ABSTRACT
Analytical solutions of rigid-plastic or elastic-plastic problems, obtained in either an explicit form or through numerical integration, have been possible in relatively few cases in which some simplifying features, such as plane strain or axial symmetry prevail. This chapter presents analytical solutions to some elastic-plastic problems of practical importance. These comprise plane strain bending of bars, combined bending and tension, bending of curved beams, bars subjected to torsion, combined torsion and tension, buckling of columns, axisymmetric bending of circular plates, thick-walled cylinders, and rotating disks of uniform thickness. In thin sheet forming, bending moment is applied to obtain the required permanent shape through plastic deformation. Bending of a circularly curved beam in the elastic range has been analyzed using the stress function approach. For a circular section in torsion the cross section does not warp and remains plane.
