Studying the Effect of the Spatial Frequency and Amplitude of Corrugation on the Stress–Strain State of Cylindrical Shells

An approach developed earlier to solve two-dimensional static problems for noncircular cylindrical shells is used to analyze the effect of the spatial frequency and amplitude of corrugation on the stress–strain state of shells. The results of the analysis are presented in the form of plots and tables     

Effect of Irradiation on the Stability and Natural Vibrations of Containment Shells

An approximate approach is proposed to solve the problem on the natural vibrations and stability of an NPP reactor containment. Radiation alters the mechanical properties of such shells and causes volumetric expansion of their material. The problems are solved within the framework of the Timoshenko kinematic hypotheses by reducing shells inhomogeneous throughout the thickness to homogeneous shells with reduced tension–compression, shear, and flexural rigidities     

Spline-approximation solution of problems of the statics of orthotropic shallow shells with variable parameters

An approach to the solution of problems of the statics of shallow orthotropic shells is proposed. It is based on reducing a two-dimensional boundary value problem to a one-dimensional one using the spline-collocation method and solution of the problem by the stable numerical method of discrete orthogonalization. Solutions are presented for problems on the stress state of orthotropic shells of double curvature for several values of the elastic constants of the material. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 60–66, July, 2000.     

Solving Stress Problems for Elastic Systems of Anisotropic Shells of Revolution with Regard for Transverse Shear and Reduction

An approach is proposed for refined solution of stress problems for elastic systems consisting of coaxial shells of revolution. Transverse shear and reduction are taken into account. Multivariant calculations made for orthotropic cylindrical shells with elliptical end-plates allow us to analyze the influence of the semiaxis ratio and intermediate supports on the stress–strain state of the shell systems under consideration     

Natural vibrations of a conical orthotropic shell with small curvatures of the generatrix

The Ostrogradskii-Hamilton principle is used with the variational-difference approach to solving eigenvalue problems as the basis for analyzing the influence of small distortions of the generatrix on the natural frequencies of vibration of free conical shells and conical shells precompressed in the axial direction. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 64–68, March 1999.     

Stability of reinforced cylindrical shells under combined loading

A new approach to solving buckling problems for ribbed cylindrical shells subject to longitudinal force and pressure is proposed. Results for shells reinforced with stringers and rings are presented     

Refined Design of Corrugated Noncircular Cylindrical Shells

An approach is proposed to solve static problems for corrugated nonthin cylindrical shells applying spline-approximation in the longitudinal direction and a stable numerical method in the circumferential direction. Solutions are presented in the form of plots and tables for isotropic and transversely isotropic shells of constant and variable thickness__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 18–24, January 2005.     

Spline-approximation solution of two-dimensional problems of statics for orthotropic conical shells in a refined formulation

An approach to solving two-dimensional stress-strain problems for orthotropic conical shells of variable thickness in a refined formulation is developed. The approach is based on the spline-approximation and the stable discrete-orthogonalization method, which is used to solve the one-dimensional problem. The dependence of the deflection and stresses on the thickness and apex angle of a shell of constant volume is given as an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 43–54, November 2007.     

Stress Analysis of Orthotropic Noncircular Cylindrical Shells of Variable Thickness in a Refined Formulation

An approach is developed to solve stress–strain problems in a refined formulation for orthotropic cylindrical shells of variable thickness and noncircular cross section. It is shown, as an example, how the distributions of deflections and stresses depend on changes in the shell thickness at constant weight     

Influence of geometrical and mechanical parameters on the stress-strain state of closed nonthin conical shells

An approach developed to solve boundary-value problems is used to analyze the effect of geometry and orthotropy parameters on the displacement and stress fields in nonthin orthotropic conical shells Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 52–62, October 2008.     

