Saint Venant solutions for elastic cylinders

Abstract

Under the Hamilton system, the dual form governing equations of the cylindrical problem are established using displacements and stresses as the basic variables, and the problem is accordingly transformed into finding the eigenvalues and eigensolutions by adopting the method of separation of variables. Furthermore, solutions for zero eigenvalues and non-zero eigenvalues are systematic studied. The study shows that zero eigensolutions are composed of all the overall deformation solutions such as the traditional tension and bending problems, while non-zero eigensolutions include the torsion and bending groups charactered by local deformations.