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

Elastoplastic analysis of compact and thin-walled structures using classical and refined beam finite element models

The paper presents results on the elastoplastic analysis of compact and thin-walled structures via refined beam models. The application of Carrera Unified Formulation (CUF) to perform elastoplastic analysis of isotropic beam structures is discussed. Particular attention is paid to the evaluation of local effects and cross-sectional distortions. CUF allows formulation of the kinematics of a one-dimensional (1D) structure by employing a generalized expansion of primary variables by arbitrary cross-section functions. Two types of cross-section expansion functions, TE (Taylor expansion) and LE (Lagrange expansion), are used to model the structure. The isotropically work-hardening von Mises constitutive model is incorporated to account for material nonlinearity. A Newton–Raphson iteration scheme is used to solve the system of nonlinear algebraic equations. Numerical results for compact and thin-walled beam members in plastic regime are presented with displacement profiles and beam deformed configurations along with stress contour plots. The results are compared against classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory, reference solutions from literature, and three-dimensional (3D) solid finite element models. The results highlight: (1) the capability of the present refined beam models to describe the elastoplastic behavior of compact and thin-walled structures with 3D-like accuracy; (2) that local effects and severe cross-sectional distortions can be detected; (3) the computational cost of the present modeling approach is significantly lower than shell and solid model ones

Who needs refined structural theories?

This paper discusses the question posed in the title and available options for the structural analysis of metallic and composite structures concerning the choice of 1D, 2D, and 3D theories. The focus is on the proper modeling of various types of mechanical behaviors and the associated solution’s efficiency. The necessity and convenience of developing higher‐order structural theories are discussed as compared to 3D models. Multiple problems are considered, including linear and nonlinear analyses and static and dynamic settings. Some possible guidelines on the proper selection of a model are outlined, and quantitative estimations on the accuracy are provided. It is demonstrated that the possibility of incorporating higher‐order effects in 1D and 2D models continues to remain attractive in many structural engineering problems to alleviate the computational burdens of 3D analyses

CUF-based Multiscale Analysis of Failure of Composite Laminates

The detection of failure onset and progression in composites requires the proper modeling of various mechanical behaviors at various scales. Furthermore, the necessity of virtual models of large structures and the nonlinear nature of failure demand computational efficiency without accuracy penalties. Over the last years, a set of modeling strategies based on refined structural theories has been developed via the Carrera Unified Formulation (CUF). Such developments range from Equivalent Single Layer (ESL) and Layer-Wise (LW) models for the macro- and mesoscale to the component-wise modeling of microscale. The computational efficiency and accuracy stem from the use of 1D or 2D models, node-dependent kinematics (NDK) and global-local strategies providing the complete 3D stress state necessary to capture failure in critical locations such as free-edges. The coupling with well-known models for micromechanics, progressive failure (including non-local methodologies based on peridynamics) and multiscale analyses led to promising outcomes with multifold reductions of computational times

Elastoplastic and progressive failure analysis of fiber-reinforced composites via an efficient nonlinear microscale model

This paper presents numerical results concerning the nonlinear and failure analysis of fiber-reinforced composites. The micromechanical framework exploits a class of refined 1D models based on the Carrera Unified Formulation (CUF) having a variable kinematic description. The recently developed CUF micromechanics is a framework for the nonlinear modeling and exploits the ability of the CUF to predict accurate 3D stress fields with reduced computational overheads. The present formulation features the von Mises J2 theory for the pre-peak nonlinearity observed in matrix constituents, and the crack-band theory to capture the damage progression. Numerical examples and comparisons with results from literature assess the accuracy and efficiency of the proposed framework. The paper highlights the applicability of CUF models as an efficient micromechanical platform for nonlinear and progressive failure analysis for fiber-reinforced composites with potentially major advantages in the perspective of multiscale modeling

Progressive damage analysis of composite laminates subjected to low-velocity impact using 2D layer-wise structural models

The present work deals with the progressive damage analysis of composite laminates subjected to low-velocity impact. We develop a numerical model using higher-order structural theories based on the Carrera Unified Formulation (CUF) with Lagrange polynomials and resulting in a 2D refined layer-wise model. To model damage, we use a combination of the continuum damage-based CODAM2 intralaminar damage model to account for fibre and matrix damage within the ply, and cohesive elements to account for delamination between successive composite plies. We carry out numerical assessments for the case of a linear elastic composite plate subjected to impact, to compare the current framework with standard approaches based on 3D finite element (FE) analysis. We, then, consider the elastoplastic analysis of a bimetallic laminated plate to compare the performance of the proposed layer-wise model and 3D-FE approaches, for the case of nonlinear impact analysis. The final assessment considers progressive damage due to low-velocity impact, and the results are compared with available literature data. The numerical predictions show a good correlation with reference experimental and simulation results, thus validating the current framework for impact analysis of composite structures. Comparisons of the proposed layer-wise structural models with those based on 3D finite elements demonstrate the improved computational efficiency of the CUF models in terms of model size and analysis time