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 offers a mode to build Saint-Venant’s suggestions, minimal power characterizations of those suggestions, and an explanation 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 ebook 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 various effects no longer present in similar texts, this e-book presents a different, unified perspective within the conception of the deformation of elastic cylinders.
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Extra resources for Classical and generalized models of elastic rods
Let us investigate the arbitrariness and the structure of complex potentials for several domains of interest. First, we investigate what is the diﬀerence in the forms of two sets of potentials (Ω, ω) and (Ω∗ , ω∗ ) that correspond to the same stresses. 52) Saint-Venant’s Problem where that 29 e [f ] denotes the real part of f . 53) where c is a real constant, and α and β are complex constants. 54) Here, m [f ] denotes the imaginary part of f . Consider now the situation in which the two sets of potentials correspond to the same displacements.
It is interesting to note that the determination of b from the condition u0 ∈ KII (F1 , F2 ) can be made in a simple way. 23, we obtain 3 1 1 u0α = − bα x33 − cα x23 − c4 εαβ xβ x3 + (cj + x3 bj )wα(j) + wα0 6 2 j=1 u03 = 1 (bρ xρ + b3 )x23 + (cρ xρ + c3 )x3 + c4 ϕ + ψ 2 where we have used the notation w30 = ψ. 25 that wα0 and Tαβ (w0 ) characterize a plane elastic state corresponding to zero body forces and null boundary data. © 2009 by Taylor & Francis Group, LLC 40 Classical and Generalized Models of Elastic Rods We conclude that wα0 = 0 (modulo a plane rigid displacement).
7. 1 Statement of Problem Throughout this section, we assume that the body occupying the cylinder B is a homogeneous and isotropic elastic material, and that a continuous body force f is prescribed on B. We consider that on the lateral boundary is prescribed the surface displacement u or the surface force t. We suppose that the surface displacement u, the surface traction t, and the body force f are all independent of x3 and parallel to the x1 , x2 -plane. 4, imply that eij and tij are all independent of x3 .