The stress-deformed state of a packet of cylindrical shells taking account of friction

We propose a method of determining the contact pressures between the shells in a packet under the influence of nonlinear internal and constant external pressure. Using the equations of the general moment theory of shells we determine the stress-deformed state of a packet of finite cylindrical shells taking account of frictional forces on the contacting surfaces. One table. Bibliography: 10 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 94–98.     

The effect of the nonuniformity properties of a material in problems of elastic equilibrium and stability of shells

On the basis of two improved models of shells that are nonuniform by thickness (based on assumptions of Timoshenko type stated separately for each layer and assuming a uniform stress-deformed state of a thin-walled element of the layered structure) we study the stressed state and stability of three-layer cylindrical shells with a nonsymmetric packet. We show the equivalence of the two models in describing the reaction of layered shells to uniform external actions. We give an analysis of the dependence of the stress-deformed state and the reserve stability of shells on the structure of the packet.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 89–93.     

Analysis of the zonal winding pattern of thin spherical shells

Conclusions 1. A method has been proposed for calculating the zonal pattern of winding thin spherical shells.2. The tested strength of shells wound by the calculated pattern correlates with the theoretical.3. The proposed calculation apparatus makes it possible to calculate winding patterns with any variants of angles and number of zones.4. A zonal pattern in a spherical shell having a connecting pipe of small diameter can give a mean constructional strength which does not exceed 0.39 times the strength of the unidirectional plastic (as against 0.5 in the ideal case for a sphere of bidirectional material), i.e., not more than 78% of the strength of the plastic is realized.5. The bearing ability of a sphere wound by the zonal method is 22% less than that of a long cylinder (with no bottom) made by the same winding method.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 625–631, July–August, 1978.     

Investigation of the Stress State of Pressure Vessels of Inhomogeneous Structure Made of Composite Materials

The problem on the stress-strain state of layered cylindrical shells with bottoms of intricate shape under the action of internal pressure is considered. The elastic system examined is formed by spiral-circular winding. Two variants of the shell bottom structure are investigated. In the first variant, one spiral layer is installed, which leads to great variations in the bottom thickness along the meridian. In the second one, the bottoms are formed according to the zone-winding scheme. The stress state of the shell constructions of the classes considered is determined by solving boundary-value problems for systems of ordinary differential equations. The solution results for cylindrical shells with elliptic bottoms for the two types of winding are given. It is shown that the zone winding leads to smaller deflections and stresses than the conventional ways of reinforcing shell bottoms.     

Optimization of the axial stability of equal-strength reinforced cylindrical pressure vessels

The class of reinforced cylindrical shells obtained by spiral winding with reinforcing ring or longitudinal layers is considered. The structure of the shells is optimal with respect to internal pressure. The reinforcement angle is selected so as to maximize the critical axial load.Translated from Mekhanika Polimerov, No. 6, pp. 1123–1126, November–December, 1973.     

Mixed Boundary Value Problems for Minimal Graphs on a Riemann Surface and Winding Staircases

In this paper we want to describe the results of our treatise on winding staircases [9] leading to boundary value problems for minimal graphs on a special Riemannian surface, the etale plane. This has been presented on the conference Nonlinear Differential Equations of the Riemann International School of Mathematics, presided by Professor Louis Nirenberg, in September 2010 at Verbania-Intra on Lago Maggiore.     

Optimal position of a strut on a cylindrical shell

A solution is given for the problem of the optimal design of a rigid structure consisting of a spherical shell and two cylindrical shells linked by a strut. The volume of the structure is minimized under constraints on the maximal equivalent stresses in each of the shells and on the geometric parameters of the strut. Among the regulating parameters are the thickness of the shells, the geometric parameters of the strut, and the length of the first of the cylindrical shells. The problem is solved by the method of geometric programming.Translated from Matematicheskie Metody i Fiziko-Mekhanicheski Polya, No. 29, pp. 76–80, 1989.     

Buckling and the initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry

A method for calculating the buckling stability of layered cylindrical shells made of composite materials with one plane of symmetry of mechanical characteristics is worked out. As a special case, shells made of fibrous materials by winding in directions not coinciding with coordinate axes are considered. An analysis of stability of shells under an axial compression, external pressure, and torsion is carried out. It is shown that, at a great number of layers and appropriate reinforcing angles, the shells can be considered orthotropic. The solution to the problem of the initial postbuckling behavior of shells made of composites with one plane of symmetry is also obtained. It is found that shells of this type can be less sensitive to geometrical imperfections. This fact is important from the practical point of view. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 213–236, March–April, 2007.     

