Elastic beam finite element with an arbitrary number of transverse cracks

This paper formulates the finite element of a beam with an arbitrary number of transverse cracks. The derivations are based on a simplified computational model, where each crack is replaced by a corresponding linear rotational spring, connecting two adjacent elastic parts. The stiffness and geometrical stiffness matrices thus take into account the effect of flexural bending deformation caused by the presence of the cracks.The expressions for calculating the coefficients of stiffness and geometrical stiffness matrices, as well as the load vector of the element, are presented in closed forms.Since the corresponding interpolation functions were implemented in the derivations, transverse displacements within the finite element can also be obtained.Due to the fact that the number of parameters describing the cracked beam's structure is thus reduced to its minimum, it can be expected that this element could be efficiently implemented, not only in static and stability analysis, but also in inverse identification of cracks in beam-like structures.