复合材料迭层板的Hamilton正则方程及其状态空间有限元法
HAMILTON CANONICAL EQUATIONS AND A STATE SPACE FINITE ELEMENT METHOD FOR LAMINATED COMPOSITE PLATES
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摘要: 本文给出了复合材料迭层板的Hamilton正则方程,并提出了与其对应的状态空间有限无法。文中通过对Hellinger-Reissner混和变分原理的修正,导出了Hamilton正则方程的对应范函,并采用分离变量法对其场变量进行离散,然后在一个方向上采用有限元插位,在另一方向上采用状态空间法给出控制坐标方向的解析解答,从而实现了有限元法与状态空间法的结合,并解决了迭层板计算中的直线假定问题。
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关键词:
- 正交各向异性材料 /
- 有限元法 /
- 状态空间法 /
- Hamilton体系 /
- 正则方程
Abstract: The Hamilton canonical equation for laminated composite plates is derived,and a semi-analytical solution is also obtained in this paper.By the separation of variables, the general finite element method can be used in the direction of the thickness and is derived by the state space control method,and the shear effect is solved.By employing the transfer matrix method,the continuity of displacem ents and stresses is satisfied, and the number of variables is greatly reduced. -
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