在复合载荷作用下变厚度圆薄板大挠度问题

本文用变厚度板壳大挠度理论的修正迭代法[1],对周边固定,在复合载荷下的变厚度圆薄板进行了求解,从而得到了精确度较高的二次近似解析解.将本文的结果退化到特殊情况就可以得到和文[1、2]完全一致的结果.本文还绘出特征曲线进行比较,其结果是理想的.     

奇异摄动法应用于扁球壳的非线性稳定问题(Ⅱ)

本文对边缘固定夹紧在均布载荷作用下弹性圆底扁薄球壳的非线性稳定性问题进行了研究.利用奇异摄动法求出几何参数k较大时的一致有效的渐近解,并导得决定中心挠度和临界载荷的解析公式,作出了稳定性曲线.这篇文章是作者文章[11]的继续.     

集中载荷作用下开顶扁球壳的非线性稳定问题

本文使用修正迭代法研究了具有硬中心的边缘固定的开顶扁球壳在中心集中载荷作用下的轴对称非线性稳定问题,得到了决定上、下临界载荷的二次近似解析公式.     

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.     

关于圆簿板大挠度问题的正交条件解法

本文重新考察了钱伟长教授求解圆薄板大挠度问题的系统近似法,发现此法实质上可视为奇异摄动理论中的变形参数法.以无量纲中心挠度为小参数,将挠度、中面薄膜力和载荷参数作渐近展开,我们对所得的递推方程给出了正交条件(可解性条件),据此可确定圆薄板的刚度特性.本文指出,利用圆薄板小挠度解和正交条件,可以不经求解方程而导得载荷参数与中心挠度关系的三阶近似以及中心点、边缘处的薄膜力的首项近似.文中对若干特例(均布载荷、复合载荷、各种边界条件)进行了具体计算,所得的结果与钱伟长、叶开沅、黄黔等人在文[1～4]中给出的结果完全相符.     

均布载荷作用下开顶扁球壳的非线性稳定问题

本文利用修正迭代法研究了具有硬中心的开顶扁球壳在均布载荷作用下的轴对称非线性稳定问题,得到了临界载荷的二次近似解析公式.     

中心分布压力作用下圆底扁球壳的变形和稳定性*

本文研究圆底扁薄球壳在中心分布压力作用下的轴对称大挠度变形和稳定性.提出了求解圆底扁球壳非线性方程的牛顿-样条函数方法.分别讨论了当几何参数λ固定时,载荷作用半径的变化对壳体失稳的影响,以及当载荷作用半径固定时,几何参数λ的变化对壳体稳定性的影响.分析了临界载荷曲线与屈曲模式之间的关系.并就v=0.3的情形给出了数值分析结果.     

变厚度圆薄板在均布载荷下大挠度问题

本文首先给出变厚度圆薄板大挠度方程,用小参数方法和修正迭代法联合求解此问题,得到三次近似解;给出特征曲线同线性理论进行了比较.     

扁薄锥壳非对称大变形问题

本文用双参数摄动法研究了扁锥壳非对称大变形问题，求得了在线性载荷作用下的扁锥壳变形的三次近似解析解并绘出了摄动点的挠度与载荷的特征曲线·应用本文方法还可对其它板壳的非轴对称大变形问题进行讨论·本文通过算例对平板及不同初挠度的扁锥壳大挠度变形进行了讨论·     

扁薄球壳非对称大变形问题

本文用修正选代法研究了扁球壳非对称大变形问题，求得了在线性液体载荷作用下的扁球壳变形的二次近似解析解并绘出了摄动点的挠度与载荷的特征曲线族．应用本文方法还可对其他板壳的非轴对称大变形问题进行讨论．本文通过算例对平板及不同初挠度的扁球壳大挠度变形进行了讨论．     

A novel matrix method for coupled vibration and damping effect analyses of liquid-filled circular cylindrical shells with partially constrained layer damping under harmonic excitation

A novel matrix method is further developed for a liquid-filled circular cylindrical shell with partially constrained layer damping (CLD), which consists of treating liquid domain with Bessel function approach, and shell domain with transfer matrix equation based on a new set of first order matrix differential equation. In order to indicate its advantage to the finite element method (FEM), free vibration analysis on such an empty shell under clamped–clamped boundary are carried out by using the present method together with FEM. Meanwhile, coincident result is yielded for the liquid-filled shell by adopting the present method with by other transfer matrix method. Finally, a series of valuable numerical results are obtained by this method.     

