Vibration and Buckling Approximation of an Axially Loaded Cylindrical Shell with a Three Lobed Cross Section Having Varying Thickness

On the basis of the thin-shell theory and on the use of the transfer matrix approach, this paper presents the vibrational response and buckling analysis of three-lobed cross-section cylindrical shells, with circumferentially varying thickness, subjected to uniform axial membrane loads. A Fourier approach is used to separate the variables, and the governing equations of the shell are formulated in terms of eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations are written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells with variable thickness by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The natural frequencies and critical loads beside the mode shapes are calculated numerically in terms of the transfer matrix elements for the symmetrical and antisymmetrical vibration modes. The influences of the thickness variation of cross- section and radius

AXISYMMETRIC PROBLEMS OF CYLINDRICAL SHELLS WITH VARIABLE WALL THICKNESS

The purpose of this paper is to give the general solutions for axisymmetric eylindrical shells with paraholically varying wall thickness.

The Exact Solution for Thick Laminated Cantilever Cylindrical Shell

Discarding any ussumption regarding displacement or strers models, the stateequation for orthotropy is established in a cylindrical system. The exact solution ispresented for the statics of thick closed laminated cantilever cylindrical shells. Everyequation of elasticity can be satisfied and all the elastic constants are taken intoaccount. Arbitrary precision of a desired order can be obtained.

ON THE STRESS CONCENTRATION IN THICK CYLINDRICAL SHELLS WITH AN ARBITRARY CUTOUT

In this paper, based on the theory of thick shells including effects of transverse shear deformations, a complex variables analytic method to solve stress concentrations in circular cylindrical shells with a small cutout is established A general solution and expression satisfying the boundary conditions on the edge of arbitrary cutouts are obtained. The stress problem can be reduced to the solution of an infinite algebraic equation series, and can be normalized by means of this method. Numerical results for stress concentration factors of the shell with a small circular and elliptic cutout are presented.

THEORY OF THICK-WALLED SHELLS AND ITS APPLICATION IN CYLINDRICAL SHELL

In this paper, a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle, with displacement and stress assumptions. The displacements are expanded into power series of the thickness coordinate. Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively. The normal extruding and transverse shear stresses are assumed to be cubic polynomials and to satisfy the boundary stress conditions on the outer and inner surfaces of the shell. The governing equations and boundary conditions are derived by means of variational principle. As an example, a thick-walled cylindrical shell is disscussed with the theory proposed. Furthermore, a photoelastic experiment has been carried out, and the results are in fair agreement with the computations.

Stability of perfect and imperfect cylindrical shells under axial compression and torsion

Stability analyses of perfect and imperfect cylindrical shells under axial compression and torsion were presented. Finite element method for the stability analysis of perfect cylindrical shells was put forward through comparing critical loads and the first buckling modes with those obtained through theoretical analysis. Two typical initial defects, non-circularity and uneven thickness distribution, were studied. Critical loads decline with the increase of non-circularity, which exist in imperfect cylindrical shells under both axial compression and torsion. Non-circularity defect has no effect on the first buckling mode when cylindrical shell is under torsion. Unfortunately, it has a completely different buckling mode when cylindrical shell is under axial compression. Critical loads decline with the increase of thickness defect amplitude, which exist in imperfect cylindrical shells under both axial compression and torsion, too. A greater wave number is conducive to the stability of cylindrical shells. The first buckling mode of imperfect cylindrical shells under torsion maintains its original shape, but it changes with wave number when the cylindrical shell is under axial compression.

腐蚀减薄柱形壳轴压屈曲特性研究

本文对不锈钢局部减薄缺陷柱形壳在轴向压力下的屈曲性能进行研究。对完好柱壳和4种外表面局部腐蚀而导致壁厚减薄的柱壳,进行几何测量、轴压试验和数值计算。5种类型柱壳的位移载荷曲线、临界载荷和失稳模式通过轴压实验获得;非线性数值分析中采用弧长法获得平衡曲线、极限载荷和柱壳后屈曲模式。在数值分析和试验的基础上,对局部减薄柱形壳屈曲问题进行研究,其中对比了减薄位置差异和减薄形状差异对柱形壳屈曲的影响。结果表明,柱形壳对腐蚀减薄形状和腐蚀减薄位置都具有敏感性,尤其对于柱壳周向长方形缺陷形状的敏感性更强。

