The theory of orthotropic layered cylindrical shells

The author examines orthotropic layered cylindrical shells for which the moduli of elasticity of the load-carrying layers substantially exceed the shear modulus between layers. This class of structure includes, in particular, shells made of orthotropic glass-reinforced plastic. In this case the classical theory based on the Kirchhoff-Love hypotheses requires refinement; the corresponding equations obtained as a result of approximating the distribution of shear stresses or displacements over the thickness of the shell by a certain known function are presented in [4, 7, 8]. In this paper equations that make it possible to construct the stress distribution over the shell thickness are obtained within the framework of the engineering theory on the basis of the hypothesis of the incompressibility of a normal element.Mekhanika Polimerov, Vol. 4, No. 1, pp. 136–144, 1968     

Mechanical stability of functionally graded stiffened cylindrical shells

This paper is concerned with the elastic buckling of stiffened cylindrical shells by rings and stringers made of functionally graded materials subjected to axial compression loading. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations, the equilibrium and stability equations are derived using the Sander’s assumption. Resulting equations are employed to obtain the closed-form solution for the critical buckling loads. The results show that the inhomogeneity parameter and geometry of shell significantly affect the critical buckling loads. The analytical results are compared and validated using the finite element method.     

Free vibrations of thick layered cylindrical shells

Two approaches to the calculation of closed thick layered cylindrical shells are developed. They are based on division of the cylindrical shell across its thickness by concentric circumferential surfaces into a series of constituent cylindrical shells. Satisfying the contact conditions on the surfaces between constituent shells, it is possible to determine the frequency of free bending vibrations of the initial shell with a sufficient accuracy. In the first approach, the distribution of unknown functions across the shell thickness is sought on the basis of an analytical solution to the corresponding system of differential equations; in the second one, the distribution is assigned by polynomial approximation functions.     

Thermal stresses in anisotropic cylindrical elastic shells

We investigate the deformation of general anisotropic and inhomogeneous shells, under the action of a given temperature distribution. We assume that the temperature field is a polynomial in the axial coordinate, and we establish the displacements produced by the prescribed thermal field. The results are obtained in the framework of the linear theory for Cosserat thermoelastic shells. The solution is used to study the special case of orthotropic cylindrical shells. Copyright © 2009 John Wiley & Sons, Ltd.     

A new refined theory of anisotropic shells

A new refined theory of anisotropic thin shells is constructed with allowance for the effects associated with all the transverse strains and stresses neglected in constructing the classical theory.Institute of Mathematics and Mechanics, Academy of Sciences of the Armenian SSR, Erevan. Translated from Mekhanika Polimerov, No. 5, pp. 884–896, September–October, 1970.     

Numerical computation of weak solutions of nonlinear motion equations of stiffened cylindrical shells

An algorithm is presented for the numerical solution of nonlinear equations of motion of stiffened cylindrical shells described by a Timoshenko-type theory. This algorithm is constructed using a weak solution of nonlinear motion equations of stiffened cylindrical shells. A difference scheme is constructed using the approximation of integral identities. A dependence was found between the steps of the time and space variables for the linearized difference scheme.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, Latvia, October, 1995.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6. pp. 808–815, November–December, 1995.     

The dynamic stability and nonlinear vibration analysis of stiffened functionally graded cylindrical shells

A theoretical model is developed to study the dynamic stability and nonlinear vibrations of the stiffened functionally graded (FG) cylindrical shell in thermal environment. Von Kármán nonlinear theory, first-order shear deformation theory, smearing stiffener approach and Bolotin method are used to model stiffened FG cylindrical shells. Galerkin method and modal analysis technique is utilized to obtain the discrete nonlinear ordinary differential equations. Based on the static condensation method, a reduction model is presented. The effects of thermal environment, stiffeners number, material characteristics on the dynamic stability, transient responses and primary resonance responses are examined.     

A variant of the theory of thick multilayer cylindrical shells

Equations are derived which describe the stress field in thick orthotropic cylindrical shells of a material whose mechanical properties vary across the thickness. An iterative computation procedure is set up which takes into account transverse strains and where the initial approximation corresponds to the hypothesis of straight normals. The convergence of this method is estimated for the case of a thick orthotropic cylinder under axisymmetric strain, and the results are compared with the exact solution.     

Spatial effects in problems on the deformation of cylindrical shells of anisotropic composites

Mechanics of Composite Materials -     

Vector and scalar optimization of stiffened cylindrical shells subject to a stochastic combined load

We discuss certain questions of multicriterion optimization of stiffened cylindrical shells subject to the combined action of determinate and random loads. By application of the apparatus of fuzzy set theory we conduct a comparative analysis of optimal shell designs obtained using two-criterion and one-criterion models.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 65–69.     

Variant of the geometrically nonlinear theory of anisotropic shells with allowance for transverse shear

A very simple variant of the geometrically nonlinear theory of anisotropic shells with allowance for the high compliance of the material in transverse shear is proposed. From this theory there follow, as a special case, the equations for an isotropic shell; these differ from the relations of [2] with respect to terms of the order of the ratio of the thickness of the shell to the radii of curvature small as compared with unity. The equations obtained are used to solve the problem of the stability of orthotropic shells of revolution relative to the starting axisymmetric state of stress.Translated from Mekhanika Polimerov, No. 5, pp. 863–871, September–October, 1969.     

Second-approximation shear theory for shallow layered shells and plates

Analysis of a second-approximation refined shear model for shallow layered composite shells and plates with a substantially inhomogeneous structure over the thickness is presented. The tangential displacements and corresponding normal stresses are expressed in the form of a polynomial of the fith degree in the transverse coordinate and contain squared rigidity characteristics. In this way, the accuracy of results and practical coincidence with the 3D solutions is ensured. Based on the refined model, a theory of shallow layered shells is developed. A system of resolving equations of sixteenth power together with appropriate boundary conditions was obtained and solved analytically. It is shown that the area of application of the formed model is extended as compared with the model of the first approximation. The model proposed allows us to examine the stress-strain state of layered composite structures of substantially different thickness and physical-mechanical characteristics of the layers, including the possibility of simulating relatively large shear deformations of rigid layers separated by a low-modulus thin interlayer pliable to transverse shear.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 363–370, May–June, 1998.     

Nonlinear equations of a timoshenko-type theory of laminated anisotropic shells

In recent years analysis of the stress—strain state of shell structures made out of composite materials has been based on refined shell theories which take into account strains in the direction normal to the reference surface. There are several approaches to the formulation of the refined theories. One can point to shell theories developed on the basis of variational principles (e.g., [1, 2]) as well as theories created with the help of iterational processes (e.g., [3–6]). A resolving system of nonlinear equations for laminated anisotropic shells has been derived in the proposed research based on the Reissner variational principle [7, 8]. A similar linear theory which takes into account the strain e₃₃ also has been developed in [1]. If the shear stiffnesses of the layers differ greatly from each other in the transverse direction, then one can treat the shell structure as a single-layer shell of nonuniform structure. In this case it is advisable to solve a problem of the type of a uniform shell with minimal stiffnesses.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 501–507, May–June, 1979.