Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

Isogeometric analysis (IGA) is known to show advanced features compared to traditional finite element approaches. Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functional grading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward a deep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complex IGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trained using the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationship between the outputs and the inputs is constructed using machine learning so that the displacements can be directly estimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA and obtain the displacement responses for different loads and gradient indexes. Results show that the recognition error is low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA for modeling the geometrically nonlinear bending behavior of FG plates.