Postcritical Deformations of Thin Elastic Anisotropic Shells with Linear Memory
The objective of this chapter is to apply the geometric method to nonlinear stability problems of anisotropic visco-elastic shells. An analytical-asymptotic solution of the corresponding differential equations of nonlinear stability problems is worth researching due to the wide practical use of shells made from new technological materials (polymers reinforced with glass fibres, etc.). For this purpose an analogue of the variational principle A for studying postcritical deformations of anisotropic visco-elastic shells will be derived. It is based on the geometric description of the shell postcritical shapes and on some physical concepts that preserve the anisotropy during postcritical deformations. The final form of the variational principle will be presented in section 2.2 in terms of Laplace transforms with respect to time of the deformation postcritical energy and work done by the external staticn load.
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