Large Displacement Analysis of Naturally Curved and Twisted Beams

This paper presents an efficient procedure for analyzing naturally curved and twisted beams undergoing large displacements and rotations but small strains. Special care is taken to accurately model the structural behavior of the beam: shearing deformations as well as torsion-related warping are taken into account. The various elastic coupling (e. g. , bending-twisting or extention-twisting) that can arise in composite beams are also modeled in a rational fashion. The equations are derived in curvilinear material coordinates, and Euler angles are used to represent the arbitrarily large rotations. The strain energy in the beam is reduced to a quadratic expression by means of a quasilinearization procedure. This expression of the strain energy is the basis for a finite-element analysis of the structure, and standard iteration techniques are used to obtain nonlinear solutions to the problem