推导弹性力学极坐标中平衡微分方程和几何方程的解析法

ANALYTICAL METHOD FOR DERIVING EQUILIBRIUM DIFFERENTIAL EQUATIONS AND GEOMETRIC EQUATIONS OF ELASTICITY IN POLAR COORDINATES

根据直角坐标和极坐标中偏微分算子的转换式、应力和应变分量的坐标变换式以及基矢量变换矩阵,提出了推导极坐标中平衡微分方程和几何方程的解析法,不需要作图,可以从直角坐标中的平衡微分方程和几何方程直接导出极坐标中的方程形式,丰富了弹性力学课程教学内容。

According to the transformation of the partial differential operator in rectangular and polar coordinates,the coordinate transformations of the stress and strain components,and the basis vector transformation matrix,an analytical method for deriving equilibrium differential equations and geometric equations in polar coordinates is proposed.No drawing is needed,the equations in polar coordinates can be directly derived from the equilibrium differential equations and geometric equations in rectangular coordinates,and the teaching content of elasticity course is enriched.