弹性力学极坐标辛体系Hamilton函数的守恒律

CONSERVATION LAW OF HAMILTONIAN FUNCTION IN SYMPLECTIC SYSTEM OF POLAR COORDINATE ELASTICITY

用弹性力学直角坐标辛体系中类似的形式,定义了极坐标问题径向和环向辛体系的Hamilton函数,对其守恒性进行了研究,由Hamilton对偶方程推出了Hamilton函数的守恒律,同时给出了守恒条件,指出两种极坐标辛体系中Hamilton函数是否守恒均取决于两侧边的荷载和位移情况。在径向和环向辛体系中都给出了算例,验证了Hamilton函数的守恒律。这一守恒律丰富了弹性力学辛体系的理论内容,不仅对于弹性力学极坐标问题的理论分析有所帮助,也为极坐标问题的数值计算分析提供了一个判断依据。

With similar form of Hamiltonian function in symplectic system of rectangular coordinate elasticity, the function is defined in both radial and circumferential symplectic system of polar coordinate problems. The conservation property of Hamiltonian function is discussed. The conservation law of Harniltonian function is deduced from Hamilton＇s dual equations, and the conservation condition is presented. It is pointed out that whether Hamiltonian function is conservative depends on the loads and displacements on two sides in two symplectic systems of polar coordinate elasticity. Two examples are given to verify the conservation law in radial and circumferential symplectic system. The law is useful in analyzing the polar coordinate elasticity and provides an estimating basis for numerical calculations in this field.