A second-generation finite element method for the analysis of multifunctional composite structures

The widespread use of composite materials in developing aeronautical structures brought out a lack of numerical models able to deal with the complex behavior of laminated structures. The classical theories of structures, on which the current finite element codes have been developed, are suitable for the analysis of metallic structures but lose accuracy when heterogeneous laminated materials are considered. The development of multifunctional composites that have sensing and morphing capabilities has made the scenario even more complex since active material and new physics must be considered. Classical models are even more inaccurate when the failure of composite structures is considered since they do not predict the complex stress fields that appear at the different material scales. The use of accurate three-dimensional models has only partially solved the problem since the computational costs limit their use to a small portion of the computational domain. Many attempts have been done in the literature to improve the actual models by enriching the kinematic approximation, one out of all is the model proposed by Reddy for the analysis of laminated plates, but most of them have found application only in academia. The introduction of the Carrera Unified Formulation, CUF, has been a game-changer in the development of higher-order kinematic models. The CUF offers a compact and unified formalism that can be used to derive any order kinematic model without the need to derive a new formulation and can be easily implemented in a computational code. CUF-based models have been extended to many multifield problems making this approach a unique tool for the design of multifunctional panels. The present work aims to show the main features of the Carrera Unified Formulation and the impact they can have on the analysis and design of complex multifunctional aerospace structures. Different kinematic models (equivalent single layer and layer-wise) will be compared to highlight the advantages offered by higher-order theories with respect to classical finite element models. Linear and non-linear applications will be considered. A fully coupled multi-physical model has been considered to predict the effects of different fields, typically piezo-electric and thermo-elastic, and hygro-elastic. The results show the capability of the present approach in terms of computational efficiency and accuracy.