Geometric equations of arbitrarily spatial curved beam under large deformation

Zeng Sen, Chen Shaofeng and So

Abstract

Geometric equations of arbitrarily spatial curved beam include curvature-angle equation, angle-displacement equation and strain-displacement equation. Under the plane cross section assumption, curvature-angle relationship is given out through rigorous mathematical derivation, when arbitrarily spatial curved beam occurs large deformation (including large rotating angle). Based on the above, angle-displacement relationship can be gotten. And finally, Green strain tensor of arbitrarily spatial curved beam under large deformation is presented, which can consider warping. On the basis of the plane cross section assumption, in the case of large rotation and large curvature, the shear deformation of the cross section is caused not only by the torsion angle but also from the other two angles whose contribution is little.