APPLICATION AND TEACHING OF LAGRANGIAN DYNAMICS EQUATIONS IN DERIVATION OF ELASTIC BODY EQUATION

To avoid the complex process of force analysis on infinitesimal elements in Newtonian mechanics, this paper uses Lagrangian mechanics to derive the Lagrangians and their equivalent dynamical differential equations for five types of elastic bodies: mass-spring systems, axial rods, bending beams, bending plates, and three-dimensional continua. In the teaching of elasticity mechanics courses, students can be encouraged to establish control equations from the perspective of energy and avoid the complex analysis of forces for infinitesimal body. In finite element method courses, students can directly perform variations and discretizations on the Lagrangians. This paper summarizes the Lagrangians and differential equations for existed elastic bodies to form students a more systematic knowledge framework.