1,720,973 research outputs found
A Model-Reduction Technique Based on Perturbation Method for the Analysis of Variable-Stiffness Shells
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Asymptotic ps-FEM for nonlinear analysis of composite shells
Full text linkNonlinear shell analysis relies typically on Finite Element Methods (FEMs) and Iterative-Incremental Procedures (IIPs). These methodologies can become computationally expensive whenever high-fidelity meshes are required to capture very localized features or extremely nonlinear responses. Aim of this study is presenting a novel computational tool based on an efficient finite element formulation, the ps-FEM, and a rapid perturbation solution procedure, the Asymptotic-Numerical Method (ANM). The proposed approach adopts a polynomial space enrichment strategy, the p-refinement, and a mesh superposition technique, the s-refinement, to build numerical models with quasi-optimal accuracy-to-error ratios. The introduced asymptotic framework enhances the effectiveness of solving nonlinear problems compared to IIPs. A set of test cases and new benchmarks is presented to validate the tool and demonstrate its potential. The present results show that challenging problems involving bifurcations, jumps, snap-backs and anisotropy-induced localizations can be solved with excellent degree of accuracy and relatively small modeling/computational effort
A Numerical-Asymptotic Framework Based on the ps-FEM for the Analysis of Laminated Shells
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A framework based on physics-informed neural networks and extreme learning for the analysis of composite structures
Full text linkThis paper presents a novel approach for solving direct problems in linear elasticity involving plate and shell structures. The method relies upon a combination of Physics-Informed Neural Networks and Extreme Learning Machine. A subdomain decomposition method is proposed as a viable mean for studying structures composed by multiple plate/shell elements, as well as improving the solution in domains composed by one single element. Sensitivity studies are presented to gather insight into the effects of different network configurations and sets of hyperparameters. Within the framework presented here, direct problems can be solved with or without available sampled data. In addition, the approach can be extended to the solution of inverse problems. The results are compared with exact elasticity solutions and finite element calculations, illustrating the potential of the approach as an effective mean for addressing a wide class of problems in structural mechanics
A neural network-based approach for bending analysis of strain gradient nanoplates
Full text linkPurpose of this paper is the presentation of a novel Machine Learning (ML) technique for nanoscopic study of thin nanoplates. The second-order strain gradient theory is used to derive the governing equations and account for size effects. The ML framework is based on Physics-Informed Neural Networks (PINNs), a new concept of Artificial Neural Networks (ANNs) enriched with the mathematical model of the problem. Training of PINNs is performed using a highly efficient learning algorithm, known as Extreme Learning Machine (ELM). Two applications of this ANNs-based method are illustrated: solution of the Partial Differential Equations (PDEs) modeling the flexural response of thin nanoplates (direct problem), and identification of the length scale parameter of the nanoplate mathematical model with the aid of measurement data (inverse problem). Comparison with analytical and Finite Element (FE) solutions demonstrate the accuracy and efficiency of this ML framework as meshfree solver of high-order PDEs. The stability and reliability of the present method are verified through parameter studies on hyperparameters, network architectures, data noise and training initializations. The results presented give evidence of the effectiveness and robustness of this new ML approach for solving both direct and inverse nanoplate problems
Analysis of Thin-Walled Composite Structures Using Physics-Informed Neural Networks and Extreme Learning
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