Abstract
In this paper, we consider a two-dimensional homogeneous isotropic elastic material state in the arch-like region a ≤ r ≤ b, 0 ≤ θ ≤ α, where (r, θ) denote plane polar coordinates. We assume that three of the edges r = a, r = b, θ = α are traction-free, while the edge θ = 0 is subjected to an (in plane) self-equilibrated load. We define an appropriate measure for the Airy stress function φ and then we establish a clear relationship with the Saint-Venant's principle on such regions. We introduce a cross-sectional integral function I(θ) 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.
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Chiriţă, S. On Saint-Venant's Principle for a Homogeneous Elastic Arch-Like Region. J Elasticity 81, 115–127 (2005). https://doi.org/10.1007/s10659-005-9008-2
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DOI: https://doi.org/10.1007/s10659-005-9008-2