Theory of Stability of Multilayered Continua in Finite Anisotropic Elasticity

The writer’s general equations for the mechanics of continua under initial stress are applied to the formulation of a rigorous theory of stability of multilayered elastic media in a state of finite initial strain. The medium is assumed incompressible. It is either isotropic or anisotropic. The problem is analyzed in the context of the writer’s earlier discussions showing the existence of internal and interfacial instability. The results provide a rigorous solution of the problem of buckling of sandwich plates. Recurrence equations are derived for the interfacial displacements. It is shown that they are equivalent to a variational principle expressed in terms of these displacements. A matrix multiplication procedure is also developed for automatic computing of critical values when a large number of layers is involved.