大厚度环肋圆柱壳结构应力特性研究

环肋圆柱壳是水下工程产品中广泛采用的一种典型耐压结构。随着工作深度需求越来越深,环肋圆柱壳结构设计逐渐呈现出大厚度的新结构特征。本文以某深海无人系统耐压结构参数为例,采用理论方法和有限元仿真方法进行计算分析,研究不同厚度特征参数(t/R)下的环肋圆柱壳结构应力特性。结果表明,基于薄壳理论的解析计算方法不适用于大厚度环肋圆柱壳结构应力计算,大厚度环肋圆柱壳结构的应力特性与传统圆柱壳结构存在较大差异,在大厚度环肋圆柱壳结构设计时应综合权衡其壳板应力和肋骨应力的特性。

变厚度旋转圆柱壳的自由振动研究

为了提高旋转圆柱壳结构的使用性能和工作效率,减轻其质量已成为有效方式之一,针对这一需求,旋转圆柱壳结构有设计为厚度沿轴向变化即变厚度的趋势。基于此,利用Chebyshev-Ritz方法,对厚度沿轴向有3种线性变化形式的变厚度旋转圆柱壳的自由振动进行研究。考虑科氏力与离心力的影响,基于Sanders壳理论,将圆柱壳的位移场近似展开为Chebyshev多项式与边界函数乘积的形式,计算变厚度旋转圆柱壳的动能与势能,再根据Ritz方法获得变厚度旋转圆柱壳的频率方程。在此基础上,将所得结果与已有文献中的结果进行比较,验证了建模方法的准确性,并对计算结果进行了收敛性研究。最后比较了不同厚度变化形式下旋转圆柱壳的自由振动,并讨论了转速、厚度变化参数、圆柱壳长径比等参数对变厚度旋转圆柱壳自由振动的影响。

大厚度环肋圆柱壳三维应力分析方法研究

随着深海应用需求的不断发展,水下工程产品的耐压环肋圆柱壳结构呈现出大深度大厚度的新型结构特点。相比于传统意义的环肋圆柱壳,应力分析一般将其简化为二维应力状态,大厚度环肋圆柱壳的应力强度应进行三维应力分析。本文通过肋骨作用力函数等效假设,将环肋圆柱壳分解为圆柱壳梁环、肋骨腹板圆环和肋骨面板圆环组成的简化力学模型,基于弹性力学平面问题分析方法,提出一种大厚度环肋圆柱壳的三维应力分析方法,给出环肋圆柱壳的典型应力计算式。算例分析表明,本文方法计算值与数值仿真计算结果基本一致,具有较好的工程应用精度。

考虑径厚比影响的圆柱壳滞回破坏机制分析

为了明确径厚比对于圆柱壳结构滞回性能的影响,通过低周往复荷载试验和数值模拟,研究了不同径厚比圆柱壳的滞回破坏模式和耗能能力。结果表明,径厚比会影响圆柱壳的最终破坏模式,随着径厚比的增大,破坏模式从底部象足式屈曲转变为褶皱式屈曲破坏。累积等效塑性应变和等效黏滞阻尼系数都随着径厚比的增大逐渐降低,径厚比越大,塑性发展越不充分,结构的耗能能力越弱。圆柱壳的塑性强化阶段随着径厚比的增大逐渐缩短,当径厚比超过250后,结构未经历塑性强化直接进入屈曲发展阶段,径厚比越大,局部屈曲出现越早,导致截面未达到全塑性弯矩即破坏,对于大径厚比圆柱壳结构的全塑性弯矩理论值应进行相应的修正。

Plastic Buckling of Cylindrical Shells Under Transverse Loading

Thick cylindrical shells under transverse loading exhibit an elephant foot buckling mode, whereas moderately thick cylindrical shells show a diamond buckling mode. There exists some intermediate geometry at which the transition between buckling modes can take place, This behavior is significantly influenced by the radius-to-thickness ratio and the material yield strength, rather than the length-to-radius ratio and the axial force. This paper presents a critical value at which the transition of buckling modes occurs as a function of the radius-to-thickness ratio and the material yield strength. The result shows that the circumferential wave number of the diamond buckling mode increases with decreasing wall thickness. The strain concentration is also intensified for the diamond buckling modes compared with the elephant foot buckling modes.

