Some identities and the structure of ${\bf N}_i$ in the Stroh formalism of anisotropic elasticity

T. C. T. Ting
1988 Quarterly of Applied Mathematics  
The Stroh formalism of anisotropic elasticity leads to a 6 x 6 real matrix N that can be composed from three 3x3 real matrices N; (/ = 1,2,3). The eigenvalues and eigenvectors of N are all complex. New identities are derived that express certain combinations of the eigenvalues and eigenvectors in terms of the real matrices N, and the three real matrices H, S, L introduced by Barnett and Lothe. It is shown that the elements of Nj and N3 have simple expressions in terms of the reduced elastic
more » ... reduced elastic compliances. We prove that -N3 is positive semidefinite and, with this property, we present a direct proof that L is positive definite.
doi:10.1090/qam/934686 fatcat:zuaz2z2cpre6pdbxkpayfbdoem