Application of the Averaging Method to the Investigation of Nonlinear Wave Processes in Elastic Systems with Circular Symmetry

We apply asymptotic methods of nonlinear mechanics (the Bogolyubov–Mitropol'skii averaging method) to the construction of approximate solutions of a system of nonlinear equations describing wave processes in elastic systems with circular symmetry. As an example, we study the dynamics of interaction of two flexural waves that propagate in a cylindrical shell under the conditions of free oscillations and periodic excitation.     

On the investigation of free vibrations of nonthin cylindrical shells of variable thickness by the spline-collocation method

For determining the dynamic characteristics of free vibrations of circular unclosed cylindrical shells of variable thickness in two coordinate directions, we have used the spline-collocation method together with the method of discrete orthogonalization. The problem has been solved within the framework of the refined Timoshenko–Mindlin theory. We have also investigated the influence of different laws of change in the shell thickness on the character of its natural vibrations. Our calculations have been carried out for different geometrical and elastic parameters of the shell under study and different boundary conditions.     

A Geometric Theory of Nonlinear Morphoelastic Shells

Many thin three-dimensional elastic bodies can be reduced to elastic shells: two-dimensional elastic bodies whose reference shape is not necessarily flat. More generally, morphoelastic shells are elastic shells that can remodel and grow in time. These idealized objects are suitable models for many physical, engineering, and biological systems. Here, we formulate a general geometric theory of nonlinear morphoelastic shells that describes both the evolution of the body shape, viewed as an orientable surface, as well as its intrinsic material properties such as its reference curvatures. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell, the so-called material manifold. Geometric quantities attached to the surface, such as the first and second fundamental forms, are obtained from the metric of the three-dimensional body and its evolution. The governing dynamical equations for the body are obtained from variational consideration by assuming that both fundamental forms on the material manifold are dynamical variables in a Lagrangian field theory. In the case where growth can be modeled by a Rayleigh potential, we also obtain the governing equations for growth in the form of kinetic equations coupling the evolution of the first and the second fundamental forms with the state of stress of the shell. We apply these ideas to obtain stress-free growth fields of a planar sheet, the time evolution of a morphoelastic circular cylindrical shell subject to time-dependent internal pressure, and the residual stress of a morphoelastic planar circular shell.     

复合荷载下波纹圆板的非线性分析*

本文按照各向同性和正交各向异性圆板的大挠度理论,研究了具有光滑中心的波纹圆板在均布和中心集中荷载联合作用下的非线性弯曲问题.应用修正迭代法,我们得到了夹紧固定和滑动固定两种边界条件下十分精确的解析解.     

变厚度扁锥壳的非线性固有频率

借助于变厚度圆薄板非线性动力学变分方程和协调方程,给出了变厚度扁薄锥壳的非线性动力学变分方程和协调方程·　假设薄膜张力由两项组成,将协调方程化为两个独立的方程,选取变厚度扁锥壳中心最大振幅为摄动参数,采用摄动变分法,将变分方程和微分方程线性化·　对周边固定的圆底变厚度扁锥壳的非线性固有频率进行了求解;一次近似得到了变厚度扁锥壳的线性固有频率,三次近似得到了变厚度扁锥壳的非线性固有频率,且绘出了固有频率与静载荷、最大振幅、变厚度参数的特征曲线图·　为动力工程提供了有价值的参考·     

Drag force and virtual mass of a cylindrical porous shell in potential flow

We study the two-dimensional potential flow due to a circular cylinder in motion relative to an unbounded fluid. The cylinder consists of a thin, circular porous shell with fluid inside. The full nonlinear hydrodynamic problem is solved by Fourier expansion of Green's theorem. The truncated series is determined numerically by sampling points around the circle. A dimensionless shell parameter is introduced. For homogeneous porous shells, a maximal drag force occurs at the value 0.433 for the shell parameter, but the virtual mass is a monotonous function of the shell parameter. For an inhomogeneous shell, we have found a maximal value for the virtual mass which is 5% above the value for a rigid cylinder. Some of the results may be relevant to offshore engineering, especially in connection with porous coating of platform legs to reduce the total force.     

黏弹性圆柱壳计及切变形和转动惯量时的动力学稳定性

根据修正的Timoshenko理论,在几何非线性中考虑了剪切变形和转动惯量,对黏弹性圆柱壳的动力稳定性进行了研究.根据Bubnov-Galerkin法,结合基于求积公式的数值方法,将问题简化为求解具有松弛奇异核的非线性积分-微分方程的问题.针对物理-力学和几何参数在大范围内的变化,研究壳体的动力特性,显示了材料的黏弹性对圆柱壳动力稳定性的影响.最后,比较了通过不同的理论得到的结果.