Analysis and Damage Identification of a Moderately Thick Cracked Beam Using an Interdependent Locking-Free Element

The Timoshenko interdependent interpolation element, based on the assumption of cubic interpolation for the transverse displacement and quadratic interpolation for the rotation, is developed for both the static and the dynamic problems. Next, the different behaviour of a beam due to the presence of a damaged zone is investigated and the problem of identifying diffused crack affecting a portion of the beam using natural frequencies is studied. The damaged zone can be completely taken into account by introducing only three parameters and, for the inverse problem, numerical optimization is applied to define their values.