Analyzing the stress–strain state of thick cylindrical shells

Two approaches to the analysis of the stress–strain state of thick cylindrical shells are elaborated. The shell is divided by concentric cross-sectional circles into several coaxial cylindrical shells. Each of these shells has its own curvature determined on its midline. The stress–strain state of the original shell is described by satisfying the interface conditions between the component shells. The distribution of unknown functions throughout the thickness is determined by finding the analytic solution of a system of differential equations in the first approach and is approximated by polynomial functions in the second approach. The stress–strain state of thick shells is analyzed. It is revealed that the effect of reduction becomes stronger with increasing curvature     

Nonlinear deformation and stability of oval cylindrical shells under pure bending and internal pressure

The stability problem of a cylindrical shell of oval cross section loaded by a bending moment and internal pressure is studied. The variational displacement finite-element method is used. For the prebuckling stress-strain state, the bending and nonlinearity are taken into account. The effects of the nonlinear nature of the deformation and the cross-sectional ovality of the shells on the critical loads and buckling modes are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 119–125, May–June, 2006.     

Homogenization and Global Responses of Inhomogeneous Spherical Nonlinear Elastic Shells

Homogenization of radially inhomogeneous spherical nonlinear elastic shells subject to internal pressure is studied. The equivalent homogeneous material is defined in such a way that it gives rise to exactly the same global response to the pressure load as that of the inhomogeneous shell. For a shell with general strain–energy function and inhomogeniety, the strain–energy function of the equivalent homogeneous material is determined explicitly. The resulting formula is used to study layered composite shells. The equivalent homogeneous material for an infinitely fine layered composite shell is examined, and is found to give not only the same global response, but also the same average stress field as the composite shell does.     

Analysis of shells reinforced by massive stiffening ribs

The paper presents results of applying a heterogeneous mathematical model “elastic body–Timoshenko shell” to design shells with massive ribs. Numerical results are obtained for a cylindrical shell with ribs. They are compared with results obtained using the theory of elasticity and the theory of Timoshenko shells with piecewise-constant thickness Published in Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 132–142, November 2008.     

Spectral Problem for Shells with Fluid

Variational eigenvalue equations describing vibrations of orthotropic shells containing an ideal incompressible fluid are obtained. The vibration frequencies are assumed to be small, which makes it possible to use linear equations and to consider the boundary of the wet surface of the shell to be unchanged. The equations of anisotropic shells are based on the linear relations of multifield theory, which allows to obtain a more accurate model of anisotropic shells that satisfies the conditions of the finite-element method. The fluid flow is considered irrotational and is described using the Laplace equation. A finite-element algorithm is designed to determine the natural frequencies and modes of vibrations of an arbitrary multilayer orthotropic shell of revolution which is partially filled with an ideal incompressible fluid. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 128–135, November–December, 2005.     

The effect of the reinforcement structure on the heat conductivity of shells of revolution with a system of tubes filled with a liquid heat-transfer agent

The initial boundary-value heat-conduction problem for shells reinforced by tubes filled with a flowing liquid heat-transfer agent is considered. The dependence of the coefficients in the heat-conduction equations on the thermophysical characteristics of the composition phases, reinforcement parameters, and shell geometry is studied. A comparative analysis of the stationary temperature fields in thin shells of revolution of different Gaussian curvature is performed for various reinforcement structures and heat-exchange regimes. It is shown that the temperature distribution in the shells depends strongly on the reinforcement structure and the shell geometry, which opens up new possibilities of designing optimal structures. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 168–177, July–August, 2000.     

Vibration analysis of bi-layered FGM cylindrical shells

In the present study, a vibration frequency analysis of a bi-layered cylindrical shell composed of two independent functionally graded layers is presented. The thickness of the shell layers is assumed to be equal and constant. Material properties of the constituents of bi-layered functionally graded cylindrical shell are assumed to vary smoothly and continuously through the thickness of the layers of the shell and are controlled by volume fraction power law distribution. The expressions for strain–displacement and curvature–displacement relationships are utilized from Love’s first approximation linear thin shell theory. The versatile Rayleigh–Ritz approach is employed to formulate the frequency equations in the form of eigenvalue problem. Influence of material distribution in the two functionally graded layers of the cylindrical shells is investigated on shell natural frequencies for various shell parameters with simply supported end conditions. To check the validity, accuracy and efficiency of the present methodology, results obtained are compared with those available in the literature.     

Stress–strain state of nonthin orthotropic spherical shells of variable thickness

The stress–strain state of an orthotropic spherical shell with thickness varying in two coordinate directions is analyzed. Different boundary conditions are considered, and a refined problem statement is used. A numerical analytic method based on spline-approximation and discrete orthogonalization is developed. The stress–strain state of spherical orthotropic shells with variable thickness is studied     

Stress–Strain State of Three-Layer Cylindrical Shells with Reinforced Light Core Under Nonstationary Loading*

International Applied Mechanics - The stress–strain state of symmetric three-layer cylindrical shells under nonstationary loads is considered. The equation of vibrations of a shell with a...     

Nonlinear vibrations of cylindrical shells with initial imperfections in a supersonic flow

The paper studies the dynamics of nonlinear elastic cylindrical shells using the theory of shallow shells. The aerodynamic pressure on the shell in a supersonic flow is found using piston theory. The effect of the flow and initial deflections on the vibrations of the shell is analyzed in the flutter range. The normal modes of both perfect shells in a flow and shells with initial imperfections are studied. In the latter case, the trajectories of normal modes in the configuration space are nearly rectilinear, only one mode determined by the initial imperfections being stable __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 63–73, September 2007.     

