By D. Iesan
Reflecting new advancements within the learn of Saint-Venant’s challenge, Classical and Generalized types of Elastic Rods makes a speciality of the deformation of elastic cylinders for 3 versions of continuum: classical elastic continuum, Cosserat elastic physique, and porous elastic fabric.
The writer provides a mode to build Saint-Venant’s ideas, minimal strength characterizations of those suggestions, and an evidence of Saint-Venant’s precept. He then discusses the deformation of nonhomogenous and isotropic cylinders in addition to the matter of loaded anisotropic elastic cylinders. The e-book additionally bargains with the deformation of cylinders in the linearized idea of homogeneous Cosserat elastic solids, the deformation of nonhomogeneous Cosserat cylinders, and the extension, bending, and torsion of porous elastic cylinders.
With a number of effects now not present in similar texts, this ebook presents a special, unified standpoint within the idea of the deformation of elastic cylinders.
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Extra info for Classical and generalized models of elastic rods
90, Fichera extended Toupin’s result to the case of an elastic cylinder subject to self-equilibrated surface tractions on each of its ends, and free of surface traction on the lateral boundary. This is the case involved by Saint-Venant’s conjecture. Various authors have studied a nonlinear version of Saint-Venant’s principle. We mention the works by Roseman , Breuer and Roseman , Muncaster , Horgan and Knowles , and Knops and Payne . For the history of the problem and the detailed analysis of various results on Saint-Venant’s principle, we refer to the works of Gurtin , Djanelidze , Fichera , Horgan and Knowles , and Horgan .
329, Toupin employs a mean value theorem due to Diaz and Payne , to obtain a pointwise estimate for the magnitude of the strain tensor at interior points of the cylinder. A similar estimate was established by Fichera  for an isotropic cylinder. We present here the estimate obtained in Ref. 90. Let D0 be a bounded regular region.
3. 20 is known as Saint-Venant’s formula for torsion. 12 depend only on the cross section and the elasticity ﬁeld. Let a be the fourdimensional vector (a1 , a2 , a3 , a4 ). 12, indicating thus its dependence on the constants as , (s = 1, 2, 3, 4). 21) Saint-Venant’s Problem 39 where b = (b1 , b2 , b3 , b4 ) and c = (c1 , c2 , c3 , c4 ) are two constant fourdimensional vectors, and w0 is a vector ﬁeld independent of x3 such that w0 ∈ C 1 (Σ1 ) ∩ C 2 (Σ1 ). 21 is a solution of the problem (P2 ) if and only if u0 is Saint-Venant’s solution.