GEOMETRICALLY NONLINEAR THEORY OF TIMOSHENKO'S BEAM WITH FINITE ROTATIONS IN SPACE

Geometrically nonlinear theory of rods with shear deformations is developed. Particular attention is paid to investigate the coupling of finite rotations due to bending, twist and shearing. A finite rotation vector plays an important role in a formulation of the present problem. When the equilibrium equations and the associated boundary conditions are derived from the principle of virtual work, the magnitude of displacements, rotations, and strains is treated as finite one. The stress-strain relationships proposed herein differ slightly with the existing ones. They yield, however, the well-known and widely accepted constitutive equations expressed by the stress resultants and moments and the generalized strains. The accuracy of the present equilibrium equations is confirmed through comparisons with those obtained by the equilibrium method.