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On Saint-Venant's Principle for an Inhomogeneous Curvilinear Rectangle

Department of Information Engineering and Applied Mathematics (DIIMA), University of Salerno, 84084 Fisciano (Sa), Italy

A two-dimensional inhomogeneous isotropic elastic material is considered in the arch-like region a r b,0 , where (r,) denotes plane polar coordinates. It is envisaged 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. An appropriate energy-like measure E() of the Airy stress function in the region between arbitrary and = is defined, and it is proved to be positive definite provided that some appropriate assumptions are satisfied by the material and geometric characteristics of the arch-like region. Then, a version of Saint-Venant's Principle for the curvilinear strip is established.

Key Words: Saint-Venant's Principle • inhomogeneous media • biharmonic equations • energetic measure • 2D isotropic media

This version was published on April 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 2, 148-163 (2007)
DOI: 10.1177/1081286505055473


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