A penalty-based multifiber finite element model for coupled bending and torsional-warping analysis of composite beams

Abstract

A new multifiber finite element model is derived for the analysis of laminated composite and sandwich beams under combined transverse and torsional loads. The proposed model decouples the problem of 3D analysis of composite beams into 2D cross-sectional analysis and 1D beam analysis. The effects of transverse shear deformations and restrained warping due to torsion are included in the formulation. The interlaminar continuity requirements of the transverse shear stresses due to bending and torsion at the interfaces between layers are satisfied in the presented formulation. The boundary requirements of shear stresses on the exterior surfaces of the beam are also fulfilled. In the derivation of the proposed model, a 2D finite element based on penalty approach is firstly developed for the approximation of the warping function over the cross-section. Then, a 1D multifiber finite element model is derived for the approximation of unknown generalized displacement of beams. Accuracy of the present multifiber finite element model is evaluated by comparing the present results with numerical and analytical results available in open literature, and 3D finite element solutions. The comparisons show that the presented formulation of this study gives quasi-3D results with a lower computational cost.