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- Saint-Venant's_theorem abstract "In solid mechanics, it is common to analyze the properties of beams with constant cross section. Saint-Venant's theorem states that the simply connected cross section with maximal torsional rigidity is a circle. It is named after the French mathematician Adhémar Jean Claude Barré de Saint-Venant.Given a simply connected domain D in the plane with area A, the radius and the area of its greatest inscribed circle, the torsional rigidity P of D is defined byHere the supremum is taken over all the continuously differentiable functions vanishing on the boundary of D. The existence of this supremum is a consequence of Poincaré inequality.Saint-Venant conjectured in 1856 thatof all domains D of equal area A the circular one has the greatest torsional rigidity, that isA rigorous proof of this inequality was not given until 1948 by Pólya. Another proof was given by Davenport and reported in. A more general proof and an estimate is given by Makai.".
- Saint-Venant's_theorem wikiPageID "14272194".
- Saint-Venant's_theorem wikiPageRevisionID "545032062".
- Saint-Venant's_theorem hasPhotoCollection Saint-Venant's_theorem.
- Saint-Venant's_theorem subject Category:Calculus_of_variations.
- Saint-Venant's_theorem subject Category:Elasticity_(physics).
- Saint-Venant's_theorem subject Category:Inequalities.
- Saint-Venant's_theorem subject Category:Physics_theorems.
- Saint-Venant's_theorem type Abstraction100002137.
- Saint-Venant's_theorem type Attribute100024264.
- Saint-Venant's_theorem type Communication100033020.
- Saint-Venant's_theorem type Difference104748836.
- Saint-Venant's_theorem type Inequalities.
- Saint-Venant's_theorem type Inequality104752221.
- Saint-Venant's_theorem type Message106598915.
- Saint-Venant's_theorem type PhysicsTheorems.
- Saint-Venant's_theorem type Proposition106750804.
- Saint-Venant's_theorem type Quality104723816.
- Saint-Venant's_theorem type Statement106722453.
- Saint-Venant's_theorem type Theorem106752293.
- Saint-Venant's_theorem comment "In solid mechanics, it is common to analyze the properties of beams with constant cross section. Saint-Venant's theorem states that the simply connected cross section with maximal torsional rigidity is a circle.".
- Saint-Venant's_theorem label "Saint-Venant's theorem".
- Saint-Venant's_theorem label "Teorema de Saint-Venant".
- Saint-Venant's_theorem sameAs Teorema_de_Saint-Venant.
- Saint-Venant's_theorem sameAs m.03czvsq.
- Saint-Venant's_theorem sameAs Q3699212.
- Saint-Venant's_theorem sameAs Q3699212.
- Saint-Venant's_theorem sameAs Saint-Venant's_theorem.
- Saint-Venant's_theorem wasDerivedFrom Saint-Venant's_theorem?oldid=545032062.
- Saint-Venant's_theorem isPrimaryTopicOf Saint-Venant's_theorem.