A co-rotational finite element for nonlinear analysis of hollow section steel frames accounting for local buckling via lumped damage mechanics

To reduce engineering costs, the search for more efficient materials and design concepts leads to slender structures. Consequently, the need for geometrically nonlinear analysis is becoming increasingly important. Besides, the phenomenon of local instability becomes more evident when dealing with structural components with hollow cross-sections composed of slender plates and shells. It is usual to employ elastoplastic shell finite element models for dealing with such problems, which leads to analyses with high computational costs. Therefore, this paper proposes a geometrical nonlinear beam finite element, developed for the nonlinear analysis of hollow section steel frames, accounting for local buckling. The finite element is locally formulated as the traditional linear Euler-Bernoulli beam element. A co-rotational description of motion is then employed to account for large displacements and rotations. The local buckling phenomenon is taken into account by a lumped damage model, which concentrates the effects at inelastic hinges. The inelastic hinge´s yield functions are defined in terms of the co-rotational nodal axial forces and bending moments, as well as in terms of damage variables. The local buckling of the hollow sections is accounted by the adopted damage evolution law. The inelastic rotations are governed by the normality rule and the evolution laws of the internal variables. A predictor-corrector algorithm is employed at element level, whereas the Newton-Raphson method solves the global nonlinear equilibrium equations. To assess the accuracy of the proposed model, the numerical results obtained in this study are compared against available numerical and experimental responses. The numerical results show good accuracy, which corroborates that the proposed model might be used in practical applications.