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Weak solutions to anti-plane boundary value problems in a linear theory of elasticity with microstructure

Shmoylova E., Potapenko S., Dorfmann A.

Archives of Mechanics

2007

Vol. 59, nr 6

519-539

In this paper we formulate the interior and exterior Dirichlet and Neumann boundary value problems of anti-plane rnicropolar 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 rnicropolar 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.