Stress state of conical shells of moderate thickness with a hole in a centrifugal force field

Kiev University. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 16–20, May, 1990.     

The ring shells under gravitative loads

This paper gives Novozlov’s equation (ref. [1]) in a simple style of ring shells with equal thickness under the actions of gravitative loads. By means of Fourier series, the special solution of the equation is established. Using the results of the homogeneous solution in ref. [2], we find out the general solution of the problem, and derive the expressions of stress and displacement.Two examples are given as the application of the above results.     

Axisymmetry problems of ring shells under arbitrary distributed loads

Extending Novozhilov's transformation, this paper simplifies successfully the axisymmetry problems of ring shells under arbitrary distributed loads, and the equation of the problems in complex form which is similar to Novozhilov's is obtained. The particular solution is obtained. Combining with Chien's general solution of homogeneous equation, this paper gives the general solution for the general symmetry problems of ring shells. Various examples of useful loads and closed ring shells are discussed respectively.     

内圈离心位移对高速角接触球轴承刚度的影响

以弹性力学理论、滚动轴承动力学和沟道控制理论为基础,计算了角接触球轴承内圈在离心力作用下的径向位移,给出了计及内圈离心位移影响时,高速角接触球轴承滚动体与内、外圈的接触刚度与轴承整体的径向刚度、轴向刚度、角刚度的计算方法和相应程序。对7012/CD轴承的计算结果表明,轴承内圈外径的离心位移随转速增加而增大,在高速条件下其值较大,不容忽视;轴承内圈离心位移对内圈接触刚度和轴承径向刚度影响较大,导致内圈接触刚度和轴承径向刚度相对增大;对外圈的接触刚度、轴承轴向刚度和角刚度的影响很小;随着转速的增加与内圈离心位移的增大,对轴承内圈接触刚度与轴承径向刚度的影响会更加明显。因此,为使高速角接触球轴承的刚度分析更加精确、更加接近实际,必须考虑内圈离心位移的影响。     

The initial postbuckling behavior of ring stiffened shells under hydrostatic pressure

In this article the initial postbuckling behavior of ring stiffened cylindrical shells under hydrostatic pressure is analyzed by Koiter's theory. The nonlinear bending equations consistent with boundary conditions have been used in prebuckling state. The eigenvalue problem is solved by Galerkin's method. The obtained buckling loads are compared with the results which are based on classical stability theory. As calculating examples, three typical outside-stiffened cylinders with different ring stiffener parameters are chosen. The results show that the strength of stiffener not only influences buckling load obviously, but also changes the imperfection-sensitivity of cylindrical shells.     

Matrix displacement analysis of plates and shells

Summary The paper presents an aperçu of a theory based on the Matrix Displacement method developed by the author for the analysis of plates and shells of arbitrary form. The philosophy of the method is exclusively founded on the use of a modern large digital computer and a sophisticated matrix interpretative scheme backed up by an allied structural language, both of which were established at the author's Stuttgart Institute. Of primary importance is the concept and use of natural modes of straining to define the deformation of elements.The first part investigates inter alia the statics and dynamics of anisotropic parallelogram plates and shells idealized into an assembly of such elements. Use is made of a so-called natural or oblique system of co-ordinates both with respect to forces, displacements, moments and rotations, all of which obey their own rule of obliquity. A kinematically consistent lumped mass matrix is given which yields a high precision in the estimation of eigenmodes and eigenfrequencies. Comparison with experimental and analytical results (where available) show an excellent agreement. The paper develops also the analysis of anisotropic triangular plates under bending and membrane action which are ideal elements to represent shells and plates of arbitrary configuration. Here too a satisfactory degree of agreement is reached with previous special analytical results. In this first part transverse shear strains are ignored and displacements assumed to be small. A generalization allowing for shear strains and large displacements is to be included in a subsequent publication which will also explore further refinements of the theory.

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Übersicht Es wird ein Überblick über eine neue Berechnungsmethode von willkürlich geformten Platten und Schalen gegeben, die auf der vom Autor entwickelten Matrizenverschiebungstheorie beruht. Die grundlegende Voraussetzung der Theorie ist die Benutzung eines modernen, großen Digitalautomaten und eines ausgeklügelten Matrizen-Interpretativ-Systems, gekoppelt mit einer Tragwerksaufbausprache, die im Stuttgarter Institut des Authors aufgestellt wurden. Von besonderer Bedeutung ist der Gedanke und die Benutzung natürlicher Verzerrungszustände, um die Deformation der Elemente zu beschreiben.Im ersten Teil wird unter anderem die Statik und Dynamik von anisotropen Parallelogrammplatten und-schalen untersucht, die in einem von Parallelogrammelementen aufgebauten System idealisiert werden können. Es werden die sogenannten natürlichen oder schiefen Koordinaten verwendet mit Bezug auf Kräfte, Verschiebungen, Momente und Verdrehungen, die alle einem besonderen Gesetz der Schiefe gehorchen. Eine kine-matisch konsequente konzentrierte Massenmatrix wird entwickelt, welche eine hohe Genauigkeit in der Berechnung von Eigenschwingungsformen und Eigenfrequenzen ergibt. Vergleiche mit experimentellen und analytischen Ergebnissen (wo vorhanden) zeigen ausgezeichnete Übereinstimmung. Ferner wird die Matrizenberechnung von anisotropen Dreiecksplatten allgemeiner Form entwickelt, die sowohl einem Biege- wie einem Membran-Zustand ausgesetzt sind, und ideale Elemente für den Aufbau von Schalen willkürlicher Formen ergeben. Eine zufriedenstellende Übereinstimmung mit vorhandenen Ergebnissen zeigt wieder die Genauigkeit der Methode. In diesem ersten Teil der Arbeit werden die transversalen Schubverzerrungen vernachlässigt und kleine Verschiebungen vorausgesetzt. Eine Verallgemeinerung, welche diese transversalen Schubverzerrungen, sowie große Verschiebungen einschließt, wird in einer zukünftigen Veröffentlichung erfaßt werden, die auch weitere Verfeinerungen der Methode enthalten wird.

