Analysis of the stress state of a flattened conical shell of moderate thickness with a structurally weakening hole

Conclusions We determined the relationship between the nature of the stress distribution on the hole surface in a flexible plate as a function of thickness. We observed a great difference between the stress densities in flattened, thin and moderate-thickness conical shells and the stress concentrations near holes in thin cylindrical shells and thin, almost cylindrical, conical shells. The stress distribution near the hole in flattened conical shells of moderate thickness is similar to the stress distribution near the holes in flexible, thick plates. During loading of conical shells by an axial force, the lowest stress concentration factor near the holes is obtained when the axis of the hole is parallel to the shell axis. As the thickness of the shell is increased, the stress concentration factor near the holes increases.Kiev University. Ukrainian Institute of Water Management Engineers, Rovno. Translated from Prikladnaya Mekhanika, Vol. 24, No. 9, pp. 65–70, September, 1988.     

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.     

圆柱壳孔边裂纹应力强度因子的计算和分析

从Reissner壳体理论出发,将“局部-整体分析法”应用于圆柱壳孔边裂纹问题,比较精确地计算了圆柱壳孔边轴向裂纹和环向裂纹的应力强度因子,获得了应力强度因子随壳体几何尺寸、开孔大小及剪切刚度变化的规律。以作者在文[7,8]中的有限元分析结果为基础,推广Petroski-Achenbach方法,建立圆柱壳孔边裂纹问题的权函数,分析计算了圆柱壳孔边裂纹问题,获得了较好的结果,最后给出了便于工程应用的较精确的计算鼓胀系数的近似公式。     

Stresses around elliptic holes in circular cylindrical shells

The stress state around an elliptic hole in a circular cylindrical shell under axial loads is measured. The test cylinders which are made of aluminum are loaded both in tension and compression. Stress-concentration factors around the hole for different eccentricities of the ellipse and different curvature parameters are evaluated. Stress-concentration factors away from the edge of the hole are also determined. The results obtained are compared with theoretical results available in the literature. The effect of bending on the stress concentration as related to the eccentricity of the elliptic hole and to the curvature parameters of the shell is discussed. The results from tension test and those from compression test are also compared, and the sensitivity of the shell to any imperfection and possible local buckling at the hole in the case of compression test are demonstrated.     

Physically and Geometrically Nonlinear Deformation of Spherical Shells with an Elliptic Hole

The elastoplastic state of thin spherical shells with an elliptic hole is analyzed considering that deflections are finite. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. Problems are formulated and a numerical method for their solution with regard for physical and geometrical nonlinearities is proposed. The distribution of stresses (strains or displacements) along the hole boundary and in the zone of their concentration is studied. The results obtained are compared with the solutions of problems where only physical nonlinearity (plastic deformations) or geometrical nonlinearity (finite deflections) is taken into account and with the numerical solution of the linearly elastic problem. The stress—strain state in the neighborhood of an elliptic hole in a shell is analyzed with allowance for nonlinear factors __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 95–104, June 2005.     

含孔边裂纹球壳的断裂分析

在依据Reissner理论得出的球壳裂纹尖端应力应变场展开式基础上,采用局部—整体分析法和权函数方法分别计算承受内压的含孔边裂纹球壳的应力强度因子.在有限元的模式中考虑剪切变形的影响,并对奇异元模式的应力应变场展开式的项数选择、奇异元最佳尺寸的选取进行了分析.本文计算和分析了在不同几何尺寸,不同开孔大小以及不同剪切参量条件下承受内压的含孔边裂纹球壳的应力强度因子及其变化规律.     

Physically and geometrically nonlinear deformation of conical shells with an elliptic hole

The elastoplastic state of conical shells weakened by an elliptic hole and subjected to finite deflections is studied. The material of the shells is assumed to be isotropic and homogeneous; the load is constant internal pressure. The problem is formulated and a technique for numerical solution with allowance for physical and geometrical nonlinearities is proposed. The distribution of stresses, strains, and displacements along the hole boundary and in the zones of their concentration is studied. The solution obtained is compared with the solutions of the physically and geometrically nonlinear problems and a numerical solution of the linear elastic problem. The stress-strain state around an elliptic hole in a conical shell is analyzed considering both nonlinearities __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 69–77, February 2008.     

