On a geometrically exact curved/twisted beam theory under rigid crosssection assumption
Abstract
A geometrically exact curved/ twisted beam theory, that assumes that the beam crosssection remains rigid, is reexamined and extended using orthonormal frames of reference starting from a 3D beam theory. The relevant engineering strain measures with an initial curvature correction term at any material point on the current beam crosssection, that are conjugate to the first PiolaKirchhoff stresses, are obtained through the deformation gradient tensor of the current beam configuration relative to the initially curved beam configuration. The stress resultant and couple are defined in the classical sense and the reduced strains are obtained from the threedimensional beam model, which are the same as obtained from the reduced differential equations of motion. The reduced differential equations of motion are also reexamined for the initially curved/twisted beams. The corresponding equations of motion include additional inertia terms as compared to previous studies. The linear and linearized nonlinear constitutive relations with couplings are considered for the engineering strain and stress conjugate pair at the threedimensional beam level. The crosssection elasticity constants corresponding to the reduced constitutive relations are obtained with the initial curvature correction term. Along with the beam theory, some basic concepts associated with finite rotations are also summarized in a manner that is easy to understand.
 Publication:

Computational Mechanics
 Pub Date:
 2003
 DOI:
 10.1007/s0046600304218
 Bibcode:
 2003CompM..30..428K