PAPER 1
The Saint Venant problem: an approach based on the average displacements values over the cross-sections.
Abstract: in the present study an alternative method to attain the solution of the Saint Venant problem is developed, based on the idea to descibe the cylinder displacement field through the generalised average displacements of the cross-section. This results in expressions of the displacements distribution formally different from the ones obtained in the classic solution, and depending on the definition assumed for the average displacements over the section. The study comes out to be, in our opinion, rather interesting from a didactic point of view, especially for clariyfing the role of the abovementioned kinematic quantities within the deformation status of the Saint Venant cylinder.
History and Credits: the study had its beginning in 2002, during the period of the PhD Course in Structural Engineering at the University of Pisa, as a consequence of the tutoring activity carried out within the Course in Structural Mechanics, run by Professor F. Cafarella. An initial handwritten version was issued in 2003, containing many of the principal aspects that feature the work in the present form. The study was developed in the following years, and underwent various actual modifications, due to the revisions of Professor S. Ligarò at first, and of Professor F. Cafarella subsequently. It assumed the present aspect approximately in 2009; but it has to be regarded as not completely fulfilled, and it is supposed to offer many hints for further studies. For this reason, any contribution or observation from the readers will be really appreciated.