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Weak solutions to anti-plane boundary value problems in a linear theory of elasticity with microstructure
Arch. Mech. 59 (6), 519-539, 2007
Keywords: anti-plane micropolar elasticity; Sobolev spaces; boundary integral equation method
Abstract
In this paper we formulate the interior and exterior Dirichlet and Neumann boundary value problems of anti-plane micropolar elasticity in a weak (Sobolev) space setting, we show that these problems are well-posed and the corresponding weak solutions depend continuously on the data. We show that the problem of torsion of a micropolar beam of (non-smooth) arbitrary cross-section can be reduced to an interior Neumann boundary value problem in antiplane micropolar elasticity and consider an example which demonstrates the significance of material microstructure.