Deformation of a system of cylindrical shells under the action of an internal nonstationary pressure wave

We study the problem of nonstationary deformation of a system of imbedded cylindrical shells under the action of an internal compression wave. The rigorous method of solution we apply makes it possible to obtain a system of Volterra integral equations with retarded arguments in the deflections of the shells. We give the results of computations for the case of a linear source and a source of finite size with limiting hardness properties. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 60–66.     

Material dispersion in dynamic deformation process of solids under impact action

The dispersion phenomenon is studied to introduce the adequate material model for the advanced states of dynamic deformation processes. The evolution problem is formulated within the frame of theory of thermodynamics and viscoplasticity. Mathematical analysis for elastic, plastic and viscoplastic material evidence the non-dispersive or dispersive property. Occurrence of dispersion in the analysis problem has the consequences not only for constitutive relation. It influences the whole problem with advantages in formulation and solution. Numerical results of example problems present qualitatively different mechanical response for materials with different dispersion. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The stress-strain state of shells under the action of concentrated heat sources

We construct a fundamental solution of a static problem of heat conduction for thin isotropic shells of positive curvature under the action of concentrated heat sources. We study the problems involved in simplifying the heat equations. Four figures. Two tables. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 70–80.     

Deformation of tape-wound cylindrical shells under internal pressure

The state of stress of a cylindrical shell would from glass tape at arbitrary angles to the generator is examined. The pressure dependence of the strains and stresses is obtained for uniform internal pressure, and the question of rationalization of the structure of the shell material is investigated. To describe the deformation characteristics associated with failure of the resin under load, a perfectly plastic model is introduced. The results of an experimental determination of the relative elongations are presented for the case of active loading and unloading.Mekhanika Polimerov, Vol. 3, No. 5, pp. 915–920, 1967     

Stability of orthotropic cylindrical shells under variable pressure

A method of determining the critical stresses is developed for elastic orthotropic cylindrical shells subjected to nonuniform pressure. It is assumed that the external pressure varies over the cross section and is constant along the length of the cylinder. A shell stability analysis is given for the case of a weakly varying load.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 897–902, September–October, 1970.     

Deformation of cylindrical composite shells under combined dynamic loading

Conclusions A procedure has been shown for calculating the stress-strain state of cylindrical multilayer shells made from composite materials under the combined action of dynamic axial compression and dynamic external pressure, as well as with different variants of combined loading with static and dynamic forces. An investigation has been made of the effect on the mode of the buckled shell surface of the ratio of the application rate of dynamic loads; ranges of loading rates have been established in which stresses predominate caused either by axial compression or external pressure. It has been shown that, as a result of preliminary static loading, a marked change occurs in the initial imperfections of the shell mode which affects subsequent dynamic buckling. To calculate the time when the first defect occurs and its location in the shell body, a procedure has been devised for layer-by-layer strength analysis employing a tensor-polynomial criterion. It was demonstrated that the level of preliminary static loading noticeably affects the time until the first failure of the layer, not only a reduction of this time being possible with an increase in the static loads, but also an increase in it.We should also point out the work in [10] where it is shown that it is possible to weaken the susceptibility of the shell to initial imperfections when internal pressure is applied.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 461–473, May–June, 1981.     

The theory of micropolar thin elastic shells

A boundary-value problem of the three-dimensional micropolar, asymmetric, moment theory of elasticity with free rotation is investigated in the case of a thin shell. It is assumed that the general stress-strain state (SSS) is comprised of an internal SSS and boundary layers. An asymptotic method of integrating a three-dimensional boundary-value problem of the micropolar theory of elasticity with free rotation is used for their approximate determination. Three different asymptotics are constructed for this problem, depending on the values of the dimensionless physical parameters. The initial approximation for the first asymptotics leads to the theory of micropolar shells with free rotation, the approximation for the second leads to the theory of micropolar shells with constrained rotation and the approximation for the third asymptotics leads to the so-called theory of micropolar shells “with a small shear stiffness”. Micropolar boundary layers are constructed. The problem of the matching of the internal problem and the boundary-layer solutions is investigated. The two-dimensional boundary conditions for the above-mentioned theories of micropolar shells are determined.     

Long-time stability of orthotropic cylindrical shells under external pressure

The problem is solved using a refined theory of shells that takes shear strains into account. The shell deformations are described by means of the relations for an orthotropic material, it being assumed that creep strains develop only as a result of shear forces. The geometrically linear problem is considered. For the sake of comparison, the long-time critical load is calculated on a Minsk-22 computer using the Kirchhoff-Love and refined models. It is shown that when shears are taken into account, in certain cases the critical load may be reduced by 30%.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 315–320, March-April, 1969.     

