弹性平面扇形域问题及哈密顿体系*
Plane Elasticity Sectorial Donain and the Hamiltonian System
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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.
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Key words:
- elasticit /
- Hamiltonian system /
- symplectic
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