Nonlinear in-plane warping deformation in elastically coupled open thin-walled beams

A study of the nonlinear in-plane warping in open thin-walled composite beams is presented. The analysis is based on a generic nonlinear formulation of the governing equations for the in-plane deformation which are solved by a numerical minimization procedure. The minimization process employs energy considerations to determine the in-plane-warping deformation of generic elastically coupled orthotropic beams. The study shows that open thin-walled orthotropic composite beams are much more sensitive to the in-plane-warping deformation than similar isotropic beams. In addition, it is shown that the in-plane warping poses an upper limit to the possible applied load. To extend the applicability of the present formulation, a discrete formulation of the governing equations for generic open geometries is also presented. The results are accompanied by an analytic approximation for open rectangular cross-section that clarifies the nonlinear nature of the problem.