ANISOTROPIC ELASTIC-MATERIALS FOR WHICH THE SEXTIC EQUATION IS A CUBIC EQUATION IN P(2)

For a two-dimensional deformation of linear anisotropic elastic materi als, the analysis requires computation of certain eigenvalues p that a re the roots of a sextic algebraic equation whose coefficients depend only on the elastic constants. It is known that the sextic equation re duces to a cubic equation in p(2) for materials of monoclinic or highe r symmetry with a symmetry plane at x(1) = 0 or at x(2) = 0. The advan tage of having a cubic equation in p(2) is not only that p can be obta ined analytically. In many cases, the solution to an anisotropic elast icity problem is much simplified. The purpose of this paper is to pres ent other anisotropic elastic materials for which the sextic equation is a cubic equation in p(2). These materials may not possess a plane o f symmetry. The author shows that as few as two restrictions on the el astic constants are sufficient to deduce these materials.