Co plate element for global/local analysis of multilayered composites, based on a 3D zig-zag model and strain energy updating

Laminated and sandwich composites, which find applications as primary structures where weight saving is crucial, absorb energy through a variety of local failure modes. Since this damage accumulation could adversely affect the structural performances and the service life, an intensive research activity has been oriented towards suitable computational models. To support the optimization processes within the damage-tolerant design approach, low computational cost, refined zig-zag models and postprocessing procedures enabling the prediction of interlaminar stresses with the desired accuracy have been recently developed. In this paper, a 3D zig-zag plate model based upon the kinematics and nodal degrees of freedom of classical plate models, corresponding finite element and related postprocessing procedures are developed to efficiently and accurately predict ply level stresses in laminated and sandwich composites. To overcome the C2 continuity requirement for shape functions which results from enforcement of the continuity of interlaminar shear and normal stresses and of the transverse normal stress gradient at the layer interfaces, the higher-order energy contributions brought about by this model are incorporated through strain energy updating into a Co parent eight-node plate element based on the first-order shear deformation plate theory. This energy updating is made possible by the coinciding functional degrees of freedom of the two models. A postprocessing iterative procedure is developed to obtain the suited interdependent interpolation of displacement and stresses required for capturing interlaminar stresses at the ply level with the desired accuracy. The accuracy of the present element is assessed by comparing its predictions with the stress fields of the elasticity solution for a very thick, simply supported sandwich beam with laminated faces, loaded by a sinusoidal heap loading. In addition, a comparison is made with the predictions of a mixed solid element recently developed by the author, in terms of accuracy and costs by a discrete-layer model. To test the present element in a situation of practical use, the damage of stiffened panels undergoing impact loads is evaluated by different criteria and compared with that detected by ultrasonic inspection, the exact elasticity solution not being available in this case. The present element appears cost-effective and able to accurately predict the interlaminar stresses also when composites are thick, and suitable for predicting impact-induced damage.