极坐标系和球坐标系几何和平衡方程统一推导方法

The Unified Derivation Method of the Geometric and Equilibrium Equations of Polar Coordinates System and Spherical Coordinates System

基于曲线坐标系下小变形的几何方程和平衡方程的一般形式,给出了极坐标和球坐标系下对应方程的一种新的推导方法。所给出的方法无需对微元体作变形和应力分析,即可在统一的计算框架下方便、快速、准确地导出几何方程和平衡方程,有利于加深对弹性力学经典方程的统一性的理解。

The paper put forward a new derivation method of the corresponding equation of the polar coordinates system and the spherical coordinates system based on the ordinary form of both geometric and equilibrium equations for small deformation in the curvilinear coordinates system. The proposed method can derive both geometric equation and equilibrium equation under the unified calculation frame in an easy, quick and accurate way and does not need to make deformation and stress analysis of the micro-component, thus helping deepen understanding of the unitarity of the classical equation of mechanics of elasticity.