Structural stability concepts in medieval and renaissance mechanics

Abstract

The identification of the origins of what we now call the theory of elastic stability is not an easy task. Most authors trace the origins to the pioneering work of Leonhard Euler in 1744, and some shift this origin to the experimental works of Petrus van Musschenbroek in 1729. However, other contemporary authors interested in the history of the discipline postulate that the works of Medieval and Renaissance scholars should be considered as the true sources of the buckling studies performed in the XVIII Century. This paper reports a historical research based on the original works of Al-Khazini, Jordanus de Nemore, Leonardo da Vinci, and Marini Merssene, in order to discuss what kind of knowledge they had about the topics of stability and lateral deflections of columns under axial loads. Our investigation shows that there were observations of the phenomenon considered, but those observations were not translated into a deeper understanding of the phenomenon, so that the causes of this effect or the role of strength on the response were not considered. Leonardo was closer than others in his understanding of the nature of the problem and produced some tentative rules of behavior; however, those were only documented in private writings and did not make an impact in his contemporaries or even 100 years later. We postulate that there was a continuity of problems between medieval authors and those who lived in the XVIII Century, rather than continuity in their concepts and approaches to solve those problems.

On the magnetorotational instability and elastic buckling

“…Because of its obvious importance to the stability of structures, the scientific investigation of buckling dates well back into antiquity, and quantitative investigations started at the very beginning of the modern scientific era. As early as the 1480s, Leonardo da Vinci produced empirical criteria addressing the stability and lateral deflection of columns under compression [13]. In the eighteenth century, Euler and Bernoulli began to consider timedependent elastic deformations and buckling [14].…”

Can complex systems really be simulated?

“…Others point out that the interest for these concepts existed well before that time, even during the Medieval and Renaissance periods [2], with early studies being traced back to ancient Greece. Now, more than two centuries after Euler, there is a vast literature dedicated to structural stability.…”

Critical buckling loads of the perfect Hollomon's power-law columns

“…The Euler's formula is limited to applications for elastic columns. For a prior history to the theory of elastic stability of columns, see [13]. In 1859, Kirchhoff extended the theory to geometrically non-linear large deflections and provided a solution of the deflection curve in terms of elliptic integrals.…”