Crack identification using improved 2D cracked finite element in conjunction with micro genetic algorithm

Abstract

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 modeled 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 Castigliano’s first principle. The element was implemented in the commercial FE code ABAQUS as a user element (UEL) subroutine. The identification of the crack location and depth is formulated as an optimization problem, and GA is used to find the optimal location and depth by minimizing 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.