Geometrically nonlinear models of elastic and elastic-plastic beams

Following the moderate rotation theory of shells, we develop a similar treatment of elastic and elastic-plastic beams, undergoing small deformations and moderate rotations. We assume that a beam can deform in a fixed vertical plane only, and that the applied load does not act on its vertical walls. No Bernoulli-type constraints are imposed. The one-dirnensional problem studied is described by a system of four ordinary differential equations, being the equilibrium equations (with boundary conditions) of the considered beams. These equations have been derived on the basis of variational techniques.