Higher-order finite element models for the static linear and nonlinear behaviour of functionally graded material plate-shell structures

Abstract

In this work, finite element formulations based on higher order shear deformation theories are used for the nonlinear static analysis of Functionally Graded Material plate-shell type structures. Linear and geometric nonlinear behaviour of the plate-shell type structures are considered. For the nonlinear analysis, the incremental equilibrium path is obtained using the updated Lagrangian procedure and Newton-Raphson incremental-iterative method, incorporating the automatic arc-length method for the cases of snap-through occurrence. The finite element models are based on a non-conforming triangular flat plate/shell element with 3 nodes and 8 or 11 degrees of freedom per node. The solutions of some illustrative plate-shell examples are performed, and the results are presented and discussed with numerical alternative models.