On Saint-Venant's Principle for an Inhomogeneous Curvilinear Rectangle
Gerardo Iovane*
Department of Information Engineering and Applied Mathematics (DIIMA),
University of Salerno, 84084 Fisciano (Sa), Italy
* To whom correspondence should be addressed.
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Abstract |
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A two-dimensional inhomogeneous isotropic elastic material is considered in the
arch-like region a 
r b, 0
a , where (r, ) denotes plane polar
coordinates. It is envisaged that three of the edges r = a, r
= b, = a 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.
