An accurate coarse mesh-based analysis approach for nonlinear bending and post-buckling problems of plates and shells utilizing recurrent neural networks with Bayesian regularization back-propagation algorithm

The fineness of element meshes strongly affects the accuracy and cost of solutions in computational mechanics. In this regards, an accurate coarse mesh-based analysis approach (CMA) for nonlinear bending and post-buckling problems of plates and shells utilizing nonlinear auto-regressive exogenous Bayesian neural networks (NARX-BNNs) is first proposed in this work. The CMA approach comprises two pivotal stages. Initially, a coarse mesh-based post-buckling isogeometric analysis is executed, yielding a preliminary equilibrium path quickly. The path includes a series of initial displacements and a series of initial loads. Subsequently, in the second stage, two initial series serve as the inputs for the trained networks to accurately predict displacements and loads. Finally, the resulting network outputs are a series of accurate displacements and a series of accurate loads leading to the attainment of an accurate equilibrium path. NARX-BNN is known as a recurrent neural network model utilizing Bayesian regularization back-propagation algorithm which can result in good generalization for difficult or noisy data sets. The post-buckling analyses were based on isogeometric analysis (IGA) and first-order shear deformation shell theory (FSDT) utilizing the von Karman assumption. Instabilities of shells considered in this work were snap-through, softening–hardening, and snap-back. High generalization, fast training and exactness of the proposed data-driven models were confirmed via solving five problems. The power, wide application, high exactness and effectiveness of the CMA approach for nonlinear bending and post-buckling problems of plates and shells were demonstrated. The concept of CMA approach can be applied and extended to a great number of problems in computational mechanics which uses element meshes in the numerical procedure to save time and labor. • A CMA approach for nonlinear bending and post-buckling problems was proposed • High generalization, fast training and exactness of the proposed model were confirmed • The power, wide application and effectiveness of the CMA approach were demonstrated • Concept of CMA approach can be extended to many problems in Computational Mechanics