Finite Timoshenko-Type Beam Element with a Crack
The paper presents a method of constructing the stiffness matrix of a Timoshenko-type finite beam element with a single nonpropagating transversal one-edge crack located in the middle of its length. The crack was modelled by adding an additional flexibility matrix to the flexibility matrix of the uncracked element. The terms of the additional matrix were evaluated according to the laws of fracture mechanics. The element was used to perform several numerical tests, the results of which were compared with results of the analytical solutions available in literature. Very good agreement between the presented model and the analytical solution was obtained. The element presented in the paper may he applied to the static and dynamic analysis of many types of structural elements with faults in form of fatigue cracks. The method of formation of the stiffness matrix described in the paper, allows to create finite elements of a beam with various types of cracks (double-edge, circumferential, internal, etc), provided their stress intensity factors are known.
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