Mathematical methods in the theory of pure bending of rectangular beams made of weakening material with symmetric stress-strain diagram

The problem of pure bending of a beam with rectangular cross-section is considered. The beam is made of the material with a diagram having the falling branch. The stress-strain state of the beam in both steady and unsteady equilibrium positions is determined by the Newton-Kantorovich method and the method of simple iterations. The analysis of pure bending stability is carried out using the catastrophe theory methods and the method of investigating stability in the first approximation. It is shown that the divergence of simple iterations corresponds to the moment of stability loss.