Moderately wrinkled plate

Abstract

The asymptotic behaviour, with respect to the small period, of the equilibrium displacements corresponding to the Koiter’s shell model of periodically perturbed plate is considered. In the limit as the period tends to zero a model describing the deformation of a wrinkled plate is obtained in the two‐scale form. The two‐scale problem can be decoupled; the longitudinal displacement satisfies the classical equations for longitudinal deformations of a plate, while the transverse displacement is a solution of a fourth‐order elliptic problem modeling the anisotropic plate. Corresponding convergence result with correctors is proved by use of two‐scale convergence method. In the case of wavy plate the effective coefficients of anisotropic plate are explicitly computed.