AI-Timoshenko: Automatedly Discovering Simplified Governing Equations for Applied Mechanics Problems From Simulated Data

Abstract

The simplified governing equations of applied mechanics play a pivotal role and were derived based on ingenious assumptions or hypotheses regarding the displacement fields for specific problems. In this paper, we introduce a data-driven method by the name AI-Timoshenko in honor of Timoshenko, father of applied solid mechanics, to automatically discover simplified governing equations for applied mechanics problems directly from discrete data simulated by the three-dimensional (3D) finite element method. The simplified governing equations are in variational form, which is compact and advantageous for data-driven discovery. AI-Timoshenko liberates applied mechanicians from burdensome labor, including assumptions, derivation, and trial and error. The simplified governing equations for Euler–Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems.