A data-driven procedure for one-dimensional dynamic analysis of thin-walled beams with arbitrary cross-sections

Abstract

This paper develops a one-dimensional dynamic model for thin-walled beams with arbitrary complex cross-sections in a data-driven way. In order to consider complicated deformations in the framework of a beam theory, a universal node system is first created to fit the deformed shape of a thin-walled cross-section, whether prismatic or curved, with or without symmetry. This helps to reduce the three-dimensional displacement field of the thin-walled beam to one dimension, and results in a preliminary higher-order beam model with limited precision loss. For the purpose of largely condense DOFs of the new model, a data-driven approach is proposed to identify cross-section deformation modes through the principal component analysis of free vibration deformation data of an unconstrained thin-walled beam. As a result, a compact set of core deformation modes are obtained and selected to update the preliminary model, leading to the refined higher-order beam model of high accuracy and efficiency. Examples are presented to illustrate the concrete implementation and check the effects of data-related controlling parameters of the proposed procedure. We also verify through numerical examples that the proposed model agrees well with plate/shell and other beam theories, and has remarkable advantages in physical interpretation, modeling simplicity and computation efficiency.