Hamiltonian System and the Saint Venant Problem in Elasticity

Zhong Wanxie; Xu Xinsheng; Zhang Hongwu

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1996 > 17(9): 781-789

Zhong Wanxie, Xu Xinsheng, Zhang Hongwu. Hamiltonian System and the Saint Venant Problem in Elasticity[J]. Applied Mathematics and Mechanics, 1996, 17(9): 781-789.

Citation:

Zhong Wanxie, Xu Xinsheng, Zhang Hongwu. Hamiltonian System and the Saint Venant Problem in Elasticity[J]. Applied Mathematics and Mechanics, 1996, 17(9): 781-789.

Citation:

Zhong Wanxie, Xu Xinsheng, Zhang Hongwu. Hamiltonian System and the Saint Venant Problem in Elasticity[J]. Applied Mathematics and Mechanics, 1996, 17(9): 781-789.

PDF( 498 KB)

Hamiltonian System and the Saint Venant Problem in Elasticity

Research Institute of Engineering Mechanics, Dalian University of Technology, Dalian 116023, P. R. China

Received Date: 1995-06-05
Publish Date: 1996-09-15

Abstract

Abstract

The traditional semi-inverse solution method of the Saint tenant problem.whichis described in foe Euclidian space under the Lagrange syslemformulation,is updated to be solved in the symplectic space under foe conservative Hamiltonian system.It isproved in the present paper that all the Saint Venant solutions can be obtained directlyvia the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix.
- Hamiltonian system,
- Saint Venant problem,
- Symplectic

FullText(HTML)

References(11)

References

[1]	B.Saint Venant,Memoire sur la torsion des prismes,Paris Memoires des Savants etrangers,14(1956),233-560.
[2]	S.Timoshenko and J.N.Goodier,Theory of Elasticity,third ed.,N.Y.McGraw-Hill Book Co.,(1970).
[3]	I.S.Sokolnikoff,Alathematical Theory of Elasticity,2nd ed.,N.Y.McGraw-Hill Book Co.,(1956).
[4]	钱伟长、叶开沅,《弹性力学》,科学出版社,北京(1956).
[5]	W.X.Zhong and X.X.Zhong,Computational structural mechanics,optimal control and semi-analytical method in PDE,Computers and Structures.37,6(1990),993-1004.
[6]	钟万勰,《计算结构力学与最优控制》,大连理工大学出版社,大连(1993),
[7]	钟万勰,条形域弹性平面问题与哈密尔顿体系,大连理工大学学报,31(4)(1991),373-384
[8]	钟万勰,互等定理与共扼辛正交关系,力学学报,24(4)(1992),432-437.
[9]	钱伟长,《八十自述》(1993).
[10]	Th.von Karman and W.Z.Chien,Torsion with variable twist,J.Aeronautical Science,13(1946).503-510.
[11]	钱伟长、林鸿荪、胡海昌、叶开沅,《弹性柱休的扭转理论》,科学出版社,北京(1956).