关键词: 弹性力学, 对称性思想, 平面应变, 梁弯曲, 轴对称问题

Abstract: This paper discusses the role of symmetry in elasticity teaching and its application to representative problems. Three cases are considered: the plane strain problem, the bending of a simply supported beam, and axisymmetric problems in polar coordinates. These examples show how symmetry reduces computational complexity, highlights the mathematical structure of problems, and provides intuitive insights into stress and displacement distributions. In teaching practice, applying symmetry as a central theme not only facilitates problem analysis but also strengthens students’ logical reasoning, modeling skills, and mechanical intuition, offering useful guidance for classroom instruction.

Key words: elasticity, symmetry, plane strain, bending of beams, axisymmetric problems