Anisotropic thin-walled beams with closed cross-sectional contours

A complete theory of free torsion and bending of anisotropic thin-walled beams with closed cross-sectional contours is developed using the stress formulation. In contrast to a displacement formulation that is traditionally used for this purpose, the stress formulation does not require the introduction of assumptions concerning the form of the warping function. The advantage of the stress formulation is the exact satisfaction of the equilibrium equations, which provides more accurate results for beams whose stiffness coefficients depend on the contour coordinate, for example, beams stiffened with stringers. Approximate compatibility conditions obtained with the aid of Castigliano's theorem describe all possible types of coupling effects and give explicit expressions for displacements of a beam with an arbitrary cross-sectional contour and material anisotropy. Theoretical results are compared to experimental data, and fair agreement is found.