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A generalized nonlocal–gradient elasticity and neural network framework for multiscale analysis of functionally graded nanoplates
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DOI：10.1016/j.compstruc.2025.108056.png)
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Abstract
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A generalized nonlocal–gradient elasticity theory is developed for the multiscale modeling of functionally graded nanoplates resting on Pasternak elastic foundations. The formulation unifies nonlocal stress and strain gradient effects into a consistent higher-order continuum model, enabling accurate capture of size-dependent behavior in nanoscale structures. Governing equations are derived using higher-order shear deformation theory and Hamilton’s principle and solved analytically via the Navier method. To enhance computational efficiency and enable rapid parametric studies, an artificial neural network surrogate model is developed and trained on high-fidelity datasets generated from the analytical solutions. This hybridization of advanced continuum theory with machine learning provides a fast yet reliable tool for design-oriented studies, which is rarely addressed in previous works. The integrated framework is applied to investigate static bending and free vibration responses under various geometric, material, and foundation parameters, including nonlocal and material length scales. The results validate the accuracy and efficiency of the proposed approach, establishing new benchmark solutions for multiscale nanostructures and demonstrating its potential for extension to more complex configurations and future applications in micro- and nano-devices. The work therefore contributes a generalized, versatile, and efficient methodology for multiscale structural analysis of functionally graded nanostructures.
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