Crack modeling and identification in curved beams using differential evolution

In this study, damage identification in planar curved beams is studied. Transfer matrix method is used to obtain the exact solution to the free vibration problems of curved beams. Crack is modeled using the concepts of linear elastic fracture mechanics. Due to the coupling between the axial force and bending moment in curved beams, the transition condition, which is written at the crack location on the beam axis, is affected by the position of the crack on the cross-section. The difference between the crack being on the top, or the bottom of the cross-section is emphasized by presenting many numerical examples. It is concluded that, in addition to locating the crack on the beam axis, this coupling effect helps to identify the crack location on the cross-section. Differential evolution method is utilized for the identification problem. Many numerical examples related to the crack identification in curved beams including cracks at different positions on their axis, and also different positions on their cross-sections are presented. In addition, a set of experimental results existing in the literature are used for crack identification purposes, and it is seen that the presented identification procedure yields very accurate results.