Low-Dimensional Galerkin Models for Nonlinear Vibration and Instability Analysis of Cylindrical Shells

This paper discusses the derivation of discrete low-dimensional models for the non-linear vibration analysis of thin shells. In order to understand the peculiarities inherent to this class of structural problems, the non-linear vibrations and dynamic stability of a circular cylindrical shell subjected to dynamic axial loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly non-linear behavior under both static and dynamic axial loads. Geometric non-linearities due to finite-amplitude shell motions are considered by using Donnell’s nonlinear shallow shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the non-linear vibration modes and the discretized equations of motion are obtained by the Galerkin method. The responses of several low-dimensional models are compared. These are used to study the influence of the modelling on the convergence of critical loads, bifurcation diagrams, attractors and large amplitude responses of the shell. It is shown that rather low-dimensional and properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.     

Stress–Strain State of Three-Layer Cylindrical Shells with Reinforced Light Core Under Nonstationary Loading*

International Applied Mechanics - The stress–strain state of symmetric three-layer cylindrical shells under nonstationary loads is considered. The equation of vibrations of a shell with a...     

Solving Problems of Elasticity of Conical Shells

The problem of a local action of normal pressure on a thin circular shell is solved by the method of asymptotic synthesis. A conical shell under the action of local radial loads is considered as an example.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 150–165, September–October, 2005.     

Postbuckling of FGM cylindrical shells under combined axial and radial mechanical loads in thermal environments

A postbuckling analysis is presented for a shear deformable functionally graded cylindrical shell of finite length subjected to combined axial and radial loads in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical shells. A singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect cylindrical shells with two constituent materials subjected to combined axial and radial mechanical loads and under different sets of thermal environments. The results reveal that the temperature field and volume fraction distribution have a significant effect on the postbuckling behavior, but they have a small effect on the imperfection sensitivity of the functionally graded shell.     

Nonlinear stability of large k-value shallow spherical shells with a symmetrically distributed line load

In this paper, we treat the nonlinear stability problem of shallow spherical shells with large values ofk(k=12(1–v) · 2f/h,f = shell rise,h = shell thickness) under the action of uniformly distributed line load along a circle concentric with the shell boundary. Load-deflection curves are computed at successive increments of uniformly distributed line loads by using both cubic B-spline approximations and iterative techniques. Our algorithm yields fairly good convergent results for values ofk as large as 400. The limiting case in which shells are loaded along a circle of small radius has been specially investigated and the computed critical loads are compared with those obtained with central point loads by other authors.     

Dynamics of an elastic half-space with a reinforced cylindrical cavity under moving loads

Partial separation of variables and reexpansion of cylindrical and plane waves are used to find the solution describing the uniform motion of a load along a thin circular cylindrical shell in an elastic half-space with the free surface parallel to the axis of the shell. This is a model problem for studying the dynamics of tunnels and shallow-buried pipelines under transport loads. Dispersion curves for the cases of sliding and tight contact between the shell and the half-space are plotted and analyzed. The effect of the shell parameters on the stress–strain state of the half-space is examined     

Postbuckling analysis of axially-loaded laminated cylindrical shells with piezoelectric actuators

A compressive postbuckling analysis is presented for a laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness, and the electric field is assumed to be the transverse component E_Z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with von Kármán–Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

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     

Analysis of shallow spherical shell with circular base under eccentrically applied concentrated loads

In this paper,problems of a shallow sphericalshell with circular base under eccentrically appliedconcentrated loads are discussed.The solutions forsix cases of eccentrically applied concentrated loadsare given,namely:(1)Normal concentrated load,(2)Meridional tangential concentrated load,(3)Circumferential tangential concentrated load;(4)Concentrated moment in the tangential plane,(5)Concentrated moment in the meridional normalplane,(6)Concentrated moment in the circumferentialnormal plane.From the solutions of concentrated loads,thesolutions of distributed line loads in the form ofcosnθalong the circle are obtained.     

Axisymmetric static and dynamic buckling of laminated thick truncated conical cap

Axisymmetric buckling analysis is presented for moderately thick laminated shallow, truncated conical caps under transverse load. Buckling under uniformly distributed loads and ring loads applied statically or as step function loads is considered. Marguerre-type, first-order shear deformation shallow shell theory is formulated in terms of transverse deflection w, the rotation ψ of the normal to the mid-surface and the stress function Φ. The governing equations are solved by the orthogonal point collocation method. Truncated conical caps with a circular opening, which is either free or plugged by a rigid central mass, have been analysed for clamped and simple supports with movable and immovable edge conditions. Typical numerical results are presented illustrating the effect of various parameters.     

Stress analysis of hyperbolic shells of revolution with non-axisymmetrical geometric imperfections

In analyzing hyperbolic shells of revolution with non-axisymmeteric imperfections, an approximate method based on simulating the effect of imperfections by the application of fictitious normal pressure loading on the perfect shell is investigated. In the analysis of a shell of revolution with a bulge-type imperfection under non-axisymmetric loads, an efficient algorithm of applying the method is developed: the effect of individual curvature errors on stress resultants and couples are separately considered, while the interactions among various curvature errors are properly treated in the analysis by an iterative procedure. This algorithm avoids repeated analyses for non-axisymmetric loads and may be implemented with a purely axisymmetric analysis capability.A hyperbolic cooling tower shell with a bulge-type imperfection is analyzed under dead load and wind load conditions by the equivalent load method. A direct analysis of the imperfect shell is also made by a specialized finite element program. Through numerical studies, the accuracy and applicability of the equivalent load method are examined.     

任意厚度层合开口柱壳的温度应力

基于层合柱壳混合状态方程和边界条件的弱形式,建立了具有固支边的层合开口柱壳的温度应力混合方程,给出了任意厚度层合开口柱壳在温度荷载和机械荷载共同作用下的解析解。     

Nonlinear Elastic State of a Composite Cylindrical Shell with a Rectangular Hole

International Applied Mechanics - Physically nonlinear boundary-value problems for an orthotropic cylindrical shell with a rectangular hole under static loads are formulated. The system of...     

任意厚度层合闭口柱壳的轴对称温度应力

基于层合柱壳混合状态方程和边界条件的弱形式，在轴对称情况下，建立了两端固支层合闭口柱壳的温度应力混合方程，给出了任意厚层合柱壳在温度荷载和机械荷载共同作用下的解析解。     

Mechanical buckling of a functionally graded cylindrical shell with axial and circumferential stiffeners using the third-order shear deformation theory

This paper deals with an analytical approach of the buckling behavior of a functionally graded circular cylindrical shell under axial pressure with external axial and circumferential stiffeners. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations and equilibrium and stability equations are derived using the third-order shear deformation theory. The resulting equations are employed to obtain the closed-form solution for the critical buckling loads. A simply supported boundary condition is considered for both edges of the shell. The comparison of the results of this study with those in the literature validates the present analysis. The effects of material composition (volume fraction exponent), of the number of stiffeners and of shell geometry parameters on the characteristics of the critical buckling load are described. The analytical results are compared and validated using the finite-element method. The results show that the inhomogeneity parameter, the geometry of the shell and the number of stiffeners considerably affect the critical buckling loads.     

Ambiguity of the critical load for spherical shells with shear damageability of the material

The structural-probabilistic approach to the modeling of combined crack formation and material deformation processes is used to develop a technique for solving bifurcation stability problems for thin-walled structural members made of damageable materials under single and repeated loadings. The example of a uniformly compressed spherical shell is used to show that, under repeated loading, thin-walled structural members made of shear damageable materials can lose stability under loads smaller than the upper critical loads. The ambiguity of the critical loads for various damage accumulation processes in the material of thin-walled structures depends on the level and character of loading. This phenomenon can be one possible cause of the experimental data spread and the discrepancy between theoretical and experimental results used to determine the critical loads for spherical and cylindrical shells.     

焊接空心球在对称环线荷载作用下的非线性稳定

本文针对目前广泛应用于网架与网壳结构中的薄壁空心球节点,对薄壁球壳在环线荷载作用下的非线性稳定性态进行了分析研究。应用Ｂ－样条函数及截断单项式。克服了理论分析中因剪力突变所带来的困难。数值分析结果表明,薄壳的非线笥稳定是工程中常用的空心球节点的控制因素。同时又表明现行规程公式的计算结果大于数值分析结果。     

On the problems of sandwich shells having the form of a surface of revolution and face layers of non-equal thicknesses

Fundamental equations which govern the behavior of an elasticsandwich shell having the form of a surface of revolution andface layers of non-equal thicknesses are derived,with the so-lution of Refs.[3]and[4]as special examples.The problems of the shell under the action of symmetricalloads are reduced to the solution of a displacement-function4～,where4αsatisfies a differential equation of sixth order.     

Some dynamical properties of a viscoelastic cylindrical shell

IntroductionTherearerarepapersonthedynamicPropertiesofviscoelasticshells.~ulosl']discussesthecaseofshallowsphericalshellandDrozdov[ZIgivesasufficientcondihonofstabilityfortheviscoelasticcylindershellbyusingtheLyapunovfunchonal.UsingtheLyapunovdirectmethod,Tyllkowski[']establishesasufficientconditionfortheasymptohcstabilityofviscoelasticcylindricalshell.ItisnotdifficulttofindthattheseexistingresultSmainlyconcentrateonthedynamicstabilityofviscoelasticshell.Thediscussionaboutthedynamicalsyste…