IDEAS ON THE HISTORY OF SCIENCE REVELATION OF THE CONCEPTS OF EULER AND NAVIER IN UP-TO-DATE STATICS

Abstract

Finite Element Method is one of the most important computational tools of modern statics. The main features of it are application of variational principles on one hand and discretizing of the domain, fitting at the nodes on the other hand. Both concepts are classical, their appearance in the mechanics is due to EULER and NAVIER, respectively. Restricting ourselves to the analysis of bars and bar structures, it can be stated that EULER was engaged with the differential equation of the elastica and with the general method of solving variational problems round 250 years ago. In his genuine investigation he made use of variations being in accordance with the simple base functions of the F.E.M. Paper shows this derivation. Navier, whose name is connected with the foundation of the theory of the elastic bars up to now, reduced the calculation of the deflection of the simply supported beam to that of the cantilever so as to iilvestigate the sections of the structure always between two point forces, while fitting the exact solutions valid on separate intervals to each other. This idea is presented as well and the traditional results are recalled in an up-to-date symbolism.