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Keywords:

  • Plate;
  • homogenization;
  • dimensional reduction;
  • variational asymptotic method;
  • in-plane heterogeneity;
  • Reissner-Mindlin plate model.

Abstract

This article is concerned with the mechanical behavior of heterogeneous composite plates with elastic moduli and layered geometries varying through the thickness direction and periodically along the in-plane directions. By using the concept of decomposition of the rotation tensor, we first formulate the three-dimensional elastic problem in an intrinsic form for application to the geometrically nonlinear problem. The variational asymptotic method is then exercised, leading to simultaneous homogenization and dimensional reduction to construct an effective and simple model suitable for plates with in-plane periodicity. In particular, having obtained the refinement terms up to the second order, we develop a refined plate model, namely a generalized Reissner-Mindlin model that is capable of capturing the transverse shear deformations. In order to deal with realistic and complex plate geometries and constituent materials efficiently and conveniently, the proposed model is implemented into a single unified formulation suitable for incorporation into a commercial analysis package. Numerical results computed herein for a few examples are compared to similar results available in the literature to demonstrate the application and performance of the present model.