Saint-Venant's principle

In Saint-Venant's principle named after the French elasticity theorist Jean Claude Barré de Saint-Venant can be stated as^[1]

".. the strains that can be produced in a body by the application, to a small part of its surface, of a system of forces statically equivalent to zero force and zero couple, are of negligible magnitude at distances which are large compared with the linear dimensions of the part." A.E.H. Love

Additional recommended knowledge

Daily Visual Balance Check

Daily Sensitivity Test

What is the Sensitivity of my Balance?

The original statement was published in French by Saint-Venant in 1855^[2]. Although stated verbally the principle is well known among mechanical engineers in this informal formulation. More recent mathematical literature gives a rigorous interpretation in the context of partial differential equations. An early contribution to this came from von Mises in 1955^[3]

References

1. ^ A.E.H. Love, "A treatise on the mathematical theory of elasticity" Cambridge University Press, 1927. (Dover reprint ISBN 0486601749)
2. ^ A. J. C. B. Saint-Venant, 1855, Memoire sur la Torsion des Prismes, Mem. Divers Savants, 14, pp. 233-560
3. ^ R. von Mises, On Saint-Venant's Principle. , Bull. AMS, 51, 555-562, 1955