Spatial Decay Estimates for the Biharmonic Equation in Plane Polars with Applications to Plane Elasticity

¹ Faculty of Mathematics, Al. I. Cuza, University of Iai, Blvd. Carol I, No. 11, 700506-Iai, Romania
² Department of Information Engineering and Applied Mathematics (DIIMA), University of Salerno, 84084 Fisciano (SA), Italy

^* To whom correspondence should be addressed.

	Abstract

The present paper considers an isotropic and homogeneous elastic body occupying the arch-like region a r b, 0 , where (r, ) denote plane polar coordinates. The arch-like body is in equilibrium under an (in plane) self-equilibrated load on the edge r = a, while the other three edges r = b, = 0 and = are traction-free and the body forces are absent. An appropriate measure is defined in terms of the Airy stress function , provided that the opening angle of the arch-like region is lower than 2/3. Then the spatial behavior of the solution is studied and a clear relationship is established with Saint-Venant's principle on such regions. In fact, for a bounded arch-like region it is shown that the measure decays at least algebraically with respect to r, while for an unbounded region our result reveals a relationship with the classical Phragmèn-Lindelöf theorem.

Key Words: Saint-Venant's principle, plane stress, biharmonic equation, arch-like region

First published on April 7, 2006, doi:10.1177/1081286506059747

Mathematics and Mechanics of Solids 2007;12:343.

A more recent version of this article appeared on June 1, 2007


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