轴对称载荷下旋转壳弹性小应变的轴向任意大挠度问题

黄黔

轴对称载荷下旋转壳弹性小应变的轴向任意大挠度问题

黄黔

上海工业大学

计量
- 文章访问数: 2183
- HTML全文浏览量: 118
- PDF下载量: 705
- 被引次数: 0
出版历程
- 收稿日期: 1984-10-01
- 刊出日期: 1986-02-15

On the Problem of Axisymmetrically Loaded Shells of Revolution with Small Elastic Strains and Arbitrarily Large Axial Deflections

Huang Qian

Shanghai University of Technology, Shanghai

摘要

摘要: 本文建议以径向位移u,轴向位移w,子午线切线转角X,径向内力H和经向弯矩M_φ作为描述轴对称载荷下旋转壳弹性小应变的轴向任意大挠度问题的状态变量.在此基础上,本文建立了整体坐标下的一阶非线性微分方方程.进而用权余法得到该问题的最小位能原理.又用引入拉格朗日乘子并加以识别的方法,得到这一问题的广义变分原理. 本文还提出了以载荷参数为尺度的变特征无量纲化方法,可以有效地提高非线性计算的成功率.所得到的无量纲微分方程和无量纲位能原理,可以作为轴对称壳任意大挠度问题数值计算的理论基础.

Abstract: For the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections, this paper suggests a group of state variables: radial displacement u, axial displacement w, angular deflection of tangent in the meridian X. radial stress resultant H and meridional bending moment M_φ. and derives a System of First-order Nonlinear Differential Equations under global coordinate system with these variables. The Principle of Minimum Potential Energy for the problem is obtained by means of weighted residual method, and its Generalized Variational Principle by means of identified Lagrange multiplier method.This paper also presents a Method of Variable-characteristic Nondimensionization with a scale of load parameter, which may efficiently raise the probability of success for nonlinearity calculation. The obtained Nondimensional System of Differential Equations and Nondimensional Principle of Minimum Potential Energy could be taken as the theoretical basis for the numerical computation of axisymmetrical shells with arbitrarily large deflections.

HTML全文

参考文献(13)

[1]	Reissner,E.,On axisymmetrical deformations of thin shells of revolution,Proc.Symp.Appl.Math.(Elasticity),3(1950),27-52.
[2]	Schmidt,R.and D.A.DaDeppo,On the theory of axisymmetrically loaded shells of revolution with arbitrarily large deflections,J.of Indus.Math.Socity,27(1977),39-50.
[3]	Reissner,E.,On the theory of thin elastic shells,H.Reissner Anniversary Volume,J.W.Edwards,Ann Arbor,Michigan(1949),231-247.
[4]	Wildhack,W.A.,R.F.Dressler and E.C.Lloyd,Investigations of the properties of corrugated diaphragms,ASME,Jan.(1957).
[5]	钱伟长,关于弹性力学的广义变分原理及其在板壳问题的应用(1964).(未能公开发表)
[6]	钱伟长,弹性理论中广义变分原理的研究及其在有限元计算中的应用,机械工程学报,15,2(1979),1-23.
[7]	钱伟长,《变分法及有限元》上册,抖字出版让(1980).
[8]	钱伟长,高阶拉氏乘子法和弹性理论中更一般的广义变分原理、应用数学和力学.4,2(1983),137-150.
[9]	饯伟长,《广义变分原理》,知识出版社.上海(1985).
[10]	Washizu,K.,Variationnal Methods in Elasticity and Plasticity,Ist edition(1968),2nd edition(1975),Pergamon Press.
[11]	Pian,T.H.H.and P.Tong,Basis of finite elements methods for solid continua,Inter.J.for Num.Methods in Eng.,1(1969),3-28.
[12]	Reissner,E.,On the equations for finite symmetrical deflections of thin shells of revolution,Progress in Appl.Mech.(Prager Anniversary Volume),Macmillan Co.,New York(1963),171-178.
[13]	Andrewa,L.E.,Elastic Elements of Scientific Instruments,Moscow.