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.     

Stability of multilayered shells under interlaminar uniformly distributed pressure

The article deals with the problem of the stability of the inner layer of a cylindrical multilayered pipe when uniformly distributed gas pressure acts in the interlaminar gap. The suggested approach takes contact between layers of the shell into account. The article investigates the effect of the divergence angle of the zone of delamination on the form of loss of stability and rigidity of the outer layers of the shell, and on the magnitude of the critical load.Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 86–90, 1990.     

Stability of cylindrical glass-reinforced plastic shells under external pressure

The stability of cylindrical glass-reinforced-plastic shells under external omnidirectional hydrostatic pressure has been the subject of an experimental investigation. The experimental data obtained are compared with calculations based on the theory of orthotropic shells.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1089–1095, 1967     

Strength of cylindrical shells of laminar composites under dynamic loading

Conclusion The methods described in the present review paper for the computation of cylindrical shells of laminar composites under various types of dynamic loads make it possible to calculate the stress-strain state at any point of the body of the shell at an arbitrary time and to determine the time of the first failure of a layer (including fatigue failure) using strength criterion of an anisotropic body for the case of a plane stressed state, and also the location of the first flaw in the shell. This makes it possible to determine the magnitude of the applied pulse (the amplitude of a pulsed loading), or the amplitude of a vibratory loading for which the first centers of failure appear in the design.Presented at the Second Soviet-American Symposium on the Problem Failure of Composite Materials (Bethlehem, Pa., USA, March, 1981).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 460–467, May–June, 1982.     

Deformation of momentless shells under internal pressure under conditions where the material undergoes creep

Relations are derived for the deformation of momentless shells under internal pressure and finite strains. The law governing the deformation of the material is assumed to be that for a typical, incompressible viscoelastic solid. The special cases of the behavior of a spherical shell under a constant internal pressure and for a constant amount of gas in the shell are solved. It is found that up to a given limit, at constant pressure the deformation of the shell falls off, while above this limit the deformation increases at an increasing rate. With a constant quantity of gas inside the shell the deformation again falls off, as far as initial application of an internal pressure to the shell, equal to the critical, elastic pressure.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1066–1072, November–December, 1972.     

Static and dynamic buckling modes of spherical shells subjected to external pressure

We investigate the possibilities for simplification of previously proposed refined linearized equations of perturbedmotion to identify, by dynamic method, the buckling mode shapes of isotropic spherical shells undergoing external hydrodynamic pressure. In the analysis of classical flexural buckling shapes of spherical shells, it is shown that preserving of nonconservative parametric terms in governing equations of formulated problem, which are related with loading of the shell with follower pressure practically does not affect the value of critical load and the resulting bucklingmode shapes in shell.     

Stability loss of reinforced cylindrical shells under isotropic external pressure

Conclusions 1. Upon the loading of a composite shell having a metallic matrix the shear effects are insignificant even in the case of comparatively large volume reinforcement contents and wall thicknesses.2. The principal modulus of a material which determines the stability of a reinforced shell upon isotropic external pressure is the secant modulus in the circumferential direction.3. In the case of complex reinforcement schemes some decrease in the stability of the shell is possible, probably due to an imperfection in reinforcement technology.Institute of Solid State Physics, Academy of Sciences of the USSR, Moscow Region. Translated from Mekhanika Polimerov, No. 1, pp. 90–95, January–February, 1977.     

Thermoelasticity of orthotropic shells under the action of a moving concentrated heat source

We solve the problem of thermoelasticity for thin orthotropic shells of nonnegative curvature under the action of a concentrated heat source that moves over the surface of the shell. A linear temperature distribution over the thickness of the shell and convective heat exchange from its lateral surfaces by the Newton law are established. Using Fourier and Laplace integral transformations, we obtain a solution in the analytic form. The influences of the thermomechanical properties of the material and parameters of heat exchange with the surrounding medium on the stress-strain state of the shell are investigated.     

Dynamical optimization of ribbed cylindrical shells under the action of periodic nonharmonic loads

Ribbed cylindrical shells that are under the action of a nonharmonic cylindrical load are considered. The problem of optimal (with respect to the criterion of minimum mass) projection is formulated in terms of nonlinear programming. Some results of a numerical experiment about the choice of optimal parameters are shown, which was carried out on an IBM with the help of the method of random search.Translated from Dinamicheskie Sistemy, No. 9, pp. 22–27, 1990.