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Refined modeling of composite plates with in-plane heterogeneity†
Version of Record online: 8 APR 2013
Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Special Issue: Refined theories of plates and shells
Volume 94, Issue 1-2, pages 85–100, January 2014
How to Cite
Lee, C.-Y., Yu, W. and Hodges, D.H. (2014), Refined modeling of composite plates with in-plane heterogeneity. Z. angew. Math. Mech., 94: 85–100. doi: 10.1002/zamm.201200209
Parts of this paper appeared in the proceedings of the 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conferences, Denver, Colorado, April 4–7, 2011 and the Proceedings of the 8th European Solid Mechanics Conference, Graz, Austria, July 9–13, 2012.
- Issue online: 7 JAN 2014
- Version of Record online: 8 APR 2013
- Manuscript Accepted: 4 MAR 2013
- Manuscript Received: 11 OCT 2012
- National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology. Grant Number: Basic Science Research Program (2012R1A1A1013388)
- Air Force Office of Scientific Research. Grant Number: FA9550-08-1-0405
- dimensional reduction;
- variational asymptotic method;
- in-plane heterogeneity;
- Reissner-Mindlin plate model.
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.