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     

Simplified Plastic Analysis of Edge-Restrained Shallow Shells

Abstract

This paper gives a brief review of recent theoretical and experimental work on compressed and edge-restrained shallow shells. Yield point and post-yield point behavior of these shells is discussed and the available theoretical results are viewed in light of some experimental evidence. It is shown that the solutions for edge-restrained shallow shells are contained in the solutions for the compressed shallow shells.     

Stability of corrugated composite noncircular cylindrical shells under external pressure

Cylindrical shells consisting of cylindrical panels of smaller radius and subjected to uniform external pressure are analyzed for stability. The geometrical parameters of the shells are approximated by Fourier series on a discrete set of points. The Timoshenko theory of shells is used. The solution is represented in the form of trigonometric series. It is shown that short-and medium-length shells with cylindrical panels are advantageous over circular shells. By selecting appropriate parameters of the panels, keeping the mass of the shell constant, it is possible to achieve a significant gain in critical loads. The shells under consideration are less effective than isotropic shells. Shells with sinusoidal corrugation under external pressure are of no practical interest __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 91–102, December 2007.     

Timoshenko-Type Theory in the Stability Analysis of Corrugated Cylindrical Shells

A technique is proposed for stability analysis of longitudinally corrugated shells under axial compression. The technique employs the equations of the Timoshenko-type nonlinear theory of shells. The geometrical parameters of shells are specified on discrete set of points and are approximated by segments of Fourier series. Infinite systems of homogeneous algebraic equations are derived from a variational equation written in displacements to determine the critical loads and buckling modes. Specific types of corrugated isotropic metal and fiberglass shells are considered. The calculated results are compared with those obtained within the framework of the classical theory of shells. It is shown that the Timoshenko-type theory extends significantly the possibility of exact allowance for the geometrical parameters and material properties of corrugated shells compared with Kirchhoff–Love theory.     

Fundamental-solution methods in stress-concentration problems for thin elastic shells

This paper deals with fundamental-solution methods applied to stress-concentration problems for thin elastic shells. Publications concerned with the relevant division of the theory of plates and shells are reviewed. The theories behind the methods are described, and specific results for static and dynamic concentrated loads are presented. The capabilities of the methods are illustrated by fracture problems for orthotropic shells with notches and holes under mechanical loading and for isotropic shells with notches under thermal loading __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 3–25, July 2007.     

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     

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     

Contact interaction between prestressed laminated shells of revolution and a flat foundation

A nonclassical model of shells that accounts for transverse shears and reduction is used to develop a method for solving the contact problem for inhomogeneous anisotropic shells of revolution subject to a field of mechanical and thermal loads. The prestresses are described by parametric terms in the linearized geometrically nonlinear equations of the second-order theory of flexible shells. The influence of the prestressed state of shells interacting with a flat surface on the contact area and the distribution of contact pressure is analyzed. Some computational features of the technique are discussed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 67–77, October 2006.     

Some features of the buckling of stringer shells

A technique for stability analysis of stringer shells is proposed. It is used to analyze the minimum critical stresses. The dependence of the dimensionless parameters σ_cr/σ_cl on the number of stringers is plotted. The linear and nonlinear theories of ribbed shells are used to examine the features of how stringer shells lose stability. It is shown that the minimum critical stresses determined using the theory of ribbed shells and a structurally orthotropic model are close within the range of stiffness parameters considered __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 59–64, February 2006.     

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.     

圆柱壳稳定性问题的研究进展

圆柱壳是工程实际中广泛应用的结构,其主要破坏形式是屈曲失稳．作为力学领域的经典问题,圆柱壳稳定性问题的研究非常之多．其中,受均匀轴向压力的圆柱壳由于临界屈曲载荷的理论预测值与早期试验结果之间的巨大差异,更是推动了壳体稳定性理论的不断发展．本文简要回顾了壳体稳定性理论的发展和分类,并对轴压圆柱壳体试验结果分散且远低于理论预测值的原因及含缺陷圆柱壳体的稳定性研究方法进行了总结,然后综述了地下空间顶管、储油罐、加筋圆柱壳及脱层圆柱壳等实际工程中广泛应用的圆柱壳结构稳定性研究的现状和趋势,最后展望了将来对工程应用中圆柱壳结构的稳定性研究的难点和方向．     

Influence of axisymmetric dents in ribbed shells on minimum critical loads

The effect of axisymmetric dents in ribbed shells on the minimum critical loads is studied analytically. The upper and lower bounds for the critical stresses in imperfect cylindrical shells reinforced with stringers, rings, and both are estimated. The upper bounds are compared with those obtained from the known solutions for perfect ribbed momentless shells and with experimental data. The effect of the amplitude of initial dents and their number on the upper and lower bounds of critical stresses is examined. The procedure used is the most efficient to determine the load-bearing capacity of ring-reinforced and ribbed shells __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 73–79, May 2007.     

