Models for Representation of Cracks in One-dimensional Finite Element Method

Resumo

Structures can develop discontinuities in their material in the form of cracks or generalized damage,
changing their properties and resulting in malfunction or even collapse. Thus, to identify and monitor the existence
of cracks, some numerical models have been proposed in recent decades, where different approaches regarding
the representation of the crack are treated. Considering this scenario, the objective of this work is to study different
ways of representing cracks in numerical models, based on the one-dimensional Finite Element Method (FEM).
For crack representation in numerical models, 3 methods are highlighted in the literature, namely the reduced
section method, the local flexibility method, and the continuous method. Thus, this work contemplates the
numerical implementation of the mentioned methods, focusing on the analysis of free vibration of Euler-Bernoulli
beams. The natural frequencies obtained by these 1D methods are compared to those obtained by other researchers
using different models (Timoshenko, 2D, etc.). Different crack configurations and boundary conditions are tested
numerically and compared to reference values presented in the literature, obtaining good results. In a comparative
analysis, the models presented divergence in the answers for deeper cracks, evidencing a significant difference
between these approaches.