The effect of transverse shear deformation on stress concentration factors for shallow shells with a small circular hole

Simplified equations are derived for the analysis of stress concentration for shear-deformable shallow shells with a small hole.General solutions of the equations are obtained,in terms of series,for shallow spherical shells and shallow circular cylindrical shells with asmall circular hole.Approximate explicit solutions and numerical results are obtianed forthe stress concentration factors of shallow circular cylindrical shells with a small hole onwhich uniform pressure is acting.     

Parametric instabilities of the radial motions of non-linearly viscoelastic shells under pulsating pressures

This paper treats the classical problem of radial motions of cylindrical and spherical shells under pulsating pressures. The novelty in this work is that the shells are taken to be non-linearly viscoelastic (of strain-rate type). It is remarkable that this classical problem, which does not treat the loss of stability to non-radial motions (but which is essential for such treatments), has such a rich dynamics due to the often neglected effects of non-linear material response, to the role of prestress under the action of the mean pressure, and to the different effects of pressure on cylindrical and spherical shells. The study of radial motions near primary resonance (when the frequency of the pulsating pressure is near the natural frequency about an equilibrium state under a constant pressure) gives formulas ensuring that the motions are of hardening or softening type depending on the constitutive functions and whether the constant mean pressure is compressive or inflational. The method of multiple scales gives asymptotic formulas for the principal parametric instability regions (Mathieu tongues) and for the stable and unstable motions at twice the forcing frequency, which closely agree with those obtained by numerical continuation methods. The dependence of frequency on amplitude and the form of instability regions are critically influenced by deviations (even very slight deviations) of material response from that of linearly viscoelastic shells, by the constant mean pressure, and by the type of shell. This paper exhibits the rich diversity of postcritical periodic motions.     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION(Ⅲ)──LARGE DEFLECTION AND POSTBUCKLING OF SHALLOW SHELLS

In this paper, exact solutions of large deflection of multilayer sandwich shallow shells under transverse forces and different boundary conditions are presented. Exact results of postbuckling of multilayer sandwich plates, shallow cylindrical shells and nonlinear deflection of general shallow shells such as spherical shells under inplane edge forces are also obtained by the same procedure.     

The classical pressure vessel problems for linear elastic materials with voids

The traditional problems of the thick walled spherical and circular cylindrical shells under internal and external pressure are solved in the context of the theory of linear elastic materials with voids. The solutions are quasi-static. The stress distributions are those predicted by isotropic linear elasticity. The displacement and solid volume fraction charge fields exhibit a volumetric viscoelasticity induced by a rate dependence of the volume fraction change.     

Dynamic interaction of an oscillating sphere and an elastic cylindrical shell filled with a fluid and immersed in an elastic medium

The paper studies the interaction of a harmonically oscillating spherical body and a thin elastic cylindrical shell filled with a perfect compressible fluid and immersed in an infinite elastic medium. The geometrical center of the sphere is located on the cylinder axis. The acoustic approximation, the theory of thin elastic shells based on the Kirchhoff—Love hypotheses, and the Lamé equations are used to model the motion of the fluid, shell, and medium, respectively. The solution method is based on the possibility of representing partial solutions of the Helmholtz equations written in cylindrical coordinates in terms of partial solutions written in spherical coordinates, and vice versa. Satisfying the boundary conditions at the shell—medium and shell—fluid interfaces and at the spherical surface produces an infinite system of algebraic equations with coefficients in the form of improper integrals of cylindrical functions. This system is solved by the reduction method. The behavior of the hydroelastic system is analyzed against the frequency of forced oscillations.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 75–86, September 2004.     

On the problem of eversion for incompressible elastic materials

The paper contains a discussion on when eversion of cylindrical tubes and spherical shells is possible. The analysis shows that eversion of a cylindrical tube of every isotropic incompressible elastic material with no applied forces is possible assuming only the E-inequalities. This is not always true for spherical shells. Conditions are given as to when this is possible and when it is not possible.     

