Global-local modeling of composite structures through node-dependent kinematics and convolutional neural networks

The widespread employment of composite materials highlights the importance of accurately describing their mechanical behavior, which is strictly tied to both their heterogeneous properties and the structural features of the analyzed problem. With the developments in the field of numerical modeling, a wide variety of advanced theories are now available. Focusing on composite plates and shells, 2D refined models can adequately depict stress and strain fields along the thickness of the structures, providing results comparable to those obtained via 3D solutions, but at a lower cost. This paper exploits the Node-Dependent Kinematics (NDK) approach based on the Carrera Unified Formulation (CUF) to assign structural theories to each node of a finite element model. NDK is a global-local approach allowing the use of refined models only where necessary. The choice of the proper distribution of theories along the model is not trivial and may require considerable computational costs. The present paper proposes a strategy based on machine learning to tackle such a problem. Convolutional Neural Networks (CNN) are used to find the best distributions of theories, i.e., to define the global and local models for a given problem. The localized refinement is chosen to minimize the computational cost of the model and maximize the accuracy. The numerical examples include static and free vibration analyses, and comparisons with benchmark solutions are provided.