A higher order thin-walled beam model including warping and shear modes

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 is 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 obtained without prior assumptions, being associated with null eigenvalues, which requires an adequate computation of a Jordan chain, whereas the higher order modes correspond to the non-null eigenvalues, which allows to measure 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.

► A higher order model for thin-walled structures with any section geometry is proposed.
► The model relies on deformation modes obtained by a quadratic eigenvalue problem.
► The model reproduces classic solutions through the generalized eigenvectors.
► The set of non-null eigenvalues define the higher order deformation modes.
► Orthogonal displacement modes are obtained from uncoupled deformation modes.