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The author wishes to thank his collaborators K. E. Buck and Kariappa for theier imaginative support, especially in programming the examples of this paper.     

Stress and finite-strain analysis of a circular ring under diametral compression

Using a moiré, large-strain analysis method, a complete solution is shown in this paper of the fields of strain and stress for a circular ring subjected to diametral compression between two flat platens. The isotheticsu andv, obtained using 1000-lines-per-inch gratings, were differentiated photographically by the shifting technique (moiré-of-moiré) to determine ?u/?x, ?v/?y, ?u/?y and ?v/?x. Using the exact finite strain-displacement relationship, the Eulerian strains ? _x ^E , ? _y ^E and γ _xy ^E were computed. From these, the principal Eulerian strains were obtained. These results were verified with the isochromatics obtained from a large-deformation photoelasticity analysis. The ring was made of a polyurethane rubber which exhibits a linear relationship between natural strain and a newly introduced concept of “natural stress”. The Eulerian strains were converted to natural strains, and from these natural stresses were computed using the newly developed concept. Results are presented graphically for the whole field of the ring.     

Transient displacement and stress in non-homogeneous elastic shells

Summary Transient displacement and stress in thick inhomogeneous cylindrical and spherical shells is investigated for situations when the surfaces are subjected to dynamic loads consistent with the production of radial vibrations. In the first instance, transformation of the governing equations is sought to a form amenable to solution via a finite Hankel transform technique. Such reduction is available for a broad class of radial variations in the material density and elastic parameters. However, the solutions generated by this method are rather involved and two other approaches are indicated. Thus, reduction of the system to the conventional wave equation is obtained under certain restrictions on the nature of the inhomogeneities and a simple correspondence principle is presented for the imposed boundary stress boundary value problem. Finally an asymptotic wave front analysis is presented which has a wide generality of application.

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Zusammenfassung Es werden die zeitlich vorübergehenden Verrückungen und Spannungsänderungen in dicken inhomgenen zylinder-und kugelförmigen Schalen für den Fall untersucht, dass die Oberfläche dynamischen Belastungen ausgesetzt ist, die strahlenförmige Schwingungen produzieren. Zunächst werden Tranformationen der auftretended Gleichungen gesucht, die eine Lösung mit Hilfe von endlichen Hankeltransformations-Techniken zulassen. Eine solche Reduzierung ist für eine grosse Klasse von abstandsabhängigen Veränderungen der Dichte-und Elastizitätsparameter \:moglich.Die so erhaltenen Lösungen sind jedoch recht kompliziert, und zwei weitere Lösungsmöglichkeiten werden angedeutet. Einmal erhält man unter gewissen Beschränkungen bezüglich der Art der Inhomogenitäten eine Reduzierung des Gleichungssystems auf die gewögnliche Wellengleichung, zum anderen wird ein einfaches Korrespondensprinzip für das betrachtete Randwertproblem aufgestellt. Schliesslich wird eine asymptotische Wellenfrontanalyse entwickelt, die vielseitig verwendbar ist.

     

General solutions of axial symmetrical ring shells

This paper gives the general solutions of axial symmetrical ring shells for all values of slenderness ratio. This solution is newly brought out, and can be used to solve various practical problems, including corrugated tubes, thermal expansion joints, Borden tubes, etc.     

Complex equations of flexible circular ring shells overall-bending in a meridian plane and general solution for the slender ring shells

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Use of a photometric method to measure the displacement of metal shells under an explosive load

Journal of Applied Mechanics and Technical Physics -     

Elastic-plastic deformation of a circular ring under loading by a spatial force system

Dnepropetrovsk Metallurgical Institute. Dnepropetrovsk University. Translated from Prikladnaya Mekhanika, Vol. 25, No. 9, pp. 109–114, September, 1989.     

Influence of temperature transients and centrifugal force on fast-response pressure transducers

This contribution focuses on the use of fast-response semi-conductor pressure transducers to measure accurately the mean and fluctuating total pressure or static pressure in a wind tunnel environment. The problem of angular sensitivity is briefly addressed when measuring total pressure. Then, the influence of temperature is described when testing under steady or transient temperature conditions. The influence of the rotational speed is analyzed when measuring with rotating transducers. The transfer function of a sensor-cavity system is also considered. Correction methods are proposed for both the effects of the temperature and the rotational speed. Several applications are presented covering turbulence measurement with a quasi-steady probe, static and total pressure measurements in the absolute frame and the relative frame.