Abstract
This paper presents a novel methodology to assess the accuracy of shell finite elements via neural networks. The proposed framework exploits the synergies among three well-established methods, namely, the Carrera Unified Formulation (CUF), the Finite Element Method (FE), and neural networks (NN). CUF generates the governing equations for any-order shell theories based on polynomial expansions over the thickness. FE provides numerical results feeding the NN for training. Multilayer NN have the generalized displacement variables, and the thickness ratio as inputs, and the target is the maximum transverse displacement. This work investigates the minimum requirements for the NN concerning the number of neurons and hidden layers, and the size of the training set. The results look promising as the NN requires a fraction of FE analyses for training, can evaluate the accuracy of any-order model, and can incorporate physical features, e.g., the thickness ratio, that drive the complexity of the mathematical model. In other words, NN can trigger fast informed decision-making on the structural model to use and the influence of design parameters without the need of modifying, rebuild, or rerun an FE model.
Highlights
Shell finite elements (FE) are standard options to model two-dimensional (2D) curved structures
This paper presents a novel methodology to assess the accuracy of shell finite elements via neural networks
The proposed framework exploits the synergies among three well-established methods, namely, the Carrera Unified Formulation (CUF), the Finite Element Method (FE), and neural networks (NN)
Summary
Shell finite elements (FE) are standard options to model two-dimensional (2D) curved structures. Shell FE have the assumptions of the classical theories [1,2,3] leading to up to six degrees of freedom (DOF) per node Such assumptions may be too restrictive in the case of composite structures in which the high transverse deformability and the transverse anisotropy require the proper modeling of shear and normal transverse stresses, and variations of the displacement field at the interface between two layers with different mechanical properties, i.e., the Zig-Zag effect [4]. Regardless of the solution scheme, the most important strategies to enhance the capabilities of shell models are either asymptotic or axiomatic The former exploit asymptotic expansions of most relevant parameter, e.g., the thickness ratio, to build models with a priori known accuracy as compared to 3D models [38,39,40,41].
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