A framework for developing a machine learning-based finite element model for structural analysis

Abstract

This paper presents a machine learning-based finite element construction method (MLBFE) to predict a precise strain field with minimal nodes. The method first establishes a standardized MLBFE model via the substructure concept and the static condensation method. Then, a training data collection method involving nodal displacements and strain fields, and considering (1) boundary continuity, (2) strain field continuity, and (3) the effect of rigid body motion, is developed. Furthermore, multivariate linear regression is adopted as the strain field prediction model for the MLBFE. The stiffness matrix and restoring forces of the MLBFE are calculated by employing the principle of virtual work and considering rigid body motion. Compared with common finite element models, the MLBFE enables refined structural simulation with fewer elements and nodes, reducing the number of degrees of freedom and computational costs. Moreover, the MLBFE exhibits high generalizability because it does not rely on specific structures or materials. This paper provides a detailed establishment of MLBFE-based planar elements and investigates the impact of the elemental settings on the computational accuracy of the elastic structural response. The ability of the MLBFE for nonlinear structural analysis is also verified.