A novel analysis-prediction approach for geometrically nonlinear problems using group method of data handling

• Published in: Computer methods in applied mechanics and engineering Vol. 354; pp. 506 - 526
• Main Authors: Nguyen, Tan N., Lee, Seunghye, Nguyen-Xuan, H., Lee, Jaehong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2019; Elsevier BV
• Subjects: Data analysis; Geometrically nonlinear problems; Group method of data handling; Isogeometric shell analysis; Machine learning; Nonlinear programming; Nonlinear response; Numerical analysis; Numerical prediction; Shear deformation; Shell theory; Solid mechanics; Time series forecasting problems; Isogeometric shell analysis; Geometrically nonlinear problems; Time series forecasting problems; Group method of data handling
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.05.052

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. •A novel analysis-prediction (ANP) approach for geometrically nonlinear problems of solid mechanics is for the first time proposed in this paper.•In the proposed approach: (1) A part of equilibrium path is traced by numerical analysis; (2) Data of this part is then used for training predictive network; (3) The rest of the equilibrium path is simply traced by pure prediction without using any analysis.•As the main advantage of the proposed approach, computational cost is significantly lower than that of the conventional approach based on pure numerical analysis.