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An orthotropic layered cylindrical sheet subject to axially symmetrical loading is considered. A solution free from the hypothesis of the straight normal is presented; the material of the shell is regarded as incompressible in the radial direction. An attempt is made to allow for the real character of the rigid fixing at the edge of the shell. The stressed state in the neighborhood of the edge is analyzed.

The present article considers the bending of a beam fabricated from a material with a low shear rigidity. A bending-theory variant that does not involve the hypothesis of plane cross sections is presented, assuming the material to be incompressible in the direction of the transverse coordinate. Results previously obtained in this area and an appropriate bibliography were given in an earlier article [3]. A solution is given that permits precise satisfaction of the condition for rigid fastening of the end of the beam. An attempt is made to take into account the actual character of the mounting.

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.

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.

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.

The deformation of an orthotropic glass-reinforced plastic is considered with allowance for the failure of the resin in the transverse layers.

The deformation of a layered orthotropic cylindrical shell under a local normal load is investigated on the basis of equations that do not depend on the hypothesis of straight normals. The solutions of the analogous classical problems were analyzed in [3]; a solution based on equations that take transverse shear strains approximately into account was proposed in [4]. The high degree of variability of the state of stress created by local loads indicates that it is quite important to take transverse shear strains rigorously into account in problems of this class. An attempt is made to estimate the error introduced by the hypothesis of straight normals and to calculate the load leading to debonding of the shell.

The design of cylindrical shells reinforced in the circumferential direction with high-strength elastic fibers is considered. The problem is solved on the basis of the deformation and flow theories. Relations are derived for the layer thickness required to obtain a structure of uniform strength and for the tension that must be applied to the glass tape during winding.