Second order effects in the flexure of isotropic incompressible elastic cylinders

Abstract

General methods of successive approximations for problems in the theory of large elastic deformations have been proposed by Signorini (9), Misicu (5), Rivlin (6), Green and Spratt (4) and Rivlin and Topakoglu (7). Rivlin has applied his method to the problem of torsion of cylinders as far as terms of the second order. A solution of the problem of second order effects in the torsion of incompressible cylinders of arbitrary cross-section has been given by Green and Shield (3) in terms of complex potential functions, and the complete details of the stress distribution can be obtained once certain integral equations are solved. Blackburn and Green (l) have considered the second order effects in the deformation of compressible cylinders by forces on the ends. For the problems of torsion and bending by couples they obtained details of the displacements and stress distributions in terms of two complex potential functions which satisfy a certain boundary condition. The second order torsion problem has also been discussed by Sheng(8).