A bar finite element for vibration and buckling analysis of cracked truss constructions

The paper presents a method of forming an inertia matrix and linear and geometrical stiffness matrices of a bar finite element with a single, non-propagating transverse one-edge open crack located in its mid-length. The presented method is based on the displacement formulation of FEM and laws of fracture mechanics. It has been found that the crack modified the inertia matrix and the linear stiffness matrix of the element, whereas the geometrical stiffness matrix remained unchanged. Taking advantage of the presented element there were done exemplary numerical calculations illustrating variations of longitudinal natural frequencies of the one sided fixed rod and variations of the values of global buckling load in a simple truss caused by the crack. The effect of inertia matrix form upon the values of longitudinal natural frequencies of the one sided fixed rod were analyzed.