On Saint-Venant's Principle for a Homogeneous Elastic Arch-Like Region

Abstract

In this paper, we consider a two-dimensional homogeneous isotropic elastic material state in the arch-like region a e r e b, 0 e e , where (r, ) denote plane polar coordinates. We assume that three of the edges r = a, r = b, = are traction-free, while the edge = 0 is subjected to an (in plane) self-equilibrated load. We define an appropriate measure for the Airy stress function ' and then we establish a clear relationship with the Saint-Venant's principle on such regions. We introduce a cross-sectional integral function I() which is shown to be a convex function and satisfies a second-order differential inequality. Consequently, we establish a version of the Saint-Venant principle for such a curvilinear strip, without requiring of any condition upon the dimensions of the arch-like region. (2000): 74G50, 74B05 Mathematics Subject Classifications

On Saint-Venant's principle in a poroelastic arch-like region

“…The spatial behavior of solutions of the biharmonic equation for a homogeneous isotropic elastic material occupying an arch-like region was recently studied by Flavin [20], Flavin and Gleeson [21], Chiriţȃ [22], and D'Apice and Chiriţȃ [23,24].…”

End effects for a generalized biharmonic equation with applications to functionally graded materials

“…This last equation was treated previously by Flavin [3], Flavin and Gleeson [4] and Chiriţȃ [5] in concern with the case when a traction is applied on the edge θ = 0, the other three edges being free of charge. Decay estimates of solutions to the biharmonic equation in an inhomogeneous rectangular strip have been established, for instance, by [6][7][8] and [9].…”