任谊滨^*， 朱炳麒， 卓家寿

（  河海大学；  ）

摘要： 通过对Hellinger-Reissner变分原理进行坐标变换，将径向模拟为时间，导向辛体系，得到Hamilton对偶方程组。将微分形式的有限差分法引入弹性力学极坐标系下径向辛体系，把对偶方程组中的微分方程直接改用差分方程代替，推导出极坐标系下问题的辛差分方程，从而得到一种全新的径向辛体系差分格式。求解方程组，可直接得到位移和应力。编程计算曲梁等算例，结果表明该辛差分格式是有效的，丰富了弹性力学辛体系差分法的内容。
关键词： 弹性力学，辛体系，有限差分法，新差分格式

Ren Yibin^*， Zhu Bingqi， Zhuo Jiashou

（  Hohai University；  ）

Abstract： With radial coordinate treated as“time”and dual variables introduced, Hamilton’s dual equations can be obtained by using Hellinger-Reissner generalized variational principle. Via introduction of the form of differential FDM into the Radial symplectic system for plane elasticity in polar coordinates and using the difference format instead of differential format in the Hamilton’s dual equations, a Symplectic difference format for plane elasticity in polar coordinates is constructed. so a new FDM under Radial symplectic system is obtained. By soluting the dual equations, displacements and stresses can be obtained directly. The problem of curved beam is calculated by programming. The numerical results show that the new FDM is not only effective but also enrich the method of symplectic FDM.

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