Edge-crack diagnosis using improved two-dimensional cracked finite element and micro genetic algorithm

In this paper, a crack diagnosis method based on an improved two-dimensional (2-D) finite element (FE) with an embedded edge crack, and micro genetic algorithm (-GA) is proposed. The crack is not physically modelled within the element, but instead, its influence on the local flexibility of the structure is accounted for by the reduction of the element stiffness as a function of the crack length. The components of the stiffness matrix for the cracked element are determined from the Castiglianos first principle. The element was implemented in the commercial FE code ABAQUS as a user element subroutine. The accuracy of the proposed improved cracked element is verified by comparing the predicted first natural frequency with the available experimental data. Subsequently, a methodology to detect the crack location and size in conjunction with the proposed improved cracked element is formulated as an optimisation problem, and -GA is used to find the optimal location and depth by minimising the cost function based on the difference of measured and calculated natural frequencies. The proposed crack detection procedure using the improved 2-D FE with an embedded edge crack, and -GA is validated using the available experimental and FE modal analysis data reported in the existing literature. The predicted crack locations and crack sizes demonstrate that this approach is capable of detecting small crack location and depth with small errors. © 2013 Taylor & Francis.