## 留言板

 引用本文: 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[J]. 应用数学和力学, 1986, 7(2): 115-125.
Huang Qian. On the Problem of Axisymmetrically Loaded Shells of Revolution with Small Elastic Strains and Arbitrarily Large Axial Deflections[J]. Applied Mathematics and Mechanics, 1986, 7(2): 115-125.
 Citation: Huang Qian. On the Problem of Axisymmetrically Loaded Shells of Revolution with Small Elastic Strains and Arbitrarily Large Axial Deflections[J]. Applied Mathematics and Mechanics, 1986, 7(2): 115-125.

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

• 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Mφ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.
•  [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.
##### 计量
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##### 出版历程
• 收稿日期:  1984-10-01
• 刊出日期:  1986-02-15

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