A Brief Discussion about the Reduction of the Classical Compatibility Equations

Abstract

The present work arises from a didactic approach to solving the so-called linear elastic problem. It is found that the six classical ‘compatibility equations' (CE) deduced by Saint-Venant in 1864 [1] can be reduced in practice to only three, which are equivalent to the six. Being three, and not the six traditionally presented, and because of the linearity in all the equations involved, the problem of conjuncting equilibrium, compatibility and Hooke's law, becomes a mathematically determined one. The scope of the present paper is essentially academic and mathematical since, in general, the solution of eventual problems using the proposed CE could obviously be tackled by the classical Saint-Venant equations. In the two equivalent groups presented herein all the CE are in terms of the strain tensor components and arbitrary functions.