Solving axisymmetric dynamic problems for reinforced shells of revolution on an elastic foundation

The dynamic behavior of reinforced shells of revolution in an elastic medium is modeled. Pasternak’s model is used. A problem of vibration of discretely reinforced shells of revolution is formulated and a numerical algorithm is developed to solve it. Results from an analysis of the dynamic behavior of a reinforced spherical shell on an elastic foundation are presented as an example Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 99–106, February 2009.     

Refined design of longitudinally corrugated cylindrical shells

A refined Timoshenko-type model based on the straight-line hypothesis is used to develop an approach to analyzing the stress state of longitudinally corrugated cylindrical shells with elliptic cross-section. The approach is to reduce the two-dimensional boundary-value problem that describes the stress–strain state of the shell to a one-dimensional one and to solve it with the stable numerical discrete-orthogonalization method. The solutions obtained using the straight-line hypothesis and the equations of three-dimensional elasticity are compared. The dependence of the stress–strain state of the shell on the number and amplitude of corrugations and the aspect ratio of the cross-section is analyzed     

Thermoelastic bending of locally heated orthotropic shells

The thermoelastic bending of locally heated orthotropic shells is studied using the classical theory of thermoelasticity of thin shallow orthotropic shells and the method of fundamental solutions. Linear distribution of temperature over thickness and the Newton’s law of cooling are assumed. Numerical analysis is carried out for orthotropic shells of arbitrary Gaussian curvature made of a strongly anisotropic material. The behavior of thermal forces and moments near the zone of local heating is studied for two areas of thermal effect: along a coordinate axis and along a circle of unit radius. Generalized conclusions are drawn __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 80–85, March 2007.     

Numerical modelling of the stability of loaded shells of revolution containing fluid flows

A mixed finite-element algorithm is proposed to study the dynamic behavior of loaded shells of revolution containing a stationary or moving compressible fluid. The behavior of the fluid is described by potential theory, whose equations are reduced to integral form using the Galerkin method. The dynamics of the shell is analyzed with the use of the variational principle of possible displacements, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure exerted on the shell by the fluid. The solution of the problem reduces to the calculation and analysis of the eigenvalues of the coupled system of equations. As an example, the effect of hydrostatic pressure on the dynamic behavior of shells of revolution containing a moving fluid is studied under various boundary conditions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 185–195, March–April, 2008     

Stability of longitudinally corrugated cylindrical shells under uniform surface pressure

The buckling problem for longitudinally corrugated cylindrical shells under external pressure is solved. The solution makes practically exact allowance for the geometry and buckling modes of the shell. The inaccuracy of the results is due to the assumption that the subcritical state is momentless. Shells consisting of cylindrical panels of smaller radius and noncircular shells with sinusoidal corrugations are analyzed for stability. The practical applicability of such shells is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 66–79, October 2007.     

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.     

Solution of contact problems on the basis of a refined theory of plates and shells

Solutions of contact mixed boundary-value problems for a plate and for a cylindrical shell are given. These solutions are obtained with the use of equations for shells constructed by expanding solutions of elasticity theory equations with respect to the Legendre polynomials. Results of numerical simulations of the stress state in the vicinity of points with changing conditions on the frontal faces of the shell are presented. The results obtained are compared with analytical solutions of elasticity theory problems and with solutions obtained on the basis of the classical equations of the shell theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 169–176, September–October, 2008.     

Geometrically nonlinear finite-element models for thin shells with geometric imperfections

A finite-element method to analyze the stress–strain state and stability of thin shells with geometric imperfections is proposed. An arbitrary curvilinear finite element with vector approximation of the displacement function is used. To solve the systems of nonlinear algebraic equations by iteration methods, linearized stiffness matrices of finite elements and residual and load vectors are formed. The stress–strain state of a thin-walled shell with real geometric imperfections under surface pressure and axial compression is analyzed. The effect of geometric imperfections on the critical combination of loads is evaluated     

Penetration of an elastic circular cylindrical shell into an incompressible liquid

The plane unsteady problem of impact of a thin elastic cylindrical shell on the surface of an ideal incompressible liquid is considered. The initial stage of interaction between the body and the liquid when the stresses in the shell attain peak values is studied. The problem is treated in a linearized formulation and is solved numerically by the normal modes method within the framework of the Wagner approach. The numerical results agree with experimental data for various types of circular cylindrical shells made from mild steel. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 186–197, November–December, 1999.     

Stability of corrugated composite noncircular cylindrical shells under external pressure

Cylindrical shells consisting of cylindrical panels of smaller radius and subjected to uniform external pressure are analyzed for stability. The geometrical parameters of the shells are approximated by Fourier series on a discrete set of points. The Timoshenko theory of shells is used. The solution is represented in the form of trigonometric series. It is shown that short-and medium-length shells with cylindrical panels are advantageous over circular shells. By selecting appropriate parameters of the panels, keeping the mass of the shell constant, it is possible to achieve a significant gain in critical loads. The shells under consideration are less effective than isotropic shells. Shells with sinusoidal corrugation under external pressure are of no practical interest __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 91–102, December 2007.