扁壳有限条的静力和动力分析

本文用限条法导出了分析二次抛物形扁壳的计算模式。所采用的曲条单元可用于分析在某一方向曲率较大的二次抛物壳体。经过蜕化,它还可计算双曲扁壳、柱壳及析板等结构。用这一摸式在微型机上编制了FORTRAN静力和动力程序,并对各种正、负及零高斯曲率扁壳进行了计算。对双曲马鞍型壳还进行了静力和动力试验,将理论计算值与实验结果进行比较,两者符合较好。将有限条法的计算情况与有限元法进行比较,前者具有计算精度高、省时、省内存等优点,并使许多问题可在微型机上解决。     

工程中板壳结构的一种实用计算方法

本文采用—维B3样条插值─—半离散法，建立了正交各向异性板壳结构位移和内力的统一计算式。编制的程序适用于两对这简支另两对边任意支承的正交各向异性矩形双曲扁壳、圆柱形扁壳和板；适用于集中、均布、线性荷载或其组合。算例表明该方法能有效地解决板壳的计算。     

无矩双曲扁壳的功的互等定理法

本文将功的互定量法＾「１－４」推广到无矩双曲扁壳的内力计算，建立了求解无矩双曲扁壳的功互等定量法。     

波纹膜片的非线性稳定

应用轴对称旋转扁壳的基本方程,研究了在任意载荷作用下各种边界条件的波纹膜片的非线性稳定问题。采用格林函数方法,将扁壳的非线性微分方程组化为非线性积分方程组。再使用展开法求出格林函数,即将格林函数展开成特征函数的级数形式,积分方程就成为具有退化核的形式,从而容易得到非线性代数方程组。应用牛顿法求解非线性代数方程组时,为了保证迭代的收敛性,选取位移作为控制参数,逐步增加位移,求得相应的载荷。作为算例,首先研究了带中心平台三波纹膜片的局部失稳现象,然后讨论了由于缺陷的存在,波纹膜片有可能出现的极值点失稳,这是一种类似扁球壳的总体失稳现象。解答可供波纹膜片的设计参考。     

冲击波作用下土中浅埋扁球壳的非线性动力响应

本文应用一维波阻法分析了土与结构的相互作用,引用法向位移ω及应力函数φ表达了扁球亮非线性轴对称变形的运动方程,将这两个基本未知函数用正交配点法及平均加速度法分别在空间与时域上离散,求得了在冲击波作用下土中浅埋周边弹性支承扁球壳的非线性动力响应,数值计算着重考察了壳的几何参数及非线性因素对动力响应的影响。     

复合材料层合板壳热弹性动力响应

本文提出了一个复合材料层合扁壳的位移场。据此导出了在力载和热载作用下的板壳运动方程。该位移场满足层间位移和横向剪应力的连续性,较充分反映了横向剪切对层合板壳力学行为的影响,但位移场的变量和运动方程均为五个,与一阶剪切变形理论相同。文中以暂态响应为例考察了横向剪切变形对层合板壳动力响应的影响,显着改善了解的精度。      

土中浅埋椭圆底椭球面扁壳的内力分析

本文通过对椭圆椭球面扁壳在不同支承条件、各种荷载工况作用下的研究，详细讨论了其受力特点和变形特特：分析结构表明：该类型扁壳对支承条件及温度应力非常敏感，尤其在冬季低温条件下，扁壳将产生较大的拉应力。     

变厚度扁球壳的非线性分析

本文利用边界元方法分析了变厚度扁球壳的非线性问题。引入了与变厚因素有关的等效载荷(?),利用板的初等函数基本解,而不是直接寻求变厚扁球壳的基本解,使原问题的难度大大减少,采用了连续性强、精度高的样条函数插值,即使在划分节点取得较少的情况下,结果的精度是令人满意的。     

双曲度覆盖件拉延回弹研究

研究了双曲扁壳覆盖件的成形机理及回弹特点,分析了双曲度拉延回弹机理.回弹与曲面部分的变形量有关,拉伸变形量增大,回弹量降低.同时,讨论分析了压边力、板材性能参数等因素对双曲度回弹的影响.     

扁壳广义协调曲面矩形元

本文从修正的扁壳胡海昌-鹫律原理泛函出发,引入两方面的广义协调条件(单元边界位移的积分型协调条件,膜应变与位移之间的积分型协调条件),使泛函退化为扁壳势能原理泛函,在此基础上导出一个具有二十个自由度的扁壳曲面矩形元。此单元对厚扁壳和薄扁壳都通用,不出现剪切闭锁和薄膜闭锁现象,具有良好的性能。     

压电梯度薄壳的高阶理论解

压电功能梯度执行器能产生较大的位移、降低应力峰值并避免了粘结层带来的问题,压电梯度超声换能器能拓展频带宽度。本文作者提出了一个简单而有效的求解压电梯度薄壳力、电行为特性的高阶理论。设定位移分量为壳厚的线性函数,而电势沿厚度方向为二次分布。考虑了压电作动元的驱动信号不同时所具有的不同形式的电荷平衡方程。应用Fourier级数法得到压电系数沿厚度坐标变化的梯度壳的力电耦合的解析解。所得结果可退化至梁、板等多种特殊情况。利用所得方程分析了一非均匀简支压电层合板,并与三维精确结果作了对比,两者吻合得很好,表明该理论的正确性。最后具体求解了压电梯度圆柱壳的力、电特性,给出了位移、应力、电势沿厚度方向的变化规律。     

