UNIFIED DERIVATION OF POLAR COORDINATE EQUATIONS FOR THE THEORY OF ELASTICITY

The polar coordinate solution for plane problems is a core chapter in the teaching of elasticity mechanics, but students often encounter two major challenges: firstly, the form of polar coordinate equations differs significantly from that of Cartesian coordinate equations, making it difficult to understand their inherent logic; secondly, the traditional derivation method is disconnected from continuum mechanics, which is detrimental to students’ learning of higher-order theories. To address this, the paper employs basic tensor knowledge to meticulously derive the equilibrium differential equations, geometric equations, and the relationships between stress components and stress functions in polar coordinates, aiming to help students clearly understand the derivation process, deepen their understanding of polar coordinate solution methods, and thereby better grasp the relevant content.