deformation of nonhomogeneous cylindrical shells is obtained by step reduction method⁽¹⁾. The general formula of displacements and stress resultants, which is used to solve the bending problems of nonhomogeneous cylindrical shells under arbitrary axial symmetric loads, is derived. Its uniform convergence is proved. Finally, it is only necessary to solve one set of binary linear algebraic equations. A numerical example is given at the end of the paper which indicates satisfactory results of displacement and stress resultants can be obtained and converge to the exact solution.     

Axisymmetric problems of cylindrical shells with variable wall thickness

The purpose of this paper is to give the general solutions for axisymmetric cylindrical shells with parabolically varying wall thickness.     

The asymptotic solutions of axisymmetrical problems for the cylindrical shells with varying wall thickness

In this paper the uniformly valid asymptotic solutions of axisymmetrical problems for the cylindrical shells with varying wall thickness are given.     

Stress-strain analysis of conical shells with different boundary conditions and thickness varying in two directions at constant mass

A method developed for solving two-dimensional problems in the theory of conical shells is used to analyze the stress-strain state of shells with different boundary conditions and thickness varying in two directions at constant mass. Numerical results are given in the form of plots and tables __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 70–79, March 2006.     

The stress state of anisotropic conic shells with thickness varying in two directions

The problem on the stress state of thin layered conic shells consisting of rigidly joint layers is considered. The material of the layers has one plane of elastic symmetry. The thickness of each layer in the meridional direction varies linearly in such a manner that it is proportional to the distance from the axis of rotation to the coordinate surface and varies arbitrarily in the circumferential direction. The desired functions are represented by the product of a power function of the radial coordinate and the unknown function of the central angle in the cross section. This makes it possible to separate out the radial coordinate and to derive the resolving system of ordinary differential equations, which is solved numerically. An example of the solution of a specific problem is given. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 81–88, May, 2000.     

圆盘匀速转动时最大径向位移在何处?

通过计算对等厚度圆盘匀速转动时径向位移最大值的计算式进行了修正,重新得出了最大位移表达式,并给出了误差分析．     

The effect of thickness on stress distribution in the region of intersection between two cylindrical shells with orthogonal axes

Summary A study for the investigation of the stress characteristics in the region of connection between two cylindrical shells with orthogonal axes was performed, within the classical elasticity theory. The stress analysis concerns the area near the intersection of two shells, except for the singular points. Three approximation levels of the analytical model make it possible to graduate the complexity of calculation according to the geometrical characteristics of the two shells.

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Sommario E' stato sviluppato uno studio per determinare le caratteristiche di tensione nella regione di collegamento fra due gusci cilindrici con assi ortogonali. Lo studio è basato sull'impiego delle formulazioni classiche della teoria dell'elasticità. L'analisi dello stato di tensione riguarda la zona prossima all'intersezione dei due gusci, con esclusione dei punti singolari. Tre gradi di approssimazione del modello analitico permettono di graduare la complessità del calcolo in relazione alle caratteristiche geometriche dei due gusci.

     

The hydrostatic/hydrodynamic behaviour of an axial piston pump slipper with multiple lands

This study considers an analytical approach towards the understanding of the hydrostatic leakage and lift characteristic of a flat slipper of the type used for piston/slipper units within an axial piston pump or motor. In particular it considers a slipper design incorporating a groove on the slipper face and also includes the effect of motion around its associated swash plate. A new set of equations are developed and in generic form for a slipper with any number of grooves. Experimental comparisons are then undertaken and extended to include the effect of relative motion around the swash plate and slipper tilt. A CFD study of the slipper is also presented. Comparisons between analytical, experimental and CFD results show a very good agreement, validating the equations presented and extending the conclusions when tilt and tangential speed are considered.     

Bäcklund transformations for the equation ∂2u/∂x1∂x1 + ∂2u/∂x2∂x2−f (u)

Bäcklund transformations for the equation ² u/x¹x ¹+ ²u/x ² x ²=f (u)here f is an arbitrary function) is studied in this paper, using the procedure of Wahlquist and Estabrook (WEP). We conclude that the condition d ² f/du ²=f is sufficient for the existence of Bäcklund transformations for the equation of our interest. A special case of our results leads to the conclusion of Leibbrandt ^[1,2].     

Asymptotic properties of solutions of an equation of order <Emphasis Type="Italic">n</Emphasis> with almost constant coefficients and pulse action

We investigate the asymptotic behavior of solutions of linear differential equations with almost constant coefficients and pulse action at fixed times as t tends to infinity. We establish conditions for the times of pulse action under which there exist values of pulse action for which the solution of the considered Cauchy problem with initial conditions that coincide with the initial conditions for a certain (arbitrary but fixed) solution of the original equation without pulse action is bounded, unbounded, or tending to infinity. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 4, pp. 444–455, October–December, 2005.     

Stochastic averaging of quasi integrable and resonant Hamiltonian systems excited by fractional Gaussian noise with Hurst index 1/2<H<1

A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise(fGn) with the Hurst index 1/2 H 1 is proposed. First, the definition and the basic property of f Gn and related fractional Brownian motion(fBm) are briefly introduced. Then, the averaged fractional stochastic differential equations(SDEs) for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.