Analysis-Aware Modelling of Spacial Curve for Isogeometric Analysis of Timoshenko Beam

摘要

Geometric fitting based on discrete points to establish curve structures is an important problem in numerical modeling. The purpose of this paper is to investigate the geometric fitting method for curved beam structure from points, and to get high-quality parametric model for isogeometric analysis. A Timoshenko beam element is established for an initially curved spacial beam with arbitrary curvature. The approximation and interpolation methods to get parametric models of curves from given points are examined, and three strategies of parameterization, meaning the equally spaced method, the chord length method and the centripetal method are considered. The influences of the different geometric approximation algorithms on the precision of isogeometric analysis are examined. The static analysis and the modal analysis with the established parametric models are carried out. Three examples with different complexities, the quarter arc curved beam, the Tschirnhausen beam and the Archimedes spiral beam are examined. The results show that for the geometric approximation the interpolation method performs good and maintains high precision. The fitting algorithms are able to provide parametric models for isogeometric analysis of spacial beam with Timoshenko model. The equally spaced method and centripetal method perform better than the chord length method for the algorithm to carry out the parameterization for the sampling points.