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The Quarterly Journal of Mechanics and Applied Mathematics 1994 47(4):663-672; doi:10.1093/qjmam/47.4.663
© 1994 by Oxford University Press
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ON STABILITY OF HOMOGENEOUS ELASTIC BODIES UNDER BOUNDARY CONDITIONS WEAKER THAN DISPLACEMENT CONDITIONS

E. I. RYZHAK

( Institute of Physics of the Earth, Russian Academy of Sciences 10 B. Gruzinskaya, Moscow 123810, Russia )

The well-known result that strong ellipticity is sufficient for homogeneous elastic bodies under displacement boundary conditions to be stable in the small is modified in the presence of material planes of symmetry. It is proved that, over the plane portions of the boundary parallel to the material planes of symmetry, the displacement condition can be replaced by the weaker conditions of tangentiality or normality of the displacements.


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