A comparison of displacement-based Timoshenko multi-fiber beams finite element formulations and elasto-plastic applications

Various formulations of displacement-based Timoshenko multi-fiber beams are com- pared in this article.After a short literature review, the presentation of the shape functions leading to the stiffness matrices and the consistent nodal forces relative to each formu- lation are presented and their performances are studied using elastic or elastic perfectly plastic constitutive laws and simple to complex static loadings. The advantages and disadvantages of each formulation are highlighted and general conclusions are drawn on the use of displacement-based Timoshenko multi-fiber beams in engineering. An innovative solution is finally proposed to improve the performance for the case of axial- bending interactions.