Transverse Displacements of Transversely Cracked Beams with a Linear Variation of Width Due to Axial Tensile Forces

Abstract

This paper considers the analysis of transverse displacements of slender beams with a linear variation of width and a single-sided transverse crack, subjected to axial tensile forces. When analysing such structures, the application of detailed 2D or 3D finite element meshes is undoubtedly the best solutions possible. However, in inverse identification of potential cracks such comprehensive models are actually not the most suitable solutions. Therefore, the presented studies implement a simplified model where the crack is represented by means of an internal hinge endowed with a rotational spring. In the first part of the research presented, solutions from the simplified model’s governing differential equations are obtained. The purpose of this study is to demonstrate the model’s ability to adequately describe the considered phenomenon and to derive an appropriate rotational spring definition. The second part of the research discussed is devoted to modelling of the phenomenon by the simple one-dimensional beam finite element. Afterwards, the implementation and the quality of the results are being presented through a comparative case study that complements the derivations.