Application of Non-homogeneous Solution for Equations of Slender Ring Shells to Overall-Bending Problem of Ω-Shaped Bellows

A linear complex equation for slender ring shells overall bending in a meridian plane is given based on E. L. Axelrad's theory of flexible shells. And the non homogeneous solution is obtained from W. Z. Chien's solution for axial symmetrical slender ring shells to investigate the overall bending problem of Ω shaped bellows subjected to pure bending moments. The values calculated in the present paper are very close to the existing experiment. Thus Chien's work on axial symmetrical problems for ring shells has been extended to overall bending problems.

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega_shaped bellows; (Ⅲ) Calculation for C_shaped bellows; (Ⅳ) Calculation for U_shaped bellows. This paper is the first part.

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅳ)-CALCULATION FOR U-SHAPED BELLOWS

This is one of the applications of Part (Ⅰ),in which the angular stiffness, and the corresponding stress distributions of U_shaped bellows were discussed. The bellows was divided into protruding sections, concave sections and ring plates for the calculation that the general solution (Ⅰ) with its reduced form to ring plates were used respectively, but the continuity of the surface stresses and the meridian rotations at each joint of the sections were entirely satisfied. The present results were compared with those of the slender ring shell solution proposed earlier by the authors, the standards of the Expansion Joint Manufacturers Association (EJMA), the experiment and the finite element method. It is shown that the governing equation and the general solution (Ⅰ) are very effective.

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅲ)-CALCULATION FOR C-SHAPED BELLOWS

This is one of the applications of Part (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of C_shaped bellows were calculated. The bellows was divided into protruding sections and concave sections for the use of the general solution (Ⅰ), but the continuity of the stress resultants and the deformations at each joint of the sections were entirely satisfied. The present results were compared with those of the other theories and experiments, and are also tested by the numerically integral method. It is shown that the governing equation and the general solution (Ⅰ) are very effective.

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅱ)- CALCULATION FOR OMEGA-SHAPED BELLOWS

is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega_shaped bellows were calculated, and the present results were compared with those of the other theories and experiments. It is shown that the non_homogeneous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself, and be more effective than by the theory of slender ring shells; but if a lateral slide of the bellows support exists the non_homogeneous solution will no longer entirely satisfy the boundary conditions of the problem, in this case the homogeneous solution of (Ⅰ) should be included, that is to say, the full solution of (Ⅰ) can meet all the requirements.

THE ASYMPTOTIC SOLVING EQUATIONS OF THICK RING SHELL AND ITS SOLUTION UNDER MOMENT M＿O

In this paper .from the .fundamental equations of three `dimensional elasticmechanics , we have found a sequence of asymptotic solving equations of thick ringshell (or body) applied arbitrary loade by the perturbation method based upon ageometric small parameter a=r_o/R_O , which may be divided into two independentequation groups which are similar to the equation groups for plane strain and torsionalproblems. Using these equations, we have also found first order and second orderapproxiniate solutions of thick ring shell applied moment M_o.

COMPLEX EQUATIONS OF FLEXIBLE CIRCULAR RINGSHELLS OVERALL_BENDING IN A MERIDIAN PLANE AND GENERAL SOLUTION FOR THE SLENDER RING SHELLS

Complex equations of circular ring shells and slender ring shells overall-bending in a meridian plane are presented based on E. L. Axelrad's equations of flexible shells of revolution render asymmetrical lending. It turns out that the equations are analogous to Novozhilov's equations of symmetrical ring shells, where general sollutions have been given by W. Z. Chien. Therefore, by analogy with Chien's solution, a general solution for equations of the slender ring shells is put forward, which can be used to salve bellow's overall-bending problems.

STRESS ANALYSIS OF THICK RING SHELL SUBMITTED TO THE ACTION OF INTERNAL PRESSURE

In this paper. from asymptotic equations of thicking shell obtained on the basis of the equations of three dimensional elastic mechanics using geometric small parameter we find the solutions of the stresses and the deformations of thick ring shell submitted to the action of internal pressure q.

DYNAMIC BUCKLING OF STATICALLY PRELOADED RING-STIFFENED CYLINDRICAL SHELLS UNDER AXIAL FLUID-SOLID IMPACT LOADING

The Initial Imperfection Amplified Criterion is applied toinvestigate the geometric nonlinear dynamic buckling of staticallypreloaded ring-stiffened cylindrical shells under axial fluid-solidimpact. Tak- ing account of the effects of large deformation andinitial geometric imperfection, the governing equations are obtainedby the Galerkin method and solved by the Runge-Kutta method. Theeffects of static preloading (uniform external radial pressure) onthe buckling features and the load-carrying ability of ring-stiffenedcy- lindrical shells against axial impact are discussed.