圆型基坑的变形特点及主要影响因素分析

圆形基坑多为应用于特殊场合的超深基坑,上海某圆形基坑的施工监测资料显示,圆形基坑的变形规律与条形基坑差异很大,对圆形基坑的水平位移、土压力监测资料进行了分析,并通过应用中厚壳理论对基坑变形和内力作的有限元模拟,认为圆形基坑以承受环向轴压为主,与主要承受经向弯矩的条形基坑有本质区别。同时,对混凝土轴向受压、槽段间泥浆受压、环向不均匀荷载等主要变形因素也进行了探讨,指出在设计和施工阶段应对不均匀荷载予以密切关注。

内压圆筒厚度计算公式分析讨论

GB 150—2011中采用的是弹性失效准则,规定对设计压力p≤0.4[σ]t的内压圆筒厚度按中径公式进行设计。JB 4732—1995中规定对设计压力p≤0.4[σ]t的内压圆筒厚度按中径公式进行设计,设计压力p>0.4[σ]t时按Tresca全屈服压力进行设计。比较研究表明:基于弹性失效准则时,中径公式算出的厚度最薄;基于塑性失效准则时,中径公式算出的厚度最厚;当径比较小时,按Tresca全屈服压力和中径公式算出的内压圆筒厚度相差很小,在工程设计中,可以统一采用Tresca全屈服压力计算内压圆筒壁厚。

厚圆柱扁壳位移型基本方程及控制方程分析

基于考虑横向剪切变形的厚壳位移型基本方程及扁壳基本假定,建立了以5个中面位移为5个独立变量的厚扁壳及厚圆柱扁壳位移型基本方程。对厚圆柱扁壳进行了动力分析,首先引入3个辅助位移函数,同时运用柯西-黎曼条件,将5个二阶微分方程变形为1个二阶和2个四阶过渡微分方程;然后引入另一辅助位移函数,建立其解耦的控制微分方程;最后利用4个辅助位移函数求出5个位移分量。结果表明,厚扁壳的位移型基本方程退化为厚圆柱扁壳及薄圆柱扁壳的位移型方程是正确的,且所推导的方程具有通用性。

厚壁圆柱壳开孔应力集中问题的复变函数解法

本文基于考虑横向剪切变形影响的厚壳理论建立了求解圆柱壳开孔应力集中问题的复变函数方法，得到了此种问题的一般解和满足任意形开孔边界条件的表达式·该应力集中问题可以简化为求解无穷代数方程组的问题·用复变函数方法可以规范地求解应力集中问题·文中给出了圆柱壳开小圆孔和椭圆孔时应力集中系数的数值结果·

壳体厚度对大口径FAE战斗部效应仿真研究

在整体型大口径 FAE 战斗部的结构设计中,提高壳体强度是设计工作中面临的新问题。采用 Lagrange坐标下的有限元方法,建立了整体型 FAE 战斗部装置的数值模型。应用 DYNA3D 有限元程序模拟了不同厚度壳体的 FAE 装置在中心分散药的爆炸载荷的驱动下膨胀、破裂的作用过程。研究了壳体厚度对圆柱壳体膨胀破裂特性及其对燃料分散的作用规律,为整体型大口径 FAE 战斗部的结构设计提供了设计依据。

圆柱壳在热载荷作用下的非线性振动

采用伽辽金原理及改进的L -P法研究了圆柱壳在热载荷作用下的非线性振动 ,并讨论分析了温度、长径比、厚径比对圆柱壳固有热振动频率的影响。

刚性快轴向冲击圆柱壳动力屈曲的计算机模拟

用ANSYS/LS—DYNA对轴向冲击的薄壁圆柱壳的动力屈曲进行了计算机模拟。模拟中考虑了大变形效应。模拟结果表明:径厚比、约束条件、冲击速度、材料参数等对柱壳的对称和非对称动力屈曲有明显的影响。当圆柱壳一端自由一端固定时,径厚比R/h≤26,柱壳发生轴对称屈曲;反之,发生非轴对称屈曲。当圆柱壳一端夹支一端固定时,轴对称屈曲的范围增大,其径厚比R/h≤31,发生轴对称屈曲。当径厚比、约束条件、材料参数等不变时,随着冲击速度的增大,屈曲由轴对称变为非轴对称。在相同条件下,柱壳高度在一定范围内时,轴对称屈曲的范围随着圆柱壳高度的增加而变大。材料的塑性强化模量?屈服应力等对薄壁圆柱壳的动力屈曲也有明显的影响。

环肋加强变厚度圆柱壳的自由振动

分析了环肋变厚度圆柱壳的自振特性。采用精细时程积分法求解圆柱壳的一阶矩阵微分方程,结合壳体厚度变换矩阵以及由环肋运动微分方程导出的环肋状态向量变换矩阵,建立了环肋变厚度圆柱壳的整体传递矩阵,并依据边界条件获得结构自由振动的频率方程,从而对变厚度环肋圆柱壳进行的自由振动特性进行分析。数值计算结果表明,用该方法处理类似的环肋加强以及变厚度结构的自由振动问题是合理可行的。