Saint-Venant's principle
Saint-Venant's principle, named after Adhémar Jean Claude Barré de Saint-Venant, a French elasticity theorist, may be expressed as follows:[1]
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... the difference between the effects of two different but statically equivalent loads becomes very small at sufficiently large distances from load.
The original statement was published in French by Saint-Venant in 1855.[2] Although this informal statement of the principle is well known among structural and mechanical engineers, more recent mathematical literature gives a rigorous interpretation in the context of partial differential equations. An early such interpretation was made by von Mises in 1945.[3]
The Saint-Venant's principle allows elasticians to replace complicated stress distributions or weak boundary conditions with ones that are easier to solve, as long as that boundary is geometrically short. Quite analogous to the electrostatics, where the electric field due to the i-th moment of the load (with 0th being the net charge, 1st the dipole, 2nd the quadrupole) decays as 1/ri+2{displaystyle 1/r^{i+2}}
See also
- Shallow water equations
References
^ A. E. H. Love, "A treatise on the mathematical theory of elasticity," Cambridge University Press, 1927. (Dover reprint .mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
ISBN 0-486-60174-9)
^ A. J. C. B. Saint-Venant, 1855, Memoire sur la Torsion des Prismes, Mem. Divers Savants, 14, pp. 233–560.
^ R. von Mises, On Saint-Venant's Principle. Bull. AMS, 51, 555–562, 1945.
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