On the mechanics of beams and shafts with cracks: A standard and generic approach

A generic methodology to deal with the mechanics of beams and shafts with cracks is presented. The elastic energy of the system under static loading is written in a comprehensive manner to remarkably reduce the 3D computations indispensable to the identification of the crack breathing mechanism. With a new reformulation of the problem, the breathing mechanism identification is distilled down to the computation of a dimensionless function that gives a fine and precise description of the system flexibility evolution when the crack breathes. This breathing function is exclusively inherent to the crack geometry and completely independent of the 3D model parameters which makes the approach more universal and could be applied straightforward to similar problems. This standard and generic methodology is completed by a detailed description of the technique of construction of a Cracked Beam Finite Element. Moreover, we give a nonlinear fitting formula of the identified function that all the process of identification could be skipped when a cracked transverse section is to be inserted in a beam-like model of a cracked shaft. A validation of the approach under static loading is given for a cantilever beam with one, then two cracked transverse sections. We also show, for a simple cracked shaft, common features of its vibrational behavior.