Stress Analysis of Laminated Shells of Revolution with an Imperfect Interlayer Contact

An approach is proposed to solve problems on the contact interaction of layers in structurally inhomogeneous shells of revolution with allowance for both the normal and tangential stresses in the contact zones. A system of algebraic equations is constructed by using a method for solution of static problems for arbitrary shells of revolution. From this system, the contact zones and contact stresses are determined by the iteration method. The restricted behavior of the adhesion layer in cleavage and shear is taken into account. As an example, the stress state of a two-layer cylindrical shell under a concentrated load is determined     

Influence of orthotropy on displacements and stresses in nonthin cylindrical shells with elliptic cross section

An approach developed to solve boundary-value problems is used to analyze the influence of orthotropy and other factors on the displacement and stress fields in nonthin orthotropic cylindrical shells with elliptic cross-section __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 82–92, June 2007.     

Influence of geometrical parameters on the stress state of longitudinally corrugated elliptic cylindrical shells

An approach developed to solve static problems for longitudinally corrugated elliptic cylindrical shells is used to analyze the influence of their geometric parameters and thickness on the stress–strain state. The circumferential distribution of stresses and displacements is analyzed for different values of the aspect ratio and number of corrugations Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 91–98, February 2009.     

Design of corrugated cylindrical shells under different end conditions

An approach to the solution of problems of statics for corrugated cylindrical shells with varying thickness is proposed. The solution is based on spline approximations along the generatrix and on the stable numerical method of discrete orthogonalization along the directrix. Problems on the stress-strain state of corrugated shells whose thickness varies along the directrix with different amplitudes and frequencies under different boundary conditions are solved. The effect of the boundary conditions, the type of end fixity, and the law of thickness variation on the parameters of the stress-strain state is analyzed. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 38–46, September, 1999.     

The R-function method used to solve nonlinear bending problems for orthotropic shallow shells on an elastic foundation

The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method and the R-function method. The developed algorithm and software are used to solve a number of test problems and to study complex-shaped shells. The effect of the shape of shells, the boundary conditions, the stiffness of the foundation, and the load distribution on the behavior of isotropic and orthotropic shells undergoing geometrically nonlinear bending is studied     

Some Approaches to the Solution of Problems on Thin Shells with Variable Geometrical and Mechanical Parameters

A number of approaches to the solution of stress problems for anisotropic inhomogeneous shells in the classical formulation are discussed. A review is made of approaches to the solution of one- and two-dimensional static problems for thin shells with variable parameters and to the solution of stress–strain problems for anisotropic shells of revolution under axisymmetric and non-axisymmetric loading, shallow convexo-convex shells, noncircular cylindrical shells, plates of various shapes, and shells of complex geometry     

Spatial Stability of Layered Anisotropic Cylindrical Shells Under Compressive Loads

International Applied Mechanics - An approach to solving spatial problems of the stress–strain state and stability of layered anisotropic cylindrical shells is developed. The anisotropy is...     

Elasto-plastic behaviour of double-curved shells under a concentrated load

The paper presents the application of the so-called geometrical elements method to the solution of the elasto-plastic behaviour of spherical shells subjected to an axisymmetrical concentrated load. The approach is based on the observation that during large deformations, the shell structure deforms in a nearly isometrical manner. The shell is sub-divided into elements of two kinds: purely-isometrically deformed elements and quasi-isometrically deformed elements. Equilibrium of the structure is defined by the stationariness of the total potential energy. The total energy is compared with Pogorelov's result for the same strain energy. The solution obtained defines the large deformation behaviour and motion of the plastic zones on the surface of the shell.A simplified solution for similar problems of the shells with double positive Gaussian curvature is also presented.     

On a Discrete Fourier Series Solution to Static Problem for Conical Shells of Circumferentially Varying Thickness

An approach is developed to solve the two-dimensional boundary-value problems of the stress-strain state of conical shells with circumferentially varying thickness. The approach employs discrete Fourier series to separate variables and make the problem one-dimensional. The one-dimensional boundary-value problem is solved by the stable discrete-orthogonalization method. The results obtained are presented as plots and tables __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 26–37, September 2005.