Application of the extended Newton method to the creep analysis of shells of revolution

Summary The extended Newton method combined with the method of finite-differences is shown to be a powerful means to the steady-state creep analysis of shells of revolution. The creep theory of von Mises type and the power creep law are assumed. As numerical examples, a simply-supported circular cylindrical shell with open ends and a clamped spherical shell, subjected to internal pressure respectively, are analysed. The results of calculation of the cylindrical shell, in particular, are compared with those of semi-infinite sandwich shell obtained by Rabotnov.

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Übersicht Das erweiterte Newton-Verfahren bildet zusammen mit der Methode der finiten Differenzen ein wirksames Werkzeug zur Berechnung der Kriecheigenschaften von rotationssymmetrischen Schalen. Dabei wird eine Kriechtheorie nach v. Mises sowie ein Potenzgesetz für das Kriechen zugrunde gelegt. Als Beispiele werden eine einfach gelagerte kreiszylindrische Schale mit freien Rändern sowie eine eingespannte Kugelschale berechnet, die beide durch Innendruck belastet sind. Die Ergebnisse für die Zylinderschale werden mit den von Rabotnov erhaltenen Ergebnissen für eine halb-unendliche Sandwich-Schale verglichen.

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The present authors wish to express their gratitude to Professor Y. Ohashi of Nagoya University for his invaluable guidance and stimulating discussions.     

The integrability,equivalence and solutions of two kinds of integrable deformed fourth-order matrix NLS equations

Nonlinear Dynamics - Based on the higher-order restricted flows, the first type of integrable deformed fourth-order matrix NLS equations, that is, the fourth-order matrix NLS equations with...     

On the problems of sandwich shells having the form of a surface of revolution and face layers of non-equal thicknesses

Fundamental equations which govern the behavior of an elasticsandwich shell having the form of a surface of revolution andface layers of non-equal thicknesses are derived,with the so-lution of Refs.[3]and[4]as special examples.The problems of the shell under the action of symmetricalloads are reduced to the solution of a displacement-function4～,where4αsatisfies a differential equation of sixth order.     

The influence of the reference geometry on the response of elastic shells

Within the scope of the nonlinear theory of an elastic Cosserat surface, this paper is mainly concerned with the influence of the reference geometry and the related aspects of material symmetry restriction on the response of thermoelastic shells. The significance of the effect of the reference geometry is discussed in the case of isotropic shells, which may be of variable thickness in a reference state.     

Existence and uniqueness of solutions to the dynamic equations for koiter shells

１ＴｈｅＰｒｏｐｏｓａｌｏｆＰｒｏｂｌｅｍＷｅｃｏｎｓｉｄｅｒａｆａｍｉｌｙｏｆｌｉｎｅａｒｅｌａｓｔｉｃｓｈｅｌｓｏｆｔｈｉｃｋｎｅｓ２ε,ａｌｈａｖｉｎｇｔｈｅｓａｍｅｍｉｄｄｌｅｓｕｒｆａｃｅＳ＝φ（ω）Ｒ３,ｗｈｅｒｅωＲ２ｉｓａｂｏｕｎ...     

Numerical analysis of the branching of solutions to nonlinear equations for cylindrical shells

A nonlinear boundary-value problem for shells is formulated. The problem statement permits us to analyze the behavior of the postbuckling solutions in a finite-dimensional space with the dimension independent of the discretization technique. A branching pattern is established for the solutions of the problem in the case of a uniform external pressure. Four characteristic types of solution are recognized in the case of an arbitrary external pressure. The associated buckling loads are determined. It is found out that five significant parameters are sufficient for a qualitative analysis of a cylindrical shell __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 103–112, January 2006.     

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 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.