The numerical analysis of an orthotropic cylindrical shell

This paper is devoted to an orthotropic cylindricall simply supported shell subjected to external pressure. This analysis is focused on determining geometrical shape of shell. Main subject of investigation is to maximize the stability of the shell. Mathematical model of double layer shell was implemented. Numerical solution was obtained for particular class of shells by using the finite element code ABAQUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Forced vibration of an initially stressed thick rectangular plate made of an orthotropic material with a cylindrical hole

The forced vibration of an initially statically stressed rectangular plate made of an orthotropic material is studied. The plate is simply supported along all its edges and contains an internal across-the-width cylindrical hole of rectangular cross section with rounded corners. The initial stresses are created by uniformly distributed normal forces applied to opposite end faces of the plate. Because of the hole, these stresses are not uniform in the plate and significantly affect the stress field caused by additional time-harmonic dynamical forces acting on the upper face of the plate. Hence, for solving the boundary-value problem considered, the superposition principle is unsuitable. Therefore, our investigations are carried out within the framework of the three-dimensional linearized theory of elastic waves in initially stressed bodies. The corresponding boundary- value problems on determining the initial and additional, dynamical stress states are solved by using the three-dimensional finite-element method. Numerical results on stress concentrations around the cylindrical hole and the fundamental frequencies, and on the influence of the initial stresses on the frequencies are presented.     

Parametric vibrations of an orthotropic cylindrical shell with an elastic core. 2. Some numerical results

It is shown that the operator of the problem belongs to the class of oscillation operators. The first five regions of dynamic instability of an elastic orthotropic cylindrical shell with an elastic isotropic core are determined in the first approximation. The effect of the core and transverse shear in the shell on the width and location of these regions of dynamic instability of the system is determined. The effect of transverse shear on the natural frequencies of the empty shell is established.     

Dual problem of optimizing an orthotropic cylindrical shell

The problem of optimizing the weight of an orthotropic cylindrical shell is examined, using the duality theory of geometrical programing.     

Dynamic stability of a viscoelastic orthotropic cylindrical shell

A method based on the use of Laplace transforms has been developed for reducing the system of equations of motion of a viscoelastic orthotropic cylindrical shell to a single integro-differential equation. The effect of the viscous components on the regions of dynamic instability is investigated (creep due to the action of the shear stresses is taken into account).Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 714–721, July–August, 1973.     

Axisymmetric vibrations of an orthotropic non-uniform cylindrical shell

The axisymmetric vibrations of a circular cylindrical shell of constant thickness, orthotropic along the principal geometrical directions and non-uniform along the generatrices, are considered. It is shown, using a particular problem as an example, that the non-uniform physical-mechanical characteristics of the shell material may lead to qualitatively new results in problems of shell dynamics.     

Dynamic stability of an elastic orthotropic cylindrical shell with allowance for transverse shears

The resolvents for the dynamic stability of an elastic orthotropic cylindrical shell are obtained in accordance with the Ambartsumyan and Timoshenko-type refined theories. The regions of instability given by the classical and refined theories are compared. The dependence of the refinements on the shell parameters, the shear moduli of the material, and the buckling modes are investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 312–320, March–April, 1973.     

Stress distribution in the vicinity of a circular hole in an orthotropic spherical shell with finite shear rigidity

The authors consider the problem of stress concentration in the vicinity of a circular hole in an orthotropic spherical shell with finite shear rigidity. The case in which the hole edges are reinforced by a thin elastic ring and some associated special cases are investigated.     

The stress-strain state of an orthotropic shell with a circular hole

We study the stress-strain state of an orthotropic shell with a circular hole. The regularities of the straiin distribution as a function of the anisotropy parameters in a spherical shell are exhibited. One table, 1 figure. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 154–158.     

Axially symmetrical deformation of an orthotropic layered cylindrical shell

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.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 5, pp. 816–823, September–October, 1972.     

Concerning the critical load for an orthotropic cylindrical shell with a viscoelastic core

The problem of determining the critical load for a cylindrical shell with a viscoelastic core is considered. An expression for the critical load under quasistationary loading is obtained on the basis of a generalization of the Winkler hypothesis.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1049–1053, November–December, 1973.     

Numerical analysis of axisymmetric oscillations of an orthotropic cylindrical shell

The frequency spectrum of shells is analyzed by numerical methods using three-dimensional and applied theories. The axisymmetric oscillations of an orthotropic cylindrical shell with Navier conditions on the edges are investigated. The effect of boundary conditions on the frequency spectrum is also studied numerically.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 55, pp. 106–109, 1985.     

