ON STABILITY OF HOMOGENEOUS ELASTIC BODIES UNDER BOUNDARY-CONDITIONS WEAKER THAN DISPLACEMENT CONDITIONS

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