圆柱壳大开孔的薄壳理论解

采用修正的Ｍｏｒｌｙ方程，以ρ０，Ｙ／Ｒ为小参数，对圆柱壳大开孔的边界条件进行渐近展开，得到了可适用于ρ０≤０．７，情况下的薄壳理论解。     

Mixed functionals in the theory of nonlinearly elastic shells

Results obtained on the basis of linearized functionals in the theory of nonlinearly elastic composite shells are analyzed and generalized. The Kirchhoff-Love and Timoshenko hypotheses are used. Possible membrane or shear locking is taken into account. New approaches are proposed to improve the convergence of numerical solution for new classes of nonlinear problems for thin and nonthin shells with a curvilinear (circular, elliptical) hole. The stress-strain state of shells is analyzed using different versions of shell theory. The influence of the nonlinear properties and orthotropy of composite materials on the stress distribution in structural members is studied.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 45–84, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

Physically and Geometrically Nonlinear Static Problems for Thin-Walled Multiply Connected Shells

Physically and geometrically nonlinear two-dimensional problems are formulated for multiply connected thin shells (weakened by several curvilinear holes). A technique and algorithm are proposed for their solution with allowance for elastoplastic strains and finite deflections of shells under static loading. Numerical results for a shell with two circular holes are presented and the stress concentration is analyzed     

STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH LARGE OPENINGS

Based on Donnell's shallow shell equation, a new method is given in this paper to ana-lyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With themethod of complex variable function, a series of conformal mapping functions are obtained from dif-ferent cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And,the general expressions for the equations of a cylindrical shell, including the solutions of stress concen-trations meeting the boundary conditions of the large openings' edges, are given in the mapping plane.Furthermore, by applying the orthogonal function expansion technique, the problem can be summa-rized into the solution of infinite algebraic equation series. Finally, numerical results are obtained forstress concentration factors at the cutout's edge with various opening's ratios and different loadingconditions. This new method, at the same time, gives a possibility to the research of cylindrical shellswith large non-circular openings or with nozzles.     

Non-linear thermal stability of bimetallic shallow shells of revolution

In this paper, a theory for non-linear thermal stability of open bimetallic shallow shells of revolution under a uniform temperature field is developed. To apply the theory to the particular case of some elastic elements in precision instruments, this paper discusses two important kinds of shells, the bimetallic shallow spherical shell with a circular hole at the center and the bimetallic truncated shallow conical shell. The more accurate solutions are obtained by the modified iteration method. All results are expressed in curves which may be applied directly to the design of the elastic elements.     

Stressed state of a composite cylindrical shell with an elliptical hole

The results of investigations of the stress-strained state (SSS) of isotropic cylindrical shells with an elliptical hole are represented in monograph [4]. The modified method of expansion in terms of minor parameter [3] is suggested for calculation of orthotropic shells. The method does not consider, however, lateral shear strains introducing a significant contribution in SSS of composite shells. The procedure for solving problems of SSS calculation near curvilinear holes in shells of arbitrary shape with variable geometrical and physical characteristics is suggested in [1] on the basis of variational-difference method (VDM). Here the relations of the linear theory of anisotropic inhomogeneous shells and the hypothesis of a straight line are taken as the initial ones for all the packet of laminated composite shell as a whole. In the present work we present the numerical results obtained according to the procedure given in [1] for an orthotropic cylindrical shell with an elliptical hole loaded by the axial force and complaint for the lateral shear.S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 57–62, November, 1993.     