The method of mixed boundary condition for a kion of linear and nonlinear composite structure

This paper deals with the axisymmetrical deformation of shallow shells in large deflection which are in conjunction with linear elastic structures at the boundary: A method of mixed boundary condition for this problem is introduced, then the problem of a composite structure is transformed into a problem of a single structure and the integral equations are given. The perturbation method is used to obtain the solutions and an example of composite structure consisting of a shallow spherical and a cylindrical shell is presented.Communicated by Yeh Kai-yuan     

Interaction of an infinite thin elastic cylindrical shell and a pulsating spherical inclusion in potential flow of ideal compressible liquid: internal axisymmetric problem

The paper proposes a method to analyze the behavior of a mechanical system consisting of an infinite thin cylindrical shell filled with a flowing compressible liquid and containing a pulsating spherical inclusion. This coupled problem is solved using linear potential flow theory and the theory of thin elastic shells based on the Kirchhoff–Love hypotheses. Use is made of the possibility to represent the general solutions of equations of mathematical physics in different coordinate systems. This makes it possible to satisfy the boundary conditions on both spherical and cylindrical surfaces and to obtain a solution in the form of a Fourier series. Some numerical results are given     

Global structural behaviour of thin and moderately thick monoclinic spherical shells using a mixed shear deformation model

Summary The static and dynamic responses of anisotropic spherical shells under a uniformly distributed transverse load are investigated. Analytical solutions using the mixed variational formulation are presented for spherical shells subjected to various boundary conditions. Numerical results of a refined mixed first-order shear deformation theory for natural frequencies, critical buckling, center deflections and stresses are compared with those obtained using the classical shell theory. A variety of simply-supported and clamped boundary conditions are considered and comparisons with the existing literature are made. The sample numerical results presented herein for global structural behaviour of monoclinic spherical shells should serve as references for future comparisons.     

Unsteady expansion of thick-wall spherical and cylindrical viscoplastic shells

One-dimensional nonstationary problems of adiabatic expansion for thick-wall spherical and cylindrical viscoplastic shells are solved exactly under the assumption that, at the initial instant of time, the distributions of radial velocities satisfy the condition of incompressibility of the shell material. The resulting solutions can easily be modified for the case of compression of such shells.     

Dynamic elastic and plastic buckling of complete spherical shells

A theoretical investigation is undertaken into the dynamic instability of complete spherical shells which are loaded impulsively and made from either linear elastic or elastic-plastic materials. It is shown that certain harmonics grow quickly and cause a shell to exhibit a wrinkled shape which is characterized by a critical mode number. The critical mode numbers are similar for spherical and cylindrical elastic shells having the same R/h ratios and material parameters, but may be larger or smaller in an elastic-plastic spherical shell depending on the values of the various parameters. Threshold velocities are also determined in order to obtain the smallest velocity that a shell can tolerate without excessive deformation. The threshold velocities for the elastic and elastic-plastic spherical shells are larger than those which have been published previously for cylindrical shells having the same R/h ratios and material parameters.     

Investigation of convection in a horizontal cylindrical layer of a saturated porous medium

The structures of the convective motions and the nature of the heat transfer in a horizontal cylindrical layer are studied numerically for the Forchheimer model of a porous medium in the Boussinesq approximation. New asymmetric solutions of the equations of convection flow through a porous medium are found. Their development, domains of existence, and stability are investigated. One consists of a multivortex structure with asymmetric vortices in the near-polar region. Another asymmetric solution is realized at large Grashof numbers in the form of a convective plume deflected from the vertical. The threshold Grashof number of formation of the asymmetric motions depends on the Prandtl number and the cylindrical layer thickness.     

