Abstract
The problem of the second-order torsion of a cylinder of compressible isotropic material is reduced to the solution of a single boundary-value problem involving two complex potential functions. Without solving this boundary-value problem, a formula for the fractional elongation of the cylinder is obtained in agreement with that found previously by Rivlin (1953). When the region occupied by any cross-section of the cylinder is bounded by a single closed curve the equation satisfied by the complex potentials reduces to that obtained by Green & Shield (1951) for the case of an incompressible cylinder, and a general method of solution was given by these authors. The problem of second-order bending of a cylinder of compressible isotropic material by couples over its plane ends is also reduced to the solution of a single boundary-value problem for two complex potential functions, in addition to the boundary-value problem for classical torsion of a cylinder. A general formula is found for the change in length of the line of centroids and one applicaton of the theory is made to right circular cylinders.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
