Generalized variational principle on nonlinear theory of naturally curved and twisted beams

Abstract

The nonlinear behavior for naturally curved and twisted beams undergoing large displacements and rotations but small strains has been investigated in this paper. An incomplete generalized variational functional for the beams with complete constrained boundaries at two ends is established by means of the Lagrange multiplier method. A set of equilibrium equations, which takes into account the effects of transverse shear deformations as well as torsion-related warping, has been derived from the stationary conditions of the functional. The various elastic couplings of bending-twisting and/or extension-twisting are also included in this analysis. The present theory can also be easily extended to other various incomplete constrained boundaries. In case of small displacement, the equilibrium equations obtained by the present theory reduce to the well-known results in literature.