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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.
The one-dimensional (1-D) Saint-Venant equations were derived by Adhémar Jean Claude Barré de Saint-Venant, and are commonly used to model transient open-channel flow and surface runoff. They can be viewed as a contraction of the two-dimensional (2-D) shallow-water equations, which are also known as the two-dimensional Saint-Venant equations.
Adhémar Jean Claude Barré de Saint-Venant (French pronunciation: [ademaʁ ʒɑ̃ klod baʁe də sɛ̃ vənɑ̃]; 23 August 1797 – 6 January 1886) [1] was a mechanician and mathematician who contributed to early stress analysis and also developed the unsteady open channel flow shallow water equations, also known as the Saint-Venant equations that are a fundamental set of equations used in ...
In the mathematical theory of elasticity, Saint-Venant's compatibility condition defines the relationship between the strain and a displacement field by = (+) where ,. Barré de Saint-Venant derived the compatibility condition for an arbitrary symmetric second rank tensor field to be of this form, this has now been generalized to higher rank symmetric tensor fields on spaces of dimension
Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886. [1] In the continuum description of a solid body we imagine the body to be composed of a set of infinitesimal volumes or material points.
Saint-Venant's theorem states that the simply connected cross section with maximal torsional rigidity is a circle. [1] It is named after the French mathematician Adhémar Jean Claude Barré de Saint-Venant .
Archimedes' principle · Bernoulli's principle; ... The simplest hyperelastic material model is the Saint Venant–Kirchhoff model which is just an extension of the ...
Archimedes' principle ... (This observation is known as the Saint-Venant's principle). Normal stress occurs in many other situations besides axial tension and ...