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A novel analysis-prediction approach for geometrically nonlinear problems using group method of data handling. (English) Zbl 1441.74116
Summary: A novel analysis-prediction (ANP) approach for geometrically nonlinear problems of solid mechanics is for the first time proposed in this paper. The key concept of this approach is: (1) A part of equilibrium path is traced by numerical analysis; (2) Data of this part is then used for training predictive network; (3) Applying the trained network, the rest of the equilibrium path is simply traced by pure prediction without using any analysis. As an illustration for ANP approach, the analysis package is in this study established based on isogeometric shell analysis using the first-order shear deformation shell theory (FSDT). As the main advantage of the proposed approach, computational cost is significantly lower than that of the conventional approach based on pure numerical analysis. In addition, the predictive networks are built via group method of data handling (GMDH) known as a self-organizing deep learning method for time series forecasting problems without requirement of big data. Some numerical examples are provided to confirm the high accuracy and efficiency of the proposed approach. The approach not only could be applied to a wide range of computational mechanics problems in which nonlinear response occurs but also to other computational engineering fields.

74K25 Shells
65D07 Numerical computation using splines
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Full Text: DOI
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