Nonlinear effects in a plane problem of the pure bending of an elastic rectangular panel

The paper presents a modification of the semi-inverse representation of the pure bending deformation of a prismatic panel with rectangular cross-section that is suitable for the method of successive approximations (or Signorinis expansion method). This modification was used to investigate with an accuracy to second order terms the plane problem of pure bending for three different models of nonlinearly elastic behavior: harmonic material, Blatz and Ko material, Murnaghan material. It was found that the typical diagram of bending has maximum point followed by falling region. To study the stability of the bent panel the bifurcation approach was used. Some results about the position of bifurcation points at the loading diagram depending on the material and geometrical parameters are presented.