Study of vibration characteristics for orthotropic circular cylindrical shells using wave propagation approach and multivariate analysis

A study of free vibration of orthotropic circular cylindrical shells is presented. The vibration control equations of shells are based on Flügge classical thin shell theory. Wave approach is used in the analysis, in which the boundary conditions of shells can be simplified according to the associated beam. The free vibration frequencies of shells can be obtained from a frequency polynomial equation of order 6. The parametric analysis of the free vibration of orthotropic cylindrical shells is investigated using a statistical method. The effects of geometrical parameters and material characteristics upon frequencies are investigated here. Multivariate analysis (MVA) can be a useful tool for this parametric study. Some statistical characteristics, including correlation analysis and ANOVA are applied. ANOVA has been conducted to predict the statistical significance of the various factors. Calculations are performed in the Minitab statistical software. The results show that the L/R, h/R and m have larger effects on the lowest frequency. The importance of input parameters is ranked according to their contributions to the total variance. A knowledge and data visualization approach, Self-organizing mapping (SOM) is also adopted here for mining some intrinsic characteristics of shells.     

VIBRATIONS OF CIRCULAR CYLINDRICAL SHELLS WITH NONUNIFORM CONSTRAINTS,ELASTIC BED AND ADDED MASS. PART II: SHELLS CONTAINING OR IMMERSED IN AXIAL FLOW

The model introduced in Part I of the present study is extended to take into account a flowing fluid, a mean radial pressure and initial pre-stress in circular cylindrical shells. The axial flow can be external, internal or annular and is described by the potential theory for inviscid and incompressible fluid. The computer program DIVA has been developed. It takes into account all the following complicating effects on the vibrations of circular cylindrical shells: (i) nonuniform boundary conditions around the shell edges including elastic boundary conditions; (ii) fluid–structure interaction including both flowing and quiescent fluids; (iii) internal, external and annular fluids; (iv) effect of a mean radial pressure and initial pre-stress; (v) elastic bed of partial extension in circumferential and longitudinal directions; (vi) intermediate constraints; (vii) added masses. It can be considered the most complete computer program specifically dedicated to dynamics of circular cylindrical shells. The Flügge theory of shells is used to describe the shell deformations. The system has been proved to be conservative for any combination of boundary conditions with restrained displacement at the shell ends. Numerical results show that shells clamped at the upstream end and simply supported at the downstream end have a larger critical velocity than simply supported shells, solving the paradox of Horáček and Zolotarev.     

Imperfection sensitivity of an orthotropic spherical shell under external pressure

In the first part of this paper, rib-stiffened thin-walled spherical shells under external hydrostatic pressure are optimized using classical approximate methods and empirical knock-down-factors. In the second part of the paper, the influence of known imperfections is investigated.The thin-walled spherical shells under external pressure are very sensitive to geometrical imperfections. Hoff recognized that for entire isotropic spherical shells the more likely imperfection will be a local circular dent, which for such shells, can always be considered as an axisymmetric one. Hoff's idea has been further investigated by Koga–Hoff, Galletly et al. These results showed that for a given depth of an imperfection a critical size of the corresponding circular dent exists, giving the minimum for the actual load carrying capacity of the shell.This paper suggests to extend Hoff's theory to isogrid and waffle-grid stiffened spherical shells. The issue of these investigations is a set of knock-down-factors plotted versus imperfection amplitude related to the total thickness of the rib-stiffened (isogrid or waffle-grid) shell. These curves fit reasonably with those established for isotropic shells by Hoff et al. or by Koiter, and enable to estimate the jeopardy of measured actual dents.     

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.     

夹芯圆柱壳在水下爆炸载荷作用下的抗冲击特性

采用声固耦合方法对夹芯圆柱壳和等质量的普通圆柱壳在爆炸载荷作用下的应变、速度和加速度进行有限元计算。结果表明:夹芯防护层对爆炸冲击波可起到较好的衰减作用,即通过芯层的塑性变形,耗散了冲击过程中产生的大部分能量,对里面的圆柱壳体起到较好的保护作用,由于夹芯防护层的存在,与等质量的普通圆柱壳相比,夹芯圆柱壳能够承受更强的爆炸冲击波,降低结构的整体变形。     

Calculating the thermoelastic stress state of medium-thickness shells of revolution

Analytic and numerical analyses are carried out to ascertain whether the theories of thin and medium-thickness shells can be used to calculate the thermoelastic state of shells of revolution. It is shown that the theory of thin shells should be used in the case of thermal loading and the theory of medium-thickness shells in the case of mechanical loading __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 58–67, May 2008.     

Natural Vibrations Of Corrugated Cylindrical Shells

A method for determining the natural frequencies and modes of corrugated noncircular cylindrical shells is presented. The influence of the length and amplitude of corrugations on the fundamental frequency of unloaded and axially compressed shells is examined. The difference between the dependences of frequencies and critical loads on shell geometry is shown. The possibility of optimizing shells in frequencies and critical loads is established__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 58–67, May 2005     

Analyzing the stress–strain state of thick cylindrical shells

Two approaches to the analysis of the stress–strain state of thick cylindrical shells are elaborated. The shell is divided by concentric cross-sectional circles into several coaxial cylindrical shells. Each of these shells has its own curvature determined on its midline. The stress–strain state of the original shell is described by satisfying the interface conditions between the component shells. The distribution of unknown functions throughout the thickness is determined by finding the analytic solution of a system of differential equations in the first approach and is approximated by polynomial functions in the second approach. The stress–strain state of thick shells is analyzed. It is revealed that the effect of reduction becomes stronger with increasing curvature