Innovative deep energy method for piezoelectricity problems

Abstract

This work introduces a novel investigation into the use of the deep energy approach for addressing multi-physics issues often encountered in the field of piezoelectricity. The deep energy approach has become known as a robust numerical technique, demonstrating remarkable ability in handling complex nonlinearities and producing very precise results. This research aims to comprehensively investigate the roles and impacts of several network characteristics, including layers, neurons, and activation functions, on the accuracy of the approach. The reliability and novelty of our technique are shown by the successful resolution of three intricate 2D piezoelectric problems, exhibiting remarkable accuracy. This is particularly evident when using the tanh activation function, which outperforms other solutions. Furthermore, our technique is expanded to include the examination of piezoelectric composite plate actuators. This expansion yields results that closely align with well-established analytical solutions and empirical evidence, therefore showcasing the flexibility and effectiveness of our approach. This study not only unveils the deep energy method as a potential alternative to traditional numerical techniques for intricate multi-physics phenomena but also provides a comprehensive understanding of the role of activation functions. The tanh activation function has demonstrated superior precision across configurations, significantly enhancing model accuracy and flexibility for real-world engineering applications.