Stability of an orthotropic cylindrical shell reinforced by ring ribs with allowance for transverse shear

A detailed discussion is given on the stability of a freely supported orthotropic cylindrical shell reinforced by similar ring ribs (frames) placed at equal distances under the action of a uniform external pressure. The shear is taken into account both in the shell itself and in the frames. The solution obtained is illustrated by examples.Translated from Mekhanika Polimerov, No. 3, pp. 490–495, May–June, 1974.     

On the finite integral transform method for exact bending solutions of fully clamped orthotropic rectangular thin plates

Exact bending solutions of fully clamped orthotropic rectangular thin plates subjected to arbitrary loads are derived using the finite integral transform method. In the proposed mathematical method one does not need to predetermine the deformation function because only the basic governing equations of the classical plate theory for orthotropic plates are used in the procedure. Therefore, unlike conventional semi-inverse methods, it serves as a completely rational and accurate model in plate bending analysis. The applicability of the method is extensive, and it can handle plates with different loadings in a uniform procedure, which is simpler than previous methods. Numerical results are presented to demonstrate the validity and accuracy of the approach as compared with those previously reported in the bibliography.     

Simplified equations and solutions for the free vibration of an orthotropic oval cylindrical shell with variable thickness

Based on the framework of the Flügge's shell theory, the transfer matrix approach and the Romberg integration method, this paper presents the vibration behavior of an isotropic and orthotropic oval cylindrical shell with parabolically varying thickness along its circumference. The governing equations of motion of the shell, which have variable coefficients are formulated and solved. The analysis is formulated to overcome the mathematical difficulties related to mode coupling, which comes from variable curvature and thickness of shell. The vibration equations of the shell are reduced to eight first‐order differential equations in the circumferential coordinate and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The proposed model is adopted to get the vibration frequencies and the corresponding mode shapes for the symmetrical and antisymmetrical modes of vibration. The sensitivity of the frequency parameters and the bending deformations to the shell geometry, ovality parameter, thickness ratio, and orthotropic parameters corresponding to different type modes of vibration is investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

The vibrations of a thin elastic orthotropic circular cylindrical shell with free and hinged edges

The problem of the existence of natural oscillations of a thin elastic orthotropic circular closed cylindrical shell with free and hinge-mounted ends and of an open cylindrical shell with free and hinge-mounted edges, when the two boundary generatrices are hinge-mounted is investigated. Dispersion equations and asymptotic formulae for finding the natural frequencies of possible vibration modes are obtained using the system of equations corresponding to the classical theory of orthotropic cylindrical shells. A mechanism is proposed by means of which the vibrations can be separated into possible types. Approximate values of the dimensionless characteristic of the natural frequency and the attenuation characteristic of the corresponding vibration modes are obtained using the examples of closed and open orthotropic cylindrical shells of different lengths.     

Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem

This paper analyses the large deflections of an orthotropic rectangular clamped and simply supported thin plate. A hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations describing the large deflections of the orthotropic plate to a set of algebraic equations. The simulation results indicate that significant errors are present in the numerical results obtained for the deflections of the orthotropic plate in the transient state when a step force is applied. The magnitude of the numerical error is found to reduce, and the deflection of the orthotropic plate to converge, as the number of sub-domains considered in the solution procedure increases. The deflection of the simply supported orthotropic plate is great than the clamped orthotropic plate. The current modeling results confirm the applicability of the proposed hybrid method to the solution of the large deflections of a rectangular orthotropic plate.     

Strain of a flexible orthotropic cylindrical shell as a function of orthotropy parameters

A procedure is proposed for calculating the stress-strain state of flexible orthotropic cylindrical shells of constant thickness with unsymtnetric load and nonhomogeneous boundary conditions. The system of nonlinear partial differential equations is solved by the method of lines. The system of nonlinear ordinary differential equations is reduced by linearization to a sequence of linear systems. The sequence of linear boundary-value problems is solved by the discrete orthogonalization method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 57–61, 1986.     

Residual stresses caused by linear incompatibility of strains in an orthotropic cylindrical shell

We analyze a healed crack in an orthotropic cylindrical nonshallow shell using a continuously distributed dislocation model. The field of residual stresses on the faces of the shell is investigated for different cases of transverse dislocations of normal opening.