Recent Advances in the Theory of Anisotropic Elasticity with Applications to Composite Materials

摘要

The Stroh formalism for anisotropic elastic materials has contributed much to the determination of solutions of anisotropic elasticity problems. In most cases, however, the solutions are in a complex form and it is desirable to have the solutions in a real form for practical applications. This requires new identities or sum rules which relate eigenvalues and eigenvectors of anisotropic elastic constants to real quantities. The identities serve two important purposes. Firstly, with the identities the problem of repeated eigenvalues disappears. Secondly, the identities enable us to express the final solutions to anisotropic elasticity problems in a real form. The identities and the structural property of certain real matrices in the solution are the keys in solving heretofore unsolved problems and in simplifying existing complex solutions to a real form solution. Reprints. (jes)