Plastic Deformations Occuring in Shells with Developable Middle Surfaces during Bending

A huge number of investigations on developable surfaces have been made, but the problem of analysis of plastic deformation during bending was usually out of the path. It is widespread in practice to make these surfaces with the means of bending. In previous papers, there has been found no note of the appearance of plastic deformations in a plate which is being bent into a cylinder. That is why analytical investigation of bending of developable shells is considered to be of great value. In the paper, analytical formulas which give the opportunity to determine the bending moments appearing due to parabolic bending of an elastic slab, as well as formulas for limitations to the slope angle of rectilinear generator of evolvent helicoids during the process of parabolic bending of an annulus into the given helicoids, are presented. The author also derived the formulas for determination of the minimum radius of a cylinder made by bending of a plate without the emergence of plastic deformation in it. © Published under licence by IOP Publishing Ltd