Stability of Multilayered Continua including the Effect of Gravity and Viscoelasticity

The theory of stability of multilayered continua is extended to include the effect of gravity and the case of viscoelastic materials. It is also applied to obtain numerical solutions for the buckling of the anisotropic plate in finite elasticity with free boundaries or embedded in an infinite medium. In the multilayered system it is shown that the effect of gravity forces may be included by a very simple process leading to a matrix multiplication scheme for the solution of the characteristic stability problem and to a new variational principle. By the correspondence principle the theory is immediately extended to the stability problem of multilayered viscoelastic media, and a general theorem is derived for the conditions under which only real values are possible for the characteristic exponents of the stability problem. As an example of gravity instability, two cases are solved numerically for purely viscous or elastic layers. The theory yields the solution for a large class of problems of technological and geophysical interest.