INFLUENCE OF GEOMETRIC NON-LINEARITIES ON THE FREE VIBRATIONS OF ORTHOTROPIC OPEN CYLINDRICAL SHELLS

This paper presents a general approach to predict the influence of geometric non-linearities on the free vibration of elastic, thin, orthotropic and non-uniform open cylindrical shells. The open shells are assumed to be freely simply supported along their curved edges and to have arbitrary straight edge boundary conditions. The method is a hybrid of finite element and classical thin shell theories. The solution is divided into two parts. In part one, the displacement functions are obtained from Sanders' linear shell theory and the mass and linear stiffness matrices are obtained by the finite element procedure. In part two, the modal coefficients derived from the Sanders–Koiter non-linear theory of thin shells are obtained for these displacement functions. Expressions for the second- and third-order non-linear stiffness matrices are then determined through the finite element method. The non-linear equation of motion is solved by the fourth-order Runge–Kutta numerical method. The linear and non-linear natural frequency variations are determined as a function of shell amplitudes for different cases. The results obtained reveal that the frequencies calculated by this method are in good agreement with those obtained by other authors. © 1997 by John Wiley & Sons, Ltd.     

A postprocess method for laminated shells with a doubly curved nine-noded finite element

A numerical method that predicts through-the-thickness stresses accurately by using in-plane displacement of Efficient Higher Order Shell Theory (EHOST) as a postprocessor is implemented in nine-noded doubly curved shell element. In the present study, an efficient postprocess method is developed in the framework of shell finite element without losing the accuracy of solutions. This method consists of two steps. First is to obtain the relationship between shear angles of First Order Shear Deformation Theory (FSDT) and EHOST. Second is to construct accurate displacement and stress fields from the FSDT solution by using EHOST displacement fields as a postprocessor. To obtain accurate transverse shear stresses, integration of equilibrium equation approach is used. In the course of calculating transverse shear stresses, the computation of third derivatives of transverse deflection is required. Simply supported curved panels and finite cylinder problems demonstrate economical and accurate solution of laminate composite shells provided by the present method. The present postprocess method should work as an efficient tool in the stress analysis of multilayered thick shells.     

Vibration analysis of twisted conical shells with tapered thickness

Considering twisted conical shells with tapered thickness, a numerical method for analyzing free vibration is developed, where an exact strain-displacement relationship of twisted conical shells is derived based on the shell theory, the equation of energy equilibrium for free vibration is formulated by the principle of virtual work, and the governing equation is obtained by the Rayleigh-Ritz procedure. The convergent property is investigated in view of the assumed displacement functions, and the comparison between the present and the available previous results for several typical conical shells is carried out in order to demonstrate the practicability and the accuracy. The effects of the tapered thickness in two directions, the twist angle, the subtended angle and the taper ratio of cross-section on the vibration behavior are discussed through the frequencies and corresponding mode shapes.     

复合材料四结点四边形多层退化壳单元

本文提出了一个复合材料四结点四边形多层退化壳单元。单元从修正的Hu-Washizu变分原理导出,独立假设位移场、每层内部应变场和应力场。文中给出了几个复合材料板和壳静力线性问题实例。计算结果表明本文的单元是准确和有效的。     

纵向稀加筋复合材料园柱层壳的稳定分析

本文引用位移函数,将文献[1]中园柱层壳的经典理论微分方程组转化成一个微分方程式,在此基础上、将W.Nowacki方法[3]推广到复合材料园柱层壳,得到了稀加筋园柱层壳临界载荷的解析解答 给出了算例、若略去筋条时,其数值计算能退化成与文献[1]中相应的数值结果完全一致.      

纤维缠绕圆柱壳轴压稳定性

本文系统地讨论了多层复合材料圆柱壳在轴向压缩载荷条件下的轴压稳定性。基于 Donnell 方程,将位移法与复数解法推广应用于纤维缠绕圆柱壳的轴压稳定性问题,考虑了八种边界条件,提出了壳体的前屈曲理论解以及屈曲模态,临界载荷的算法,特别着重考虑了各类边界条件与耦合效应。其理论和结果可直接应用于固体火箭发动机壳体的结构设计。     

On modeling of extension and flexure response of electroelastic shells under biasing fields

Summary The authors develop a two-dimensional model for the extension and flexure response of electroelastic shells under biasing fields. Applications of the model in analyzing buckling of two circular cylindrical piezoelectric shells, one single-layered and the other double-layered, are included, and the analysis indicates that the piezoelectric coupling has a strengthening effect against buckling.     

外压作用下椭圆截面柱壳的弹性屈曲

基于能量法推导了外压作用下椭圆截面柱壳弹性屈曲临界荷载的理论解,推导中考虑了椭圆截面连续变化的曲率,引入带有衰减系数的位移函数以反映外压作用下椭圆柱壳的变形特点,并利用里兹法求解外压椭圆柱壳的能量方程。由椭圆柱壳理论解退化求得的圆柱壳外压屈曲荷载与已有文献的经典解吻合良好,与有限元分析结果的比较进一步验证了该文理论解的准确性。基于理论解的参数分析表明:在外压作用下,椭圆柱壳具备比圆柱壳更优越的力学性能;椭圆柱壳的外压屈曲荷载随椭圆截面比的增大而增大,随壳体名义径厚比的减小而增大;椭圆柱壳的外压屈曲荷载随壳体长度的增大而降低,但当名义长径比大于1左右后,屈曲荷载基本保持不变。     

点式玻璃建筑中四点支承玻璃板的受弯分析

现有的玻璃幕墙规范(JGJ102-96)对点式支承玻璃的应力和位移分析尚未作出明确规定。本文在弹性板壳力学的基础上进行相应的受弯分析,针对实际工程给出了简单适用的计算方法,其结果与有限元分析和试验研究结果相吻合。本计算方法简单明了,可为规范修改和工程设计提供必要理论依据。