弹／粘塑性压力容器的塑性失稳破坏

依据压力容器拉伸塑性失稳破坏特征,计算了旋转薄壁壳压力容器在弹/粘塑性材料下的塑性失稳破坏,文中就圆柱壳形、圆球壳形、抛物线壳形封头等压力容器的失稳状态,分别求出它们的应力应变。     

Torsional,flexural, and torsional-flexural buckling modes of a cylindrical shell under combined loading

Stability problems for cylindrical shells under various loading modes were considered in numerous papers. A detailed analysis of such problems can be found, e.g., in the monograph [1]. We refer to the solutions presented in this monograph as classical.For long cylindrical shells in axial compression, one of the buckling modes is the purely beam flexural mode similar to the classical buckling mode of a straight rod. It is well known that it can be studied by using the nonlinear or linearized equations of the membrane theory of shells. In [2], it was shown that, on the basis of such equations constructed starting from the noncontradictory version of geometrically nonlinear elasticity relations in the quadratic approximation [3], under the separate action of the axial compression, external pressure, and torsion, there are also previously unknown nonclassical buckling modes, most of which are shear ones.In the present paper, we show that the use of the above equations for cylindrical shells under compression and external pressure with simultaneous pure torsion or bending permits revealing the earlier unknown torsional, beam flexural, and beam torsional-flexural buckling modes, which are nonclassical, just as those found in [2]. The second of these buckling modes is realized when axially compressing forces are formed in the shell with simultaneous torsion, and the third of them is realized under compression combined with pure bending.It was found that, earlier than the classical buckling modes, the torsional buckling modes can be realized for relatively short shells with small shear rigidity in the tangent plane, while the second and third buckling modes can be realized for relatively long shells.     

Postbuckling analysis and imperfection sensitivity of general shells by the finite element method

Buckling and imperfection sensitivity are the primary considerations in analysis and design of thin shell structures. The objective here is to develop accurate and efficient capabilities to predict the postbuckling behavior of shells, including imperfection sensitivity. The approach used is based on the Lyapunov–Schmidt–Koiter (LSK) decomposition and asymptotic expansion in conjunction with the finite element method. This LSK formulation for shells is derived and implemented in a finite element code. The method is applied to cylindrical and spherical shells. Cases of linear and nonlinear prebuckling behavior, coincident as well as non-coincident buckling modes, and modal interactions are studied. The results from the asymptotic analysis are compared to exact solutions obtained by numerically tracking the bifurcated equilibrium branches. The accuracy of the LSK asymptotic technique, its range of validity, and its limitations are illustrated.     

旋转薄壳轴对称自由振动的转点问题

在用渐近法求解任意旋转薄壳(圆柱壳和球壳除外)的轴对称自由振动方程时,在一定的频率参数范围内,存在转点问题。其中,对于存在唯一简单转点的情况,至今未获解决。本文解决了这一问题。     

Stress-fit applications to experimental shell analyses

The stress-fit method is a procedure for determining complete stress distribution in shells from experimental data. Displacement, slope and shearing-force distributions may also be calculated. The method is applicable to all shell configurations for which closed-form solutions have been formulated and may be applied to certain asymmetrically loaded shells as well as those loaded axisymmetrically. Application to cylindrical and spherical shells is discussed in detail, and the procedure is shown to be verfied experimentally.     

A unified Chebyshev–Ritz formulation for vibration analysis of composite laminated deep open shells with arbitrary boundary conditions

In this paper, a unified Chebyshev–Ritz formulation is presented to investigate the vibrations of composite laminated deep open shells with various shell curvatures and arbitrary restraints, including cylindrical, conical and spherical ones. The general first-order shear deformation shell theory is employed to include the effects of rotary inertias and shear deformation. Under the current framework, regardless of boundary conditions, each of displacements and rotations of the open shells is invariantly expressed as Chebyshev orthogonal polynomials of first kind in both directions. Then, the accurate solutions are obtained by using the Rayleigh–Ritz procedure based on the energy functional of the open shells. The convergence and accuracy of the present formulation are verified by a considerable number of convergence tests and comparisons. A variety of numerical examples are presented for the vibrations of the composite laminated deep shells with various geometric dimensions and lamination schemes. Different sets of classical constraints, elastic supports as well as their combinations are considered. These results may serve as reference data for future researches. Parametric studies are also undertaken, giving insight into the effects of elastic restraint parameters, fiber orientation, layer number, subtended angle as well as conical angle on the vibration frequencies of the composite open shells.     

An Exact Analysis for Free Vibration of a Composite Shell Structure-Hermetic Capsule

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