Study of Bending of Beams Made of Material with a Nonlinear Deformation Diagram

The widespread introduction of new polymer and composite materials, as well as a number of technological processes, for example, those associated with cold bending of pipes, faces difficulties in engineering calculations, which is due to the nonlinearity of the deformation diagram in the area of working loads. This article presents the derivation of equations for determining the real elastic bending characteristics of materials with a nonlinear deformation diagram based on an analysis of the dependence of the displacement of the point of application of force on its magnitude during cantilever or three-point bending of beams. The obtained equations can be used in calculations of elastoplastic bending of metal elements of structures and bending of structures made of polymer and composite materials.