正交异性表层的夹层圆柱扁壳的非线性稳定性

本文采用大挠度理论,对正交各向异性表层的夹层扁壳进行了几何非线性的稳定性分析,求出了屈曲载荷并研究了后屈曲特性.     

正交各向异性板壳理论中的Schrǒdinger方程

本文是文[1～5]的继续。在本文中: (1) 将正交各向异性薄壳的小挠度振动问题或Winkler地基上正交各向异性薄板的小挠度振动问题所服从的Love-Kirchhoff方程化归为矩阵各向异性Schr(?)dinger方程的求解,由此可以利用文[1]和[3～5]中的方法得到这两类问题的通解; (2) 将正交各向异性扁壳大挠度问题的Von K(?)rm(?)n-BaacoB方程(其特例为正交各向异性薄板大挠度问题的von Karman方程)化归为AKNS方程即Dirac方程的形式,从而可以利用文[4～5]中的散射反演方法得到这两类问题的精确解。 波纹板壳和加肋板壳的小挠度问题的通解或大挠度问题的精确解,作为特例包含在本文中。     

正交各向异性旋转扁壳的非线性振动*

本文提出一种时间模态假设,由此导出描述圆柱正交各向异性薄扁球壳和锥壳非线性轴对称自由振动的非线性耦合的代数和微分特征值方程组.我们求出了该方程组的近似解析解,并获得壳体振动的幅频响应关系的渐近展开式.文中还讨论了壳体的几何及材料参量对其振动性态的影响.     

具有弹性边拱及拉杆支承的双曲扁壳(一)

本文利用变分原理建立了具有弹性边拱及拉杆支承的双曲扁壳的平衡方程式及相应的边界条件和角点条件,这里假定边拱只在其本身平面内有刚度,边拱的扭转刚度和垂直于其平面的弯曲刚度都略去不计,本文研究了不许自由外伸的角点铰支条件,以及能够自由外伸的角点简支条件,前者相当于周边有拉杆限制角点外伸位移的情况,后者相当于周边无拉杆的情况.对于前者而言,本文近似地假定边拱沿弧方向的抗拉伸刚度为无穷大,亦即假定扁壳的边界切向位移为零,边拱只通过其垂直于扁壳平面的弯曲来产生弹性支承的作用.这些支承条件是近似地符合当前双曲扁壳屋盖的设计条件的.本文利用双三角级数解法求得具有弹性边拱及拉杆支承的方形底球面扁壳在自重载荷下的正确解.其特点在于先将边界条件积分处理使先满足角点条件,然后求解平面应力微分方程使满足积分后的边界条件.本文的结果直接给出拉杆中的拉力,对于具体设计问题是有用的.本文提出的积分形式的边界条件方法,对于弹性支承的边界问题在板壳方面的应用中是有它的普遍实用意义的.本文还给出了具有弹性边拱支承的方形底扁球壳的数值结果,角点为铰支或简支的,选取的参数值为λ=11.5936.计算结果表明级数收敛很快,并得出了边拱的弹性变形对壳体内力、内力矩及挠度分布规律的影响.     

多夹层板壳的非线性理论及应用(Ⅱ)──正交异性材料扁壳的基本方程

本文把文[1]建立的多夹层壳体的中小转动一阶大挠度理论,具体地运用到多夹层扁壳中去给出了正交异性材料的多夹层扁壳的大挠度问题平衡方程和边界条件及其特例,宏观各向同性材料多夹层扁壳的大挠度方程.     

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.     

静载荷作用下正交各向异性旋转扁壳的非线性自由振动

本文用加权残值法和Lindstedt－Poincare摄动法研究了圆柱型正交各向异性扁薄球壳和锥壳在均布静载荷作用下的轴对称非线性自由振动问题，得到了其非线性固有频率和振幅间的特征关系，并讨论了静载荷及壳体的几何参数和材料参数对其振动特性的影响。     

均布载荷下正交异性变厚度圆薄板大挠度问题

本文导出了正交各向异性变厚度圆薄板大挠度问题的基本方程,用修正迭代法求解了正交各向异性变厚度圆薄板在均布载荷下的大挠度问题.作为特例,令ε=0,则由本文结果得到的表达式与J.Nowinski用摄动法得到的正交各向异性等厚度圆薄板大挠度问题的解完全一致.     

多夹层板壳的非线性理论及应用（II）——正交异性材料扁壳的基本…

本文把文［１］建立的多夹层壳体的中小转动一阶大挠度理论，具体地运用到多夹层扁壳中去，给出了正交异性材料的多夹层扁壳的大挠度问题平衡方程和边界条件及其特例，宏观各向同性材料多夹层扁壳的大挠度方程。     

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。     

Some optimal and inverse problems for orthotropic noncircular cylindrical shells

In this paper, we consider problems of optimal control involving stressed or strained states of orthotropic, noncircular cylindrical shells. It is assumed that the thickness of the shell is variable. The thickness and the radius of curvature of the directrix of the shell are assumed to be the controls. Existence of solutions for the optimal control problems considered is shown. In particular, existence of solutions for the problem of the minimal weight shell and the problem of nearest-to-equal-strength shell is shown. We present results on the approximation of the optimal control problems by a sequence of finite-dimensional problems, which may be reduced to nonlinear programming problems.     

