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     

Elastoplastic state of flexible cylindrical shells with two circular holes

The elastoplastic state of thin cylindrical shells with two equal circular holes is analyzed with allowance made for finite deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The distribution of stresses along the hole boundary and in the stress concentration zone (when holes are closely spaced) is analyzed by solving doubly nonlinear boundary-value problems. The results obtained are compared with the solutions that allow either for physical nonlinearity (plastic strains) or geometrical nonlinearity (finite deflections) and with the numerical solution of the linearly elastic problem. The stresses near the holes are analyzed for different distances between the holes and nonlinear factors.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 107–112, October 2004.     

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.     

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.     

Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes

The elastoplastic state of thin cylindrical shells weakened by two circular holes is analyzed. The centers of the holes are on the directrix of the shell. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. The distribution of stresses along the hole boundaries and over the zone where they concentrate (when the distance between the holes is small) is analyzed using approximate and numerical methods to solve doubly nonlinear boundary-value problems. The data obtained are compared with the solutions of the physically nonlinear (plastic strains taken into account) and geometrically nonlinear (finite deflections taken into account) problems and with the numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between them and the nonlinearities accounted for __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 88–95, November 2005.     

Calculation of shells with large rectangular holes in the presence of finite bending deflections

The stability of shells perforated by large holes has been investigated previously [1–6]. The results published in the cited papers lead to the conclusion that the problem of the stability of shells with large holes is in a stage of vigorous development. The application of standard numerical methods in these problems is impeded by the fact that they are incapable of refining the stress concentration and local stability in the vicinity of corners of the holes and give an approximate smoothed distribution pattern of the forces and torques. Methods of approximation of the solutions in terms of regular functions [2] are complicated by the poor convergence of the corresponding series near the edges of a hole.Structural Engineering Institute, St. Petersburg. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 41–48, February, 1994.     

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.     

On the Stress State of a Truncated Conic Shell of Medium Thickness with Square Holes

The stress concentration at the periphery of rectilinear holes in truncated cone shells of medium thickness under axial compression has been measured by the photoelastic method. Maximum stress diagrams for various arrangements of holes are presented and compared in some cases with theoretical data     

Nontraditional Substructuring Procedure for Analysis of Free-Form Shells

An efficient nontraditional scheme of the substructuring method is expounded. It is based on the curvilinear mesh method (CMM) used for analysis of complex shell structures. In forming the stiffness matrix, this approach excludes fully the shell displacement approximation errors. A numerical algorithm that preserves the efficiency of the CMM for shells of arbitrary form is developed. The stress–strain problem for a boxed beam with diaphragms and a cylindrical roof shell is solved numerically. The results are compared with those obtained by other numerical methods     

Inelastic deformation of flexible cylindrical shells with a curvilinear hole

The elastoplastic state of thin cylindrical shells weakened by a curvilinear (circular) hole is analyzed considering finite deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The distributions of stresses (strains, displacements) along the hole boundary and in the zone of their concentration are studied. The results obtained are compared with solutions that account for physical (plastic strains) or geometrical (finite deflections) nonlinearity alone and with a numerical linear elastic solution. The stress-strain state around a circular hole is analyzed for different geometries in the case where both nonlinearities are taken into account __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 115–123, December, 2006.     

含缺陷轴对称体的安定与极限分析

利用静力安全定理得到了计算轴对称体安定与极限载荷的统一格式，采用温度参数法构造安定分析所需的残余应力场，为了克服对工程实际问题进行安定分析时解题规模与计算精度的矛盾，针对轴对称体的特点，采用两种线性化方案对屈服面进行线性化处理，即直接内接法和在降维应力偏量空间中对屈服面的线性化处理，使安定分析转化为一线性规划问题，在简化过程中合理选择线性化方案以便使应力校核点接近精确的屈服面；为了减小计算量，在求     

Elastoplastic Deformation of Flexible Cylindrical Shells With Two Circular Holes under Axial Tension

The elastoplastic state of thin cylindrical shells with two circular holes under axial tension is analyzed considering finite deflections. The distributions of stresses along the contours of the holes and in the zone of their concentration are studied by solving doubly nonlinear boundary-value problems. The solution obtained is compared with the solutions that account for either physical nonlinearity (plastic deformations) and geometrical nonlinearity (finite deflections) alone and with a numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between the holes and the nonlinear factors accounted for__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 52–57, May 2005.     

