Thin-Walled Structures: Warping Modes

Abstract

A thin-walled beam model that considers higher order effects is presented in this paper. The beam displacement field is approximated through a linear combination of products between a set of linear independent functions, which are defined over the beam cross section, and the associated amplitudes that are only dependent on the beam axis. The beam model governing equations are then obtained through the integration over the cross section of the corresponding elasticity equations weighted by the cross section approximation functions. A set of uncoupled beam deformation modes are obtained from a non linear eigenvalue problem that stems directly from the general solution of the differential homogeneous equilibrium equations. The classic deformation modes are naturally obtained, being associated with a null eigenvalue, which requires an adequate computation of a Jordan chain, whereas the higher order modes correspond to the non null eigenvalues, which allows the measurement of the mode decay along the beam axis. A numerical example is presented in order to verify the model capabilities to simulate the non classic effects associated with thin-walled beam higher order deformation modes.