Nonlinear beam theory

This lecture covers the strain-displacement relations for a nonlinear beam, simplifications of the general theory, first-order constitutive relation for linear elastic behavior, equations of equilibrium from variational methods, and small strain with moderate rotation for circular rings. The instructor discusses the equilibrium shape of a bent beam, energy functional, weak form of the problem, and the strong form of the problem. The lecture also delves into Eulzer's elastica, total energy, and the weak form of the problem. Furthermore, it explores the equilibrium equation, nonlinear beam theory, and the organization of material. The lecture concludes with the introduction of fundamental issues that arise in plate and shell theory.