扁球壳在热-机械荷载作用下的稳定性分析

基于扁壳几何非线性理论,应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件,运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时,上临界荷载随几何参数的增加单调增加,下临界荷载在很小范围内随几何参数的增加而增加,之后随几何参数的增加而减小.给定几何参数时,考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加,使下临界荷载和临界几何参数显著减小.     

扁球壳在均布压力与均匀温度场联合作用下的屈曲

根据扁壳几何非线性理论,推导了均布压力与均匀温度场联合作用下的扁球壳的位移型几何非线性控制方程.考虑夹紧边界条件,采用打靶法得到了扁球壳轴对称弯曲与屈曲的数值结果.讨论了壳体几何参数对平衡路径、临界荷载的影响.给出了壳体临界几何参数.当几何参数大于临界几何参数时,上、下临界荷载都随几何参数增加而增加.给定几何参数时,考察了不同均匀温度场对壳体上、下临界荷载、临界几何参数以及平衡构型的影响.均匀升温会使上临界荷载显著增加,会使下临界荷载略有减小.均匀变温会使临界几何参数改变.     

双层网格开顶扁球壳的非线性稳定性分析

根据基于等效夹层壳思想的双层网格圆底扁球壳在极坐标下的平衡方程、相容方程,采用修正迭代法,对外边缘滑动固定、内边缘悬空和外边缘夹紧固定、内边缘悬空两种边界条件下,双层网格开顶圆底扁球壳的非线性稳定性进行了分析,得出了非线性载荷 位移关系及临界荷载的解析表达式,并讨论和分析了网壳几何参数对临界屈曲载荷的影响.     

薄扁球壳受冲击载荷作用时动力屈曲的数值计算

本文在轴对称变形的假设前题下,通过将扩展了的Marguerre’s方程化为差分方程,对其上作用荷载面积不同时的固支弹性薄扁球壳的屈曲问题作了一些探讨.由此发现,固支薄扁球壳在外界冲击荷载作用下,在λ(=2[3(1-v~2)]~(1/4)(H/h)~(1/2))的某一范围内发生了跳跃屈曲,并得到轴对称跳跃屈曲荷载随壳体上荷载作用面积的增大而提高的结论.     

球壳的环向剪切屈曲

通过球壳微元初始屈曲的微分几何分析,推导出一组新的精确的屈曲分支方程,并且应用Galerkin变分法研究铰支球壳承受环向剪切力时的整体稳定性,构造了接近分支点变形状态的屈曲模式,首次求得了从扁球壳到半球壳大范围内的扭转屈曲临界特征值,临界荷载强度和临界应力.     

考虑横向剪切的对称圆柱正交异性层合扁球壳的热屈曲

研究了对称层合圆柱正交异性扁球壳在温度场和均布压力联合作用下的热屈曲问题．考虑横向剪切的影响,应用修正迭代法获得了温度场影响下的临界荷载的解析表达式,讨论了剪切刚度和温度场对临界荷载的影响．     

考虑横向剪切的对称层合圆柱正交异性扁球壳的非线性稳定问题

本文建立了计及横向剪切的复合材料对称层合圆柱正交异性扁球壳的大挠度理论。应用修正迭代法,研究了均布压力作用下对称层合圆柱正交异性固定边扁球壳的非线性稳定问题,得到了临界荷载的解析解。此解可直接应用到工程设计中。     

借助于薄板的解求薄扁壳的解(微分方程降六阶)

如果与薄扁壳的边界形状及荷载相同的薄板弯曲问题的解为已知,则相应的薄扁球壳弯曲方程组降阶为一个非齐次的Helmholtz方程而易于求解.给出了例题说明本文方法的应用.     

复合材料圆锥壳体的外压稳定性*

本文采用Donnell型扁壳理论,在文献[1]的基础上,应用能量变分法分析了在均布外压作用下复合材料叠层圆锥壳体的稳定性问题,得到了临界载荷的近似表达式.数值结果表明,临界载荷的理论预示值与实验结果非常吻合.最后,讨论了材料弹性常数、铺层参数等因素对临界载荷的影响.本文所得结果对航空航天结构设计具有重要参考价值.     

对称圆柱正交异性层合扁球壳的非线性稳定问题

本文建立了对称圆柱正交异性层合扁球壳的大挠度理论.依据这一理论.并应用修正迭代法.我们得到了均布压力作用下具有夹紧固定边界的对称圆柱正交异性层合扁球壳的临界载荷解析解.     

