Stability of Slightly Wrinkled Plates Interacting with an Elastic Subsoil

The first aim of the contribution is to formulate an engineering theory describing the linear stability of periodically waved shallow shell-like structures (slightly wrinkled plates, cf. Fig. 1) interacting with a Winkler foundation. On the basis of the proposed theory, the effect of elastic foundation on the value of a critical force is investigated. The second aim is to compare the proposed model of wrinkled plates resting on elastic medium with the known theories of orthotropic plates. It is shown that the obtained solutions depend on the shell wavelength parameter I. The general results are illustrated by an example.