Data-driven approach for a one-dimensional thin-walled beam analysis

Abstract

This study presents a data-driven approach for developing a one-dimensional thin-walled beam model. In order to analyze complicated deformations occurring in a thin-walled beam by a beam theory, it is important to identify core cross-sectional deformations that are the bases for the one-dimensional beam analysis. In this study, we derive core cross-sectional deformations through data processing using the shell-based static analysis results of a thin-walled beam. We perform a principal component analysis for the data processing, in which the desired core cross-sectional deformations are obtained without specific assumptions pertaining to the behavior of the beam’s sectional deformations. Then, the core cross-sectional deformations can be obtained in explicit functional forms (shape functions) to facilitate the subsequent one-dimensional higher-order beam analysis. Important issues related to the establishment of a well-defined dataset are addressed. Using the data-driven shape functions, a series of static, vibration and buckling analyses are performed for various thin-walled beams. We demonstrate by numerical examples that the present data-driven results agree well with those obtained by shell analysis results. While the shape functions are obtained only from the static analysis results, the vibration and buckling analyses using them were also found to be sufficiently accurate.