A higher-order beam model for tubes

Abstract

Abstract A refined beam model is proposed for tubes to improve the prediction of the transverse shear deformation and study its influence on the mechanical response of tubes. The current beam model adopts a Laurent series expansion form for the displacement field, instead of the conventional Taylor series expansion form used by most higher-order beam models. This new form can capture the geometric features of tubes very well and, more importantly, shear stress can be vanished readily on the inner and outer surfaces. Both a generalized theory and a simplified third-order model are presented. It is found that the transverse shear stress distribution of the third-order model is very close to that predicted by the Saint-Venant solution. Moreover, the static bending, wave propagation, and free vibration problems are studied, whose results are also compared with those obtained from other beam models and three-dimensional elasticity solutions to show the advantage of the current model.