ANALYSIS OF SOUND RADIATION FROM THE RING-STIFFENED CYLINDRICAL SHELL COATED WITH VISCOELASTIC LAYER IN FLUID MEDIUM

The Donnell theory of shell is applied to describe shell motion and layer motion is described by means of three-dimensional Navier equations.Using deformation harmonious condi- tions of the interface,the effects of stiffeners and layer are treated as reverse forces and moments acting on the cylindrical shell.In studying the acoustic field produced by vibration of the sub- merged ring-stiffened cylindrical coated shell,the structure dynamic equation,Helmholtz equation in the fluid field and the continuous conditions of the fluid-structure interface compose the cou- pling vibration equation of the sound-fluid-structure.The extract of sound pressure comes down to the extract of coupling vibration equation.By use of the solution of the equation,the influ- ences of hydrostatic pressure,physical characters and geometric parameters of the layer on sound radiation are discussed.

AXISYMMETRY PROBLEMS OF RING SHELLS OF ELLIPTICAL CROSS SECTION UNDER ARBITRARILY DISTRIBUTED LOADS

A simplified equation for the axisymmetry problems of ring shells of elliptical cross section under arbitrarily distributed loads in complex form has been obtained. The equation is equivalent to the exact equations within the error range of the thin shell theory, with the singularities at the points of meridional extreme values eliminated. The equivalent integral equations and the numerical solutions are given. Three examples of expansion joints, ring shells under hydro-pressure and sealing ring of semi-elliptical cross section are calculated and compared with the exact solutions and the experimental results.

ANALYTICAL SOLUTION OF RADIATED SOUND PRESSURE OF RING－STIFFENED CYLINDRICAL SHELLS IN FLUID MEDIUM

In this paper, analytical formularions of radiated sound pressure of ring-stiffenedcylindrical shells in fluid medium are derived by means of Hamilton's principleHuygens principle and Green function . These formulations Can be used to compute the sound pressure of the shell's surface nearfield and farfield.

深海无人系统大长径比环肋圆柱壳结构设计与试验研究

环肋圆柱壳是深海无人系统广泛采用的一种耐压结构形式,保障其结构安全是系统研制过程中非常重要的一环。针对环肋圆柱壳的结构特征推导了组合结构重量关系式和结构参数简化估算方法,并以一种超长型深海无人系统耐压结构为例,围绕大长径比环肋圆柱壳的结构形式、设计计算、仿真分析、模型验证等开展研究。研究表明提出的大长径比环肋圆柱壳结构设计参数简化估算方法具有较好的适应性。相关计算和分析结果可以为该型深海无人系统结构设计提供技术支撑,也可以为其他类似耐压结构设计提供参考。

弹性环梁支撑下圆形深基坑支护结构变形解析解

将环梁和支护结构分别视为弹性圆环和弹性圆柱薄壳,基于环梁和圆柱壳的变形协调,得到了具有任意数目弹性环梁支撑圆形深基坑支护结构变形的解析解.在验证解析解合理性和可靠性的基础上,针对某一实际圆形基坑工程,比较了在刚性和弹性环梁支撑下支护结构变形和内力的差异,并分析了支护结构底部边界条件、环梁弹性模量、尺寸和数量以及位置等参数对支护结构变形和内力分布的影响.研究结果表明:相对于刚性环梁支撑,弹性环梁支撑处内力变化较小,环梁弹性模量和尺寸的改变只对基坑挖掘面以上支护结构变形和内力影响显著,而对挖掘面以下的支护结构变形和内力几乎没有影响.该研究成果为圆形基坑支护结构设计提供了理论依据和指导.

圆形基坑极正交各向异性支护结构变形解析分析

考虑圆形深基坑支护结构轴向和环向配筋的差异,将支护结构简化为极正交各向异性圆柱薄壳,研究了分层土体中具有弹性支撑环梁约束的支护结构轴对称变形和内力特征.首先,将弹性支撑环梁的约束解除,代之以沿环向分布的未知集中力,基于弹性环梁和圆柱壳的边界条件和变形协调条件,得到了分层土体中具有弹性支撑环梁支护结构轴对称变形的解析解.其次,以上海地区某一圆形深基坑支护结构为例,揭示了支护结构环向和纵向弹性模量、环梁刚度、土体重度和静止土压力系数等因素对支护结构内力和变形的影响,结果表明:支护结构以环向承压为主,轴向弯曲为辅,故其环向刚度对径向位移的影响要明显大于其轴向刚度的影响,但材料参数对内力分布影响较弱;环梁刚度的增加可有效限制支护结构的变形,但会引起支护结构在支撑环梁处内力的显著增大;土层性质相差不大区域的支护结构可按均质土中支护结构进行分析,而土层性质有较大突变区域的支护结构分析则需考虑土层的分层效应.

