Computational Modeling of Crack Detection for a Beam using the Finite Element Method

Abstract

Nowadays the presence of crack in different engineering structures becomes a serious threat to performance. Since most of the civil and mechanical structures may be damaged due to material fatigue, mechanical vibration, environmental attack and long-term service. Cracks in structural bodies lead to local changes in their stiffness, flexibility and consequently their static and dynamic behavior is affected. Moreover, dynamical systems of a beam usually possess non-linear characteristics, which causes practical difficulties on the model-based damage detection techniques. So it becomes essential to study the dynamic response characteristics in order to avoid any catastrophic failures and to follow structural integrity and performance. In the present study, a numerical simulation using the Finite Element Method (FEM) is carried out on a simply supported concrete beam of length 0.12m and width 0.015m with two open transverse cracks, to analyze the response characteristics for which the parameters considered are crack depth and its location. Its natural frequency and mode shapes are determined by applying suitable boundary conditions. A vibration-based model is employed to simulate the results by using COMSOL Multiphysics. By performing the computational analysis it is observed that, after applying load the frequencies of the cracked beam changes with the variation of the location of the crack for the all modes of vibration. It also found that frequencies are proportional to the increase in load and maximum frequency (around 2304.3 Hz) reserved at the cracked stage. Finally, it also revealed that the effects of crack are closer to the fixed end than at the free end, and by following this approach, very small sizes of crack (near 0.05 mm) can be identified in any structural beam.