An efficient two-node finite element formulation of multi-damaged beams including shear deformation and rotatory inertia

A computationally efficient beam finite element is presented for the static and dynamic analysis of frame structures with any number and location of concentrated damages, whose macroscopic effects are simulated with a set of longitudinal, rotational and transversal elastic springs at the position of each singularity. The proposed mathematical model exploits positive Dirac’s deltas in the corresponding flexibility functions of the beam elements, and allows also considering shear deformations and rotatory inertia. Such contributions may have a huge impact on the higher modes of vibration, as confirmed by the numerical examples.