Nonlinear dynamic analysis of thin-walled structures adopting a mixed beam finite element model with out-of-plane cross-section warping

This paper focuses on the dynamic response of thin-walled structural elements. A mixed three-dimensional (3D) beam formulation is adopted, that includes the effect of inertia forces under dynamic loading conditions and accounts for out-of-plane cross-section warping. This is introduced by adding a specific displacement field to those due to rigid body motions, and is interpolated in the element volume with the definition of specific shape functions. The element governing equations are derived by expressing the Lagrangian functional in terms of four independent fields, i.e. the material rigid displacements, the strains and stresses and the additional warping displacement field. Four Lagrange’s equations of motion result, corresponding to the element compatibility condition enforced in weak form, the material constitutive law, and two sets of element equilibrium conditions associated to the rigid and warping displacements, respectively. The FE model has been implemented in a standard numerical code and used to investigate the effect of cross-section warping on the dynamic response of thin-walled structures. A T-shape beam is analyzed by performing modal decomposition and time-history analyses under linear elastic and nonlinear constitutive behavior.