弹性介质中受轴向冲击载荷作用的圆柱壳的屈曲临界载荷计算分析

建立并求解了弹性介质中圆柱壳的径向位移控制方程,考虑边界条件及相容条件,得到了应力波传播及反射过程中圆柱壳的动力屈曲分叉条件.通过计算得到了不同时间段屈曲临界载荷与应力波波阵面到达圆柱壳的位置、弹性介质的刚度、壳体未嵌入弹性介质部分的长度与总长之比的关系.数值计算结果表明,弹性介质中的圆柱壳发生轴对称屈曲和非轴对称屈曲趋势一致;嵌入弹性介质部分越深、弹性介质刚度越大圆柱壳越难屈曲;屈曲临界载荷随着弹性介质刚度的增大经历了增长缓慢、增长迅速以及增长较慢3个阶段;应力波反射前波阵面通过分界面后,屈曲仅发生在应力波传播区域,反射波波阵面通过分界面前,临界载荷较小时屈曲先发生在反射端部,随着轴向阶数增大,屈曲覆盖整个圆柱壳区域,反射波波阵面通过分界面后,壳体发生的屈曲始终覆盖整个圆柱壳区域.     

Nonlocal effect on axially compressed buckling of triple-walled carbon nanotubes under temperature field

This paper studies the small scale effect on the buckling behaviors of triple-walled carbon nanotubes (TWCNTs) with the initial axial stress under the temperature field. The TWCNTs are modeled as three elastic shells coupled together through vdW interaction between different layers. Buckling governing equations of CNTs are firstly formulated on the basis of nonlocal elastic theory and the small scale effect on CNTs buckling results with the change of temperature are then achieved. The results show that the critical buckling load is dependent on the temperature, scale parameter and wavenumber. Some conclusions are drawn that small scale effect will arise gradually with the increases of wavenumber, and the temperature can influence the ratio between the nonlocal buckling load and the corresponding local load. Furthermore, with or without effects of nonlocal considered, the same results is obtained that the axial buckling load increases as the value of temperature increases at low and room temperature condition, while at high temperature condition the axial buckling load decreases as the value of temperature increases.     

Static and dynamic buckling modes of spherical shells subjected to external pressure

We investigate the possibilities for simplification of previously proposed refined linearized equations of perturbedmotion to identify, by dynamic method, the buckling mode shapes of isotropic spherical shells undergoing external hydrodynamic pressure. In the analysis of classical flexural buckling shapes of spherical shells, it is shown that preserving of nonconservative parametric terms in governing equations of formulated problem, which are related with loading of the shell with follower pressure practically does not affect the value of critical load and the resulting bucklingmode shapes in shell.     

Effect of the stiffness of the elastic core on the buckling mode and the critical load for glass-reinforced plastic cylindrical shells in axial compression

The effect of the stiffness of the core, treated as a three-dimensional elastic body, on the buckling mode and the critical load is investigated for orthotropic cylindrical shells in axial compression. Parametric equations that permit the easy determination of the critical loads are obtained together with an expression for the stiffness parameter at which the buckling mode changes. The effect on the critical load of a central opening in the core is considered.Translated from Mekhanika Polimerov, No. 5, pp. 931–939, September–October, 1971.     

Buckling Instability of Sectional Noncircular Cylindrical Composite Shells under Axial Compression

The problem of buckling instability of cylindrical shells under axial compression is considered. The shells consist of cylindrical sections of smaller radius. The geometrical parameters of the shells are approximated by Fourier series on a discrete point set. A Timoshenko-type shell theory is used. The solution is obtained in the form of trigonometric series. It is shown that shells consisting of cylindrical sections have considerable advantages over circular ones. At a constant shell weight, the choice of suitable parameters of shell sections leads to a significant increase in the critical load. The composite shells considered possess higher efficiency indices in comparison with isotropic ones.     

薄球壳在均布外压与温度耦合作用下的热屈曲研究

从张量方法推导出的轴对称薄球壳屈曲方程出发,推导出在均布外压与温度耦合作用下用位移表示的薄球壳热屈曲方程;应用虚功原理建立薄球壳屈曲最小势能泛函;进一步用Ritz(里兹)法分析了周边简支的半球壳的3种热屈曲问题.得到了: 1) 温度不超过屈曲临界温度值时,均布外压的临界载荷;2) 均布外压载荷为0时,屈曲临界温度值;3) 均布外压载荷不超过临界载荷时,屈曲临界温度值.     

Stability analysis of a liquid filled barrelled horizontal tank

The present work is devoted to the stability of liquid filled horizontal tanks. The possibility of substitution of a cylindrical tank with a barrelled one is investigated. A family of barrelled shells was created and subjected to the numerical analysis. The model of the shell was simply supported at both ends and subjected to the hydrostatic pressure. The values of the critical load and the buckling shapes were determined. The advantages of barrelled shells and their behaviour under hydrostatic load are described. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)