Simplified equations and solutions for the free vibration of an orthotropic oval cylindrical shell with variable thickness

Based on the framework of the Flügge's shell theory, the transfer matrix approach and the Romberg integration method, this paper presents the vibration behavior of an isotropic and orthotropic oval cylindrical shell with parabolically varying thickness along its circumference. The governing equations of motion of the shell, which have variable coefficients are formulated and solved. The analysis is formulated to overcome the mathematical difficulties related to mode coupling, which comes from variable curvature and thickness of shell. The vibration equations of the shell are reduced to eight first‐order differential equations in the circumferential coordinate and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The proposed model is adopted to get the vibration frequencies and the corresponding mode shapes for the symmetrical and antisymmetrical modes of vibration. The sensitivity of the frequency parameters and the bending deformations to the shell geometry, ovality parameter, thickness ratio, and orthotropic parameters corresponding to different type modes of vibration is investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

大几何参数的变厚度开顶扁薄壳的非线性屈曲问题的奇摄动解

该文利用修正多重尺度法研究了大几何参数的变厚度的具有刚性中心的开顶扁球壳，在均布载荷作用下的非线性稳定问题．求得了扁壳几何参数k值较大时，本问题的一致有效的渐进解，并进行了余项误差估计．     

Stress state of orthotropic shells with a straight slit

A shallow orthotropic shell of arbitrary curvature with a straight slit is examined. Results are presented to describe the numerical effect of the curvature of the shell and the length and orientation of the slit on the stress and moment intensity factors in orthotropic shells made of various orthotropic materials.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 63–65, 1987.     

浅水方程初边值问题几种新的差分格式及其数值试验

本文提出几种有限差分法求解绝对坐标系中浅水方程的新方法;对五个对角线矩阵也提出了效率高而且简单的两级迭代计算的有效方法.这种迭代法可以用来处理浅水方法的多格计算.最后我们研究了初始边界值问题.通过数值试验证明,线性正弦波会逐步变为非线性的圆锥型波.     

弹性地基上双曲率扁壳的优化设计问题

本文讨论位于弹性地基上的双曲率扁壳优化设计的一个方法。其实质是取扁壳的初始挠曲函数作为待求的控制函数或设计变量,以载荷的势能作为判定双曲率扁壳优化设计的质量准则,故势能泛函即为目标函数,而优化条件及等周条件均作为约束条件,从而得到本问题优化设计的必要条件。同时引入一共轭函数,最后将问题归结为求解共轭函数的微分方程及初始挠曲函数两个边值问题。     

处理一类非线性与线性组合结构的混合边界条件方法

本文处理边界与线弹性结构连接的扁壳轴对称大挠度问题,提出了处理此类问题的混合边界条件方法,将组合问题转化为独立结构问题。给出了问题的积分方程组,用摄动法求得了解答。计算了扁球壳与柱壳组合问题的算例。     

Analytical and numerical method of finite bodies for calculation of cylindrical orthotropic shell with rectangular hole

To solve the boundary-value problem for cylindrical orthotropic shell with sizeable rectangular hole we suggest analytical and numerical method of finite bodies. For determination of the stress state of orthotropic thin-walled cylinder we use a systemof equations that exactly satisfies the equilibrium equations of orthotropic cylindrical shell. Representation of the solutions is divided into basic and self-equilibrium state. For some loads of a shell we build the basic stress state. We obtain a countable number of resolving functions that exactly satisfy the equations of a shell and describe the self-equilibrium stress state. We develop the algorithm of the analytical and numerical solutions of boundary-value problem based on approximation of the stress state of a shell by finite sum of resolving functions and propose a universal way of reduction of all conditions of the contact parts of the enclosure and the boundary conditions to minimize the generalized quadratic forms. We establish criteria under which the construction of approximate solutions coincides with the exact one.     

多重尺度法应用于变厚度开顶扁球壳在复合载荷下的非线性稳定问题

利用改进多重尺度法研究了大几何参数的变厚度的具有刚性中心的开顶扁球壳,在复合载荷作用下的非线性稳定问题,求得了扁壳几何参数k值较大时,本问题的一致有效的渐近解,并进行了余项误差估计。     

The three-dimensional problem of the axisymmetric deformation of an orthotropic spherical layer

A 3D problem of the deformation of an elastic orthotropic spherical layer that is subjected to normal pressure applied to its outer and inner surfaces is analyzed. Asymptotic first-order approximation solutions are obtained for a slightly orthotropic layer for which the elastic moduli in the meridional and circumferential directions have similar values. The solutions that are obtained are used for analyzing the scleral shell under intraocular pressure; however, they can also be used for solving the inverse problem of analyzing the stress–strain state of a human eye during intravitreal injections. The influence that the meridional and circumferential elastic moduli have on the magnitudes of changes in the relative layer thickness and in the length of the anteroposterior eye axis due to elevated intraocular pressure is studied.