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

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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