Optimal winding of filament-wound reinforced plastic shells designed to resist buckling under external pressure or axial compression

The optimal method of winding the reinforcement of thin cylindrical shells subjected to external pressure or axial loading is investigated. Various types of winding — normal, simple oblique, crossed, and isotropic — are considered. An approximate formula is obtained for the critical external pressure. This formula is used to analyze the possibility of raising the critical load by adopting oblique winding. In the case of axial compression different buckling modes are examined and the optimal winding determined.Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 864–875, September–October, 1968.     

Free oscillations of shells of complex geometry with finite shear stiffness

By applying isoparametric approximations we develop a finite-element method for studying the oscillations of shells whose middle surfaces are Monge surfaces. As the starting point we take the model of shells of Timoshenko type. To solve the eigenvalue problem we apply the method of iterations in a subspace. Two figures. Five tables. Bibliography: 14 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 13–17.     

The stressed state of elastoplastic shells with nonthrough cracks

We study the problem of the stressed state and limiting equilibrium of shells with nonthrough surface cracks. Several assumptions make it possible to reduce the three-dimensional problem to the two-dimensional problem and the latter to a system of singular integral equations whose solution is constructed using numerical methods. For cylindrical and spherical shells weakened by nonthrough cracks situated along the coordinate lines we carry out a numerical analysis of the dependence of the crack opening on the load and the geometric and physico-mechanical parameters of the shells.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 147–151.     

On sensitive elliptic singular perturbation problems and logarithmic oscillations: the case of shells with edges

This work deals with singular perturbation problems depending on small positive parameter ?. The limit problem as ? → 0 has no solution within the classical theory of PDEs, which uses distribution theory. A very particular and less‐known phenomenon appears: large oscillations. These problems exhibit some kind of instability; very small and smooth variations of the data imply large singular perturbations of the solution. That kind of problems appears in elasticity for highly compressible two‐dimensional bodies and thin shells with elliptic middle surface with a part of the boundary free. Here, we consider certain properties of that oscillations and extend the theory to shells with edges. Copyright © 2012 John Wiley & Sons, Ltd.     

Investigation of the performance of composite shells under repeat internal pressure

The effect of the winding material and its thickness on the residual strains and the mode of failure of a composite shell is analyzed. The results of low-cycle fatigue tests on composite shells are presented.P. I. Baranov Central Institute of Aircraft Engine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1060–1065, November–December, 1973.     

Phase Field Modeling of Fracture in Plates and Shells

The numerical modeling of failure mechanisms in plates and shells due to fracture based on sharp crack discontinuities is extremely demanding and suffers in situations with complex crack topologies. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. In this paper, we extend ideas recently outlined in [1, 2] towards the phase field modeling of fracture in dimension-reduced continua with application to Kirchhoff plates and shells. The introduction of history fields, containing the maximum reference energy obtained in history, provides a very transparent representation of the coupled balance equations and allows the construction of an extremely robust operator split technique. The performance of the proposed models is demonstrated by means of representative numerical examples. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Volume preserving flows with cyclic winding numbers groups and without periodic orbits on 3-manifolds

We construct examples of volume preserving non-singular C ¹ vector fields on closed orientable 3-manifolds, which have cyclic winding numbers groups with respect to the preserved volume element, but have no periodic orbits. Received: 17 January 1998 / Revised version: 31 March 1998     

Calculation of the geodesic winding characteristics of glass-reinforced plastic shells of revolution

A method of determining the winding laws for filament-wound shells is considered. The method is based on a natural approach to the derivation of the equation of motion of the winder as a function of the rotation of the wound shell about its own axis.Moscow Bauman Higher Technical College. Translated from Mekhanika Polimerov, No. 6, pp. 1020–1025, November–December, 1970.     

Statistical analysis of some characteristics of cylindrical glass-fiber-reinforced plastic materials

The results are given of a statistical treatment of experimental data on several characteristics of glass-fiber-reinforced plastic cylindrical shells, prepared from glass fabric TS8/3-250 and epoxide binder IF-ÉD-6 (TU-26-59) at the "Électroizolit" factory by winding an impregnated fabric cloth on a mandrel. The experim ental data on the mechanical properties of the glass-fiber-reinforced plastic material were obtained in tests on representative samples cut from the margin of the cylindrical shells. The results of the statistical analysis can be used to evaluate the mechanical reliability of structures made of glass-fiber-reinforced plastic material of the above type.Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 906–910, September–October, 1973.     

On an approach to the design of reinforced shells that is optimal in terms of reliability

We consider questions of optimal design of shallow spherical shells reinforced by a grid of struts taking account of reliability. It is assumed that the independent random variable acting on the structure is distributed according to the Weibull law.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 60–63.     

Polynomial Invariants of Special Groups Generated by Reflections

Generators are obtained for the ring of invariants of the group H created by reflections and which satisfy the following condition: the H-orbits of the directions of symmetry of this group are infinite and their linear shells form a triplet of planes with pairwise zero intersections. Conditions are identified such that the ring of invariants of the group H is not free.