STATIC AND EIGENVALUE ANALYSIS OF CRACKED TIMOSHENKO BEAM BY NEW MACRO ELEMENT CONTAIN ARBITRARY NUMBER OF CRACKS

In this paper the finite element of beam element with arbitrary number of transverse cracks is derived for fatigue and fracture applications. The new element is one-dimensional with arbitrary number of embedded edge cracks in arbitrary position of beam element with any depth. The cracks are not physically modeled within the element, but instead, their influences on the local flexibility of the structure are considerated by the modification of the element stiffness as a function of the cracks depth and cracks position. 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 components of the stiffness matrix for the cracked element are derived using the superposition principle, compatibility relations, and Betti’s theorem. The stiffness matrix for transversely cracked beam element is derived and all expressions are given in symbolic forms. Models using the presented stiffness matrix are shown to produce accurate results, although with significantly less computational effort than physical modeling of the crack in 2D finite element models.