Enhanced beam formulations with cross-section warping under large displacements

This work investigates the capabilities of two different approaches for the analysis of thin-walled structures, both based on enriched beam theories that include out-of-plane cross-section warping, being the in-plane deformations neglected. First approach relies on a three-dimensional beam finite element based on a four-field mixed formulation, where cross-section warping displacement is introduced as additional independent field to the standard rigid-body displacements, strains, and stresses and is interpolated with the definition of specific shape functions: along the element axis and over the general cross-section. Geometric nonlinearity is included through a corotational approach that considers the coupling between axial and torsional stress/strain components, known as Wagner effect. As opposed to the first approach, a simpler but coarse descriptor of warping displacement field is adopted in the second approach, assuming a priori the warping profile over the cross-section. By adopting nonlinear hyperelastic relations, generalized cross-section constitutive responses are portrayed, accounting for Wagner term. Geometric nonlinearity is also included. In this case, the nonlinear equilibrium equations of the enriched beam model are solved through a finite difference technique. For selected specimens, modal decompositions and step-by-step incremental analyses are conducted under small and large displacements, comparing the results obtained with both models with analytic solutions and numerical outcomes. Advantages and disadvantages of each approach are discussed, aiming at supplying the reliability ranges of the two models and depict new potential research lines based on a suitable ‘combination’ of the relevant formulations.