Three-dimensional non-linear elasticity-based 3D cubic B-spline finite element shear buckling analysis of rectangular orthotropic FGM plates surrounded by elastic foundations

In the present paper, shear buckling analysis of the orthotropic heterogeneous FGM plates is investigated for the first time. Moreover, influence of the Winkler-type elastic foundation is considered. The material properties are assumed to have in-plane orthotropy and transverse heterogeneity. The most accurate approach, i.e., the three-dimensional elasticity is employed instead of using the approximate plate theories. In contrast to all of the available displacement-based buckling analyses that have employed C-0-continuous commercial finite element codes or semi-analytical methods, present formulations are C-2-continuous due to using the proposed 3D cubic B-spline element. Results are derived based on principle of minimum potential energy and a non-linear finite element procedure utilizing a Galerkin-type 3D cubic B-spline solution algorithm. Buckling loads are detected based on a generalized geometric stiffness concept. In this regard, effects of both the prebuckling and buckling states are considered. To present a better imagination and more detailed discussions, details of the buckling mode shapes and the foundation interaction are discussed for plates with simply-supported edges. In addition, the more practical free and clamped edge conditions are also considered. (C) 2013 Elsevier Ltd. All rights reserved.