Moderately wrinkled plate

Article type: Research Article

Authors: Aganović, I. | Jurak, M. | Marušić‐Paloka, E. | Tutek, Z.^;

Affiliations: Department of Mathematics, University of Zagreb, Bijenička 30, 41 000 Zagreb, Croatia

Note: [] Corresponding author. Fax: +385 1 46 803 35; E‐mail: tutek@cromath.math.hr.

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.

Journal: Asymptotic Analysis, vol. 16, no. 3-4, pp. 273-297, 1998