https://doi.org/10.1140/epjp/s13360-025-06704-3
Regular Article (incl. Technical & Progress Reports)
Physics-informed modeling and deep learning-driven optimization of GO–CNT hybrid nanocomposites-reinforced car hood doors under nonlinear dynamic loading
1
Geely Automotive Institute, Hangzhou Vocational & Technical College, 310018, Hangzhou, China
2
FAW Audi Sales Company, Ltd., 310000, Hangzhou, China
3
Department of Computer Engineering, College of Computer Science, King Khalid University, 61421, Abha, Saudi Arabia
Received:
21
May
2025
Accepted:
30
July
2025
Published online:
6
September
2025
This work presents a comprehensive nonlinear dynamic analysis of moderately thick car hood doors reinforced with graphene oxide–carbon nanotube (GO–CNT) as the hybrid nanocomposites. The structural configuration is modeled as a doubly car hood door, and geometric nonlinearities are captured using the sinusoidal shear deformation theory (SSDT) integrated with von Kármán kinematics. The governing nonlinear partial differential equations are systematically derived via Airy’s stress function and discretized using a coupled Galerkin scheme. A time-domain solution is achieved through a fourth-order Runge–Kutta method. To address computational challenges and facilitate real-time performance prediction, a deep neural network (DNN) surrogate model is developed. The predictive accuracy and efficiency of various optimizers, including SGDM, RMSProp, and Adam, are benchmarked, with the Adam algorithm achieving optimal generalization for capturing complex nonlinear behavior. In this work, while the training time for the DNN models can vary depending on the architecture and dataset size (typically ranging from minutes to hours), once trained, the DNNs provide significant speed-ups during prediction, ranging from 
faster than traditional numerical simulations. The results highlight the significant enhancement in dynamic stability and energy absorption capacity due to the synergistic reinforcement effects of GO and CNTs. The integration of nanomechanics, nonlinear modeling, and machine learning offers a novel and efficient framework for optimizing advanced automotive structures subjected to impact and vibration, contributing to physics-based lightweight and high-performance material design.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
