New finite element for transversely cracked slender beams subjected to transverse loads

The paper covers the derivation of a new finite element for beams with transverse cracks. The derivation is based on a simplified computational model that has already proved itself suitable for the inverse identification of cracks. The model embodies all the necessary major information about the structure’s response from the inverse identification point of view, where the presence and location and, if possible, the depth of the crack should be detected from the measured response, usually dynamic. In such situations the stress distributions obtained from 2D finite elements analysis are not as important as the computational model being capable of reliably describing the displacement of the structure.However, from numerical studies it also became evident that the relevance of the model decreases with element thickness. This indicated that shear forces should be included in the analysis process.Therefore, derivation of a new finite element with the inclusion of shear forces effect has been executed. The stiffness matrix for transversely cracked slender beams, as well as the derivation of interpolation functions is presented and all expressions are given in symbolic forms. The example shows that, although with significantly less computational effort than with 2D FE meshes, significant improvement in transverse displacements can be obtained with the presented beam finite element.