Non uniform warping for beams: Theory and numerical applications - El Fatmi, Rached (European Journal of Computational Mechanics, 2008)
A non-uniform warping beam theory including the effects of torsion and shear forces is presented. Based on a displacement model using three warping parameters associated to the three St Venant warping functions corresponding to torsion and shear forces, this theory is free from the classical assumptions on the warpings or on the shears, and valid for any kind of homogeneous elastic and isotropic cross-section. This general theory is applied to analyze, for a representative set of cross-sections, the elastic behavior of cantilever beams subjected to torsion or shear-bending. Numerical results are given for the one-dimensional structural behavior and the three-dimensional stresses distributions; for the stresses in the critical region of the built-in section, comparisons with three-dimensional finite elements computations are presented. The study clearly shows when the effect of the restrained warping is localized or not.