Inelastic deformation of flexible cylindrical shells with an elliptic hole

The elastoplastic state of isotropic homogeneous cylindrical shells with elliptic holes and finite deflections under internal pressure is studied. Problems are formulated and numerically solved taking into account physical and geometrical nonlinearities. The distribution of stresses (displacements, strains) along the boundary of the hole and in the zone of their concentration is analyzed. The data obtained are compared with the numerical solutions of the physically nonlinear, geometrically nonlinear, and linear problems. The stress-strain state of cylindrical shells in the neighborhood of the elliptic hole is analyzed with allowance for nonlinear factors __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 46–54, May 2007.     

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.     

Stress concentration around several holes in structural elements

Conclusions Our analysis of specific numerical results for nonclassical problems has thus established two conclusions.1. The stresses do not increase monotonically as the holes are brought closer together (in the case of problems for shells under static loading and for plates under dynamic loading).2. For several holes in the case of problems for plates under dynamic loading, the maxima of the stress concentration factors can occur in the interior of the main region rather than at the edges of the holes, depending on the frequency and form of the applied load.These conclusions do not apply to classical problems (the planar problem under static loading) and must therefore be taken into account when stress concentrations are created.Because of space limitations, the concluding part of this article was not included in the EPMESC'92 Conference Proceedings and is therefore published here in its entirety.This is the complete text of a paper that was presented by the author at the EPMESC'92 International Conference in Talien, China, June 30-August 2, 1992, but was not published in its entirely in the Conference Proceedings.S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 4, pp. 6–13, April, 1994.     

Numerical study of the stability of geometrically imperfect shells of general form

The method of curvilinear grids and the method of basis reduction are used to devise an efficient numerical algorithm for studying the nonlinear deformation of shells of arbitrary form. The results obtained with the algorithm are proven to be sufficiently reliable. The influence of initial geometric imperfections on the stability of a ribbed folded structure is studied as an example. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 82–85, June, 1999.     

突出煤层深孔控制爆破时控制孔的作用

为进行煤层深孔爆破应力传播和有关控制孔作用的研究,以松藻煤电公司实际采用的爆破、炸药和煤层参数为基础,利用三维数值模拟方法,建立煤层长柱状药包爆破数值计算模型。分析了松软煤介质深孔爆破在有控制孔时应力波传播的特点和因爆破作用的抽放影响区域。研究表明:在距爆破孔10 m范围内,有控制孔的孔壁平均有效应力较没有控制孔相同条件下高48%~66%.并随着与爆破孔距离的增加,尽管煤体所受有效应力衰减,但有控制孔的平均有效应力值较无控制孔的比率增大。上述研究结果与现场爆破前后实际取得的瓦斯抽放数据相比基本吻合,证明了爆破前预先设置控制孔的必要性。     

Removal of shallow shell restriction from Touratier kinematic model

A mathematical model to quantify the variation of the displacement field through the thickness of a laminated shell has been proposed previously by Beakou and Touratier (1993). Transverse shear deformations were taken into account and thickness correction factors were not required but the analysis was restricted to shallow shells (i.e. the principal radii of shell curvature were both assumed to be large relative to the shell thickness). In this technical note the later restriction is removed by replacing the Cartesian coordinate form of elasticity tensor with the more general curvilinear form. The modified laminate level model coefficients are derived from the expressions for the curvilinear transverse shear stress components by: applying zero transverse shear stress boundary conditions at the top and bottom of the shell and enforcing interlayer layer continuity at each internal lamina interface. The purpose of this model enhancement is to facilitate the development of a degenerate finite element type that can be used to compute the deformation of a non-shallow laminated shell.     

Neumann's method for boundary problems of thin elastic shells

The possibility of using Neumann's method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann's method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann's method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.     

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.