COGNITIVE VALUE AND APPLICATION CASES OF DIMENSIONAL ANALYSIS IN THE TEACHING OF ELASTIC MECHANICS

Dimensional analysis is an important bridge connecting physical intuition and mathematical form, and it has unique cognitive value in the teaching of elasticity mechanics. This paper explores the application of dimensional analysis in the establishment of stress formulas from a teaching perspective, aiming to help students understand the essence of elasticity mechanics equations through the relationships of physical quantities. Taking three typical problems as examples including the problem of a wedge-shaped gravity dam, the problem of a wedge—shaped body with a wedge surface subjected to distributed forces, and the problem of a wedge—shaped body subjected to concentrated forces and couples at the top, this paper demonstrates that dimensional analysis can intuitively speculate the form of stress characteristics without relying on complex derivations. Teaching practice shows that this method can effectively stimulate students’ physical thinking and promote the cognitive transformation from formula memorization to physical understanding.