On the stress concentration in thick cylindrical shells with an arbitrary cutout

1.IntroductionThefocusofmuch'researcllforalongtimehasbeenontheinvestigationofstressconcentrationsofthincylindricalshellsll--41.Thestressproblemisdiscussedinreferences[5,6].Whentheratioofthicknesshofshellstothecutoutsizeroisnotrathersmall,thegoverningequationofReissuer'sshallowshellincludingtheeffectoftransversesheardeformationsmustbeusedl7-sl.Thethickshelltheorymakesupweaknessesoftheclassicaltheoryofthinshells.Thetheoryofthickshellscanbeusedforanalyzingstressconcentrationsofcircularcylindrica…     

层合圆柱壳的振动与横向应力

应用分层壳理论并在壳厚方向彩二次插值函数推导出正交层合圆醉壳的动力学方程,并得出了简支层合圆柱壳自由振动方程的解,所给出的振动频率与三维分析的结果吻合良好,计算了前四阶模态对应的壳中应力,与第三、四阶模态对应的横向正应力与面内应力的比值远高于第一、二阶模态的应力比,计算结果说明,很高的横向正应力是高频动力响应中导致分层壳脱层破坏的一个主要因素。     

An approximation to red blood cells with a model of three-center-combined shells

Red blood cells present a biconcave shape and bear an inner pressure (osmotic pressure) when they are in the static state. In this paper, a model of “three-center-combined shells”, which consists of two spherical shells and a toroidal shell, is employed to describe the geometric shape of red blood cells. Surface area and volume of the combined shells model are very close to those measured from experiment. The stress distribution in the cell membrane is formulized as a closed form according to the Novozhilov's theory of the three-center-combined shells. Calculating results in terms of Novozhilov's formula give a good agreement with the numerical results given by ABAQUS when using actual measurements. It is concluded that the combined shells model can well approximate to the biconcave structure of red blood cells. In addition, stress calculation shows that the membrane of biconcave red blood cells can carry bending moments, and the moments reach a maximum value in the vicinity of joint line of the spherical shell and the toroidal shell in the combined shells model.     

内压椭球壳塑性变形的发生部位与扩展过程分析

对内压椭球的就发布作了图形描述，指出椭球壳上一点的应力状态只与壳体的轴比λ和该点在壳体上的位置有关，并进一步分析了内压椭球壳的塑性变形的发生部位及其扩展过程。     

Analysis of a spherical tank under a local action

A spherical tank, being perfect as far as weight is concerned, is used in spacecraft, where the thin-walled elements (shells) are united by frames. Obviously, local actions on the shell and hence the stress concentration in the shell cannot be avoided. Attempts to make weight structure of the spacecraft perfect inevitably decrease the safetymargin of the components, which is possible only if the stress-strain state of the components is determined with a controlled error. A mathematical model of shell deformation mechanics is proposed for this purpose, and its linear differential equations are obtained with an error that does not exceed the error of Kirchhoff assumptions in the theory of shells. The algorithm for solving these equations contains procedures for estimating the convergence of the Fourier series and the series of the hypergeometric function with a prescribed error, and the problem can be solved analytically.     

Elastoplastic state of flexible conical shells with a circular hole under axial tension

The elastoplastic state of thin conical shells with a circular hole is analyzed assuming finite deflections. The distributions of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are studied. The stress–strain state of shells around the hole under axial tension is analyzed taking into account two nonlinear factors. The numerical results are presented as plots and tables     

Optimization of hole shapes in circular cylindrical shells under axial tension

Hole shapes are optimized in circular cylindrical shells subjected to axial load considering only the predominantly large membrane stresses present around the holes. Two-dimensional photoelastic isochromatics obtained with a special-purpose polariscope are utilized for the optimization process. The process leads to a significant decrease in the membrane stress-concentration factor and a modest decrease in weight, thus yielding a considerable increase in strength-to-weight ratio. This paper presents results for certain typical ratios of hole diameter to shell diameter. Previous theoretical and experimental studies for the circular hole have also been verified