Stress–Strain Analysis of Smooth and Ribbed Shells under Local Loads

Static problems for smooth and discretely reinforced cylindrical shells under local loads and complex boundary conditions are solved. The stress–strain states of the casing and ribs are determined by the technical theory of shells and the Kirchhoff–Clebsch theory of rods, respectively. The reinforcing elements are arranged eccentrically. They are of equal or different stiffness, which is also variable along the length. The problems are solved using the finite-difference method. Theoretical results obtained from a refined mesh are compared with experimental data     

Thermoelastoplastic Nonaxisymmetric Stress-Strain Analysis of Laminated Shells of Revolution

A technique for nonaxisymmetric thermoelastoplastic stress–strain analysis of laminated shells of revolution is developed. It is assumed that there is no slippage and the layers are not separated. The problem is solved using the geometrically linear theory of shells based on the Kirchhoff–Love hypotheses. The thermoplastic relations are written down in the form of the method of elastic solutions. The order of the system of partial differential equations obtained is reduced by means of trigonometric series in the circumferential coordinate. The systems of ordinary differential equations thus obtained are solved by Godunov's discrete-orthogonalization method. The nonaxisymmetric thermoelastoplastic stress–strain state of a two-layered shell is analyzed as an example     

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.     

Stability and efficient design of cylindrical shells of metal composites subject to combination loading

A study is made of the stability of boron-aluminum shells under a combination of axial compression and uniform external pressure. An approximate theoretical model is constructed to describe the deformation of a layer of a fiber composite consisting of elastoplastic components. The model is used to derive the equations of state of multilayered shells reinforced by different schemes. The nonlinear equation describing the subcritical state is solved by the method of discrete orthogonalization with the use of stepped loading. The homogeneous problem is also solved by discrete orthogonalization. It is shown that shells can be efficiently designed for combination loading by plotting the envelope of the boundary curves for specific reinforcement schemes. The envelope is convex for elastic shells and is of variable curvature for elastoplastic shells. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 67–73, June, 1999.     

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     

Stability of Axially Compressed Noncircular Cylindrical Shells Consisting of Panels of Constant Curvature

The stability problem is solved for an axially compressed cylindrical shell. Its cross section is formed by circular arcs of radius r with ends supported on a closed circle of radius R. The solution is based on the Flügge equations of the classic theory of deep cylindrical shells. It is shown that the critical axial load for shells of medium length and appropriately chosen cross-sectional profile can be increased by a factor of R/r approximately, compared with the circular shell. The shells length affects considerably the efficiency of noncircular shells of this type. This design model allows us to find out how the local properties of the shell and its stiffness are related     

Dynamic problems for and stress–strain state of inhomogeneous shell structures under stationary and nonstationary loads

This paper reviews studies and analyzes results on the effect of discrete ribs on the dynamic characteristics of rectangular plates and cylindrical shells. Use is made of the vibration equations derived from the classical theories of beams, plates, and shells. The effect of Pasternak’s elastic foundation on the critical velocities of a structurally orthotropic model of a ribbed cylindrical shell is determined. Nonstationary problems are solved for perforated and ribbed shells of revolution filled with a fluid or resting on an elastic foundation and subjected to moving or impulsive loads. Results from studies of the behavior of sandwich shell structures under impulsive loads of various types are presented     

Forced Nonstationary Vibrations of a Sandwich Cylindrical Shell with Cross-Ribbed Core

The equations of nonaxisymmetric vibrations of sandwich cylindrical shells with discrete core under nonstationary loading are presented. The components of the elastic structure are analyzed using a refined Timoshenko theory of shells and rods. The numerical method used to solve the dynamic equations is based on the integro-interpolation method of constructing finite-difference schemes for equations with discontinuous coefficients. The dynamic problem for a sandwich cylindrical shell under distributed nonstationary loading is solved with regard for the discreteness of the core__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 60–67, February 2005.     

Investigation of high elastoplastic straining of shells of revolution under complex tensile and torque loading

A method of the numerical solution of nonlinear unsteady problems of axisymmetric elastoplastic straining of shells of revolution with allowance for torque loading at high strains is proposed. The method is based on the geometrically nonlinear theory of the Timoshenko shells and the plasticity theory with due allowance for combined isotropic and kinematic hardening. The problem is solved with the use of the variational difference method. Results of numerical and experimental investigations of elastoplastic straining of cylindrical shells under proportional and sequential kinematic tensile and torque loading are reported.     

Stability of Orthotropic Corrugated Cylindrical Shells

A technique for stability analysis of cylindrical shells with a corrugated midsurface is proposed. The wave crests are directed along the generatrix. The relations of shell theory include terms of higher order of smallness than those in the Mushtari–Donnell–Vlasov theory. The problem is solved using a variational equation. The Lamé parameter and curvature radius are variable and approximated by a discrete Fourier transform. The critical load and buckling mode are determined in solving an infinite system of equations for the coefficients of expansion of the resolving functions into trigonometric series. The solution accuracy increases owing to the presence of an aggregate of independent subsystems. Singularities in the buckling modes of corrugated shells corresponding to the minimum critical loads are determined. The basic, practically important conclusion is that both isotropic and orthotropic shells with sinusoidal corrugation are efficient only when their length, which depends on the waveformation parameters and the geometric and mechanical characteristics, is small