‎"LAMÉ, G. (+) B. P. E. CLAPEYRON.‎
‎Mémoire sur l’équilibre intérieur des corps solides homogènes. - [VERY EARLY WORKS ON THE THEORY OF ELASTICITY]‎

‎[Berlin, G. Reimer, 1831]. 4to. Without wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 1831, Pp. 145-69.‎

Reference : 49764

‎First printing of Lamé and Glapeyron seminal paper which constitute one of the very earliest works on the theory of elasticity.Lame's stress ellipsoid, here presented for the first time is an alternative to Mohr's circle for the graphical representation of the stress state at a point. The surface of the ellipsoid represents the locus of the endpoints of all stress vectors acting on all planes passing through a given point in the continuum body.""During their service in St. Petersburg, these two engineers wrote their important memoir ""Sur l'équilibre interieur des corps solides homogénes"" [...]. This memoir owes its importance to the fact that it contains not only a derivation of the equations of equilibrium (which were already known at that time from the work of Navier and Cauchy) but also some applications of these general equations to the solution of problems of practical interest.In the first section of the memoir they deduce the equations of equilibrium using Navier's notion of the molecular forces and show that the same equations are obtained by using the concept of stresses, introduced by Cauchy. In the second section the stresses at a point of an elastic body are studied and it is shown that if, for each plane passing through the point, the corresponding stress is represented by a vector drawn from that point, the ends of all such vectors will be on the surface of an ellipsoid. This is the so-called 'Lamé stress ellipsoid'."" (Timoshenko, History of Strength and Materials Pp. 115-6).""Following his graduation in 1820, he went to Russia with his friend Bénoit Clapeyron. There he was appointed director for the School of Highways and Transportation at St. Petersburg and introduced mechanical testing for the iron used in the construction of suspension bridges. Praised by Todhunter and Pearson for the clarity of his exposition and the depth of his though, Lamé's greatest contributions were made through his lectures and textbooks. He wrote extensively on elasticity and was the first to advance the theory of failure based upon an ultimate tensile stress. His name is immortalized by the ""Lamé Equations"" for determining the strength of thick cylinders"" (Bibliotheca Mechanica, P. 193).‎