基于ALE方法的加筋圆柱壳水下接触爆炸计算研究

随着水下制导技术的发展,接触爆炸对水下结构的毁伤问题越加受到关注。为研究加筋圆柱壳结构水下接触爆炸毁伤特性,采用LS-DYNA软件的任意拉格朗日-欧拉(ALE)方法模拟爆炸冲击波的形成、传播及其对圆柱壳结构的毁伤过程,探讨水下接触爆炸作用下单、双层加筋圆柱壳的毁伤响应特性,并分析不同药量和爆距条件下加筋圆柱壳的破坏模式。研究结果表明:在不同药量和爆距的水下接触爆炸条件下,加筋圆柱壳呈现多种破坏模式,加筋和加肋位置处易出现撕裂状破口,板壳结构的破坏主要表现为凹陷变形及沿着加筋位置处扩展的裂纹,其中爆距对破坏模式的影响更明显。本文结果可为水下接触爆炸冲击波作用下水下航行体结构强度分析和防护设计提供参考。

Janus-Helmholtz换能器与Janus-Hammer Bell换能器的振动模态研究

Janus-Helmholtz(JH)换能器和Janus-Hammer Bell(JHB)换能器外观结构类似,但两者振动模态不同。为明确二者振动模态的不同,分析了其结构参数对振动模态的影响。结果表明:在其他参数确定的条件下,JH换能器中圆环壳轴向长度L与圆环壳内侧半径a的关系应满足2<L/a<5.7,JHB换能器对应圆环壳长径比L/a的取值范围为0.1<L/a<0.3。利用有限元方法并设置特殊边界条件分析了JH换能器与JHB换能器谐振峰对应的振动模态,发现JH换能器中较低频振动模态为Janus纵振模态,高频振动模态为液腔谐振模态;JHB换能器中较低频振动模态为Janus纵振模态,较高频振动模态为圆环呼吸模态。进一步对比了JH换能器和JHB换能器的径向与轴向发送电压响应,发现JH换能器可以实现更宽的工作带宽和更高的发送电压响应;JHB换能器工作带宽较窄,但径向方向发射电压响应起伏较小。

复合材料环支撑圆柱壳结构振动特性分析研究

该文基于一阶剪切变形理论,结合波动法,构建了不同边界条件下环支撑复合材料圆柱壳结构振动特性分析模型。结合波函数形式为位移变量,对位移比例参数、位移矩阵和力参数矩阵进行设置。通过结合边界条件矩阵,对环支撑条件下复合材料圆柱壳结构的总体控制方程进行推导。通过与现有文献结果进行对比,验证所建立的振动特性分析模型的准确性。开展了相关参数化分析研究,探讨了材料参数、几何参数以及环支撑位置的影响情况。

基于塑性弦线法的深水爆炸下加筋锥柱壳变形模型

为探究凸型加筋锥柱壳在静水压与深水爆炸载荷联合作用下的动态响应,在塑性弦线模型基础上考虑静水压载荷、锥角因素,将问题简化为求解拥有初边界值的波动方程,利用特征值展开将肋间板壳径向位移表示为无穷级数的形式,并对每个特征值计算相应的卸载时间,以此显示冲击波载荷的衰减特性。使用有限元程序Abaqus对半锥角为20°的凸型加筋锥柱壳开展最大深度500 m、最大冲击因子0.79 kg 0.5/m的水下爆炸数值模拟研究,对邻近结合处的柱段、锥段肋间板壳的理论模型计算结果进行验证对比和讨论。研究结果表明:与不计静水压相比,静水压使得肋间板壳刚度减小——最大位移出现时刻延滞,最终径向位移随水深而增大;在不同冲击因子下,理论模型与数值模拟最终径向位移误差最大为21.7%(锥段),最小为2.0%(柱段);由于锥角的存在,肋间板壳位移不再关于中心点对称分布,中心点最终位移较柱段减小40%以上。

压电圆环径向弯曲振动与激励研究

针对压电圆环换能器的径向弯曲振动问题,从薄壳理论出发进行相关数理推导,讨论了压电效应的影响及电学短路与开路下的弯曲振动方程.进行相关解析求解,给出了两种条件下的多阶谐振频率预测公式,并利用有限元法分析了两式的适用范围.使用模态理论,定义模态权值函数,研究了电学激励条件对多阶弯曲振动模态的具体影响,得到了单模态激励、局部等幅激励和单端激励等作用于多个目标模态的有效方法.经有限元仿真(FEM)、实验与理论对比验证,三者吻合较好,相关结论可以为压电圆环弯曲振动模态识别、模态激励的精细化调控提供理论基础.