On the Bending Analysis of Multi-Cracked Slender Beams with Continuous Height Variations

We studied the implementation of a multi-stepped multi-cracked beam finite element for analysing beams of various heights’ variations along the length. The genuine continuous variation of height was modelled by an adequate series of steps and for the cracks, the model of internal hinges endowed with rotational springs was applied. As the increased number of steps simultaneously increases the possibility that the crack location and step location may coincide, the continuous conditions at the steps were rewritten to a more general form in order to cover this combination. The newly presented form is also capable of taking a transverse concentrated force into account. Numerical evaluations were performed for several structures under various loads and the transverse displacements, nodal reactions, and inner forces were studied. The results obtained are positioned side by side with the results from more detailed 2D finite element meshes. The comparisons show excellent matching of the beam’s response providing the mesh of steps was dense enough. The examples demonstrate the potential of the present approach proving that the model is suitable for achieving computationally-efficient and truthful analyses.