Transient Dynamic Analysis of Piezoelectric Solids by the Spectral Integrated Neural Networks With Large Time Steps

Abstract

This study presents a novel neural network architecture called spectral integrated neural networks (SINNs), which combines physics-informed neural networks (PINNs) with time-spectral integration techniques to efficiently solve two- and three-dimensional dynamic piezoelectric problems. To avoid the numerical instability associated with time-differential operators, the coupled system of mechanical and electrical equilibrium equations is reformulated into a weak time-integral form. The temporal derivatives of displacement and voltage fields, treated as the primary unknown physical quantities, can be approximated utilizing fully connected neural networks (FCNNs). The displacements and electric potential are subsequently recovered through time-spectral integration of their respective derivatives. A physical-informed loss function is formulated by the weak time-integral type of the governing equations and boundary conditions, with the initial conditions embedded within the integral expressions. The proposed SINNs demonstrate superior stability and accuracy, even under large time steps conditions. Numerical verification is accomplished through three representative test cases of the method, and a comparison analysis is presented between the results obtained by the SINNs and those from the PINNs.

Keywords

dynamic / large time step / physics-informed neural networks / piezoelectric / spectral integrated neural networks

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