极坐标系中弹性力学平面问题的Hamilton正则方程及状态空间有限元法

THE HAMILTON CANONICAL EQUATIONS OF THEORY OF ELASTICITY IN POLAR COORDINATES AND THE VARIABLE CONTROL FINITE ELEMENT METHOD

摘要: 本文给出了极坐标系下弹性力学平面问题的Hamilton正则方程,并提出一种求解该方程的状态空间有限元法。文中通过对Hellinger-Reissner混和变分原理的修正,导出了Hamilton正则方程及其对应能量泛函,然后采用分离变量法对其场变量进行分离变量,这样就可在θ方向采用通常的有限元插值,而沿半径r方向采用状态空间法给出解析解答,从而实现了有限元法与控论制中状态空间的结合。通过计算表明,本文方法精度高。

Abstract: The Hamilton canonical equations of elasticity in polar coordinate is deduced and the variable control finite element method is proposed. By the-separation of variables,the conventional interpolation method in finite element method is applied in θ direction while the analytical solution is given in r direction, the combined application of the method of finite element and the variable control is rendered.