Selection of element-wise shell kinematics using neural networks

This paper presents a novel approach to evaluate the role of non-classical effects, e.g., shear deformability, over a shell finite element model. Such an approach can identify the areas of a structural model in which the use of first-order shear deformation theories may lead to significant inaccuracies. Furthermore, it can indicate optimal distributions of structural theories over the finite element mesh to trade-off accuracy and computational costs. The proposed framework exploits the synergies among four methods, namely, the Carrera Unified Formulation (CUF), the Finite Element Method (FEM), the Node-Dependent Kinematics (NDK), and Neural Networks (NN). CUF generates the FE matrices for higher-order shell theories and provides numerical results feeding the NN for training. Via NDK, the shell theory is a property of the node; that is, a distribution of various shell theories over the FE mesh is attainable. The distributions of theories and the thickness of the structure are the inputs of multilayer NN to target natural frequencies. This work investigates the accuracy and cost-effectiveness of well-known NN. The results look promising as the NN requires a fraction of FE analyses for training, can evaluate the accuracy of FE models, and can incorporate physical features, e.g., the thickness ratio, that drives the complexity of the mathematical model. In other words, NN can inform on the FE modeling without the need to modify, rebuild, or rerun an FE model

Best Spatial Distributions of Shell Kinematics Over 2D Meshes for Free Vibration Analyses

This paper proposes a novel approach to build refined shell models. The focus is on the free vibrations of composite panels, and the node-dependent-kinematics is used to select shell theories node-wise. The methodology shown in this work can provide at least two sets of information. First, it optimizes the use of shell models by indicating the minimum number of refined models to use. Then, it highlights which areas of the structures are more vulnerable to non-classical effects. Moreover, by varying various problem features, e.g., boundary conditions, thickness, and stacking sequence, the influence of those parameters on the modelling strategy is evaluated. The results suggest the predominant influence of thickness and boundary conditions and the possibility to improve the quality of the solution via the proper use of the refinement strategy

Accuracy and Efficiency of Structural Theories for Free Vibration Analyses via Axiomatic/Asymptotic Method and Neural Networks

This paper presents novel approaches to investigate the accuracy and computational efficiency of 1D and 2D structural theories. The focus is on free vibration problems in metallic and composite structures. Refined theories are built via the Carrera Unified Formulation (CUF), and the influence of higher-order generalized variables is analysed via the Axiomatic/Asymptotic Approach (AAM). Best theory diagrams (BTD) are built by considering those models minimizing the computational cost and maximizing the accuracy. BTD can estimate the accuracy and efficiency of any structural models, including classical models and refined theories from literature. The construction of BTD can be a cumbersome task as multiple finite element (FE) problems are required. Machine learning through neural networks can significantly reduce such overhead. In other words, surrogate structural models are built using a limited number of FE analyses for training and having as input a structural theory and providing as output the natural frequencies without the need for finite element analyses. Finally, extensions to node-dependent kinematics (NDK) are presented for further optimization of the computational cost

On the use of neural networks to evaluate performances of shell models for composites

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