A quasi-3D finite element model for the analysis of thin-walled beams under axial–flexural–torsional loads. (July 2021) - Lezgy-Nazargah, M.; Vidal, P.; Polit, O.
Abstract: A quasi-3D finite element model (FEM) with a low computational cost is presented for coupled bending and torsional–warping analysis of thin-walled beams. The presented FEM converts the problem of 3D analysis of thin-walled beams into separated 2D cross-sectional and 1D modeling. The warping function over the cross-section of the thin-walled beams is firstly approximated, via a 2D FEM. Then, a 1D FEM is developed for computing the axial variations of the displacement field variables. For describing the kinematic of the thin-walled beam due to axial extension and bending, the concept of hypothetical equivalent layered composite cross-section (HELCS) is employed. Using the HELCS, the non-classical effects like transverse shear flexibility can be easily incorporated into the formulation. A refined sinus theory is employed to describe the displacement fields of the equivalent layered cross-section. In contrast to other refined models of literature, the present model does not require the calculation of any geometric, torsional and warping constants. For validation of the proposed model, comparisons are made with the results of 2D/3D finite element analysis as well as the numerical and analytical results reported by other researchers. The proposed model not only gives accurate results but also reduces the number of involved degrees-of-freedom (DOFs) significantly. Considering the effects of the restrained warping due to torsion, no need to use the shear correction factor, satisfaction of zero-conditions of shear stresses on the exterior surfaces of beams are other advantages of the proposed FEM. Highlights: A new FEM is developed for flexural–torsional analysis of thin-walled beams. The formulation is based on the concept of equivalent layered composite section. The shear strains due to bending are modeled using a Cosine shape function. The proposed FEM reduces the number of degrees-of-freedom significantly.