弹性平面扇形域问题及哈密顿体系*
Plane Elasticity Sectorial Donain and the Hamiltonian System
-
摘要: 通过变量代换及变分原理,将平面弹性扇形域的方程导向哈密顿体系,从而可用分离变量法、本征函数展开等方法求解扇形域的分析单元,这样便可以与有限元的程序系统相结合。显示了哈密顿体系、辛数学的应用潜力。Abstract: The governing equations of plane elasticity in sectorial domain are derived to be in Hamiltoinan form via variable substitutes and variationl principles. The method of separation of variables and eigenfunction expansion method are derive to solve the finite element analytically for the sectorial domain elasticity problem, so that such kind of analytical element can be installed into FEM program systems. It demonstrates the potential of the Hamiltonian system theory and symplectic mathematics.
-
Key words:
- elasticit /
- Hamiltonian system /
- symplectic
-
[1] Timoshenko, S. P. and J. N. Goodier, Theory of Elasticity, McGraw-Hill, NY(1951). [2] 钱伟长、叶开沅,《弹性力学》,科学出版社(1956). [3] 钟万勰、钟翔翔,计算结构力学、最优控制及偏微分方程半解析法,计算结构力学及其应用,7(1)(1990),1-15. [4] 钟万勰、钟翔翔,LQ控制区段混合能矩阵的微分方程及其应用,自动化学报,183) (1992),325-331. [5] Zhong Wan-aie and Zhong Xiang-giang, Elliptic partial differential equation and optimal control, Numerical Methods for Partial Differential Equations,8(2)(1992), 149-169. [6] 钟万勰,条形域平面弹性问题与哈密尔顿体系,大连理工大学学报,31(4) (1991), 373-384. [7] Zhong Wan-gie and Yang Zai-shi, Partial differential equations and Hamiltonian system, Computational Mechanics in Structural Engineering, eds, Cheng, F.Y.and Fu Zi-zhi, Elsevier (1992), 32-48. [8] 俞寿文,薄膜一基底的几个力学问题,力学与实践,15(4) (1993), 1-8. [9] 钱伟长,《变分法及有限元(上册)》,科学出版社(1980). [10] 胡海昌,《弹性力学中的变分原理及应用》,科学出版社(1981). -
点击查看大图
计量
- 文章访问数: 1732
- HTML全文浏览量: 62
- PDF下载量: 471
- 被引次数: 0
下载:
