A mixed 3D corotational beam with cross-section warping for the analysis of damaging structures under large displacements

This paper presents the formulation of a tri-dimensional (3D) beam-column finite element (FE) with cross-section warping, based on a corotational approach for the analysis of damaging structures including material and geometric nonlinear effects. The model derives from an extended Hu–Washizu formulation and is an enhancement of a previously proposed beam FE formulation originally adopted for steel and reinforced concreted structures under linear geometry. The warping of the cross-sections is described by introducing additional degrees of freedom to those standard for a classic 3D beam FE and interpolating the corresponding displacement field with polynomial shape functions. The effects of large displacements are modeled through a corotational approach also including the axial-torsion interaction due to the Wagner effect. A 3D plastic-damage model is introduced to reproduce the degrading phenomena typical of many structural elements. This is used to simulate both damage occurring in ductile materials under large deformations and the non-symmetric tensile-compressive damage of brittle-like materials. The paper concludes with some numerical studies to validate the proposed FE and investigate the performances of the adopted corotational approach.