New Timoshenko-cracked beam element and crack detection in beam-like structures using genetic algorithm

In this paper, a crack identification approach is presented for detecting crack depth and location in beam-like structures. For this purpose, a new beam element with a single transverse edge crack, in arbitrary position of beam element with any depth, is developed. The development is based on a simplified model, where each crack is substituted by a corresponding linear rotational spring, connecting two adjacent elastic parts. The localised spring may be represented based on linear fracture mechanics theory. The components of the stiffness matrix for the cracked element are derived using the superposition principle, compatibility relations, and Betti's theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e. to gain accurate natural frequencies of the beam-like structures knowing the cracks' characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional finite element results and available experimental measurements. Moreover, by knowing the natural frequencies, an inverse problem is established in which the cracks location and depth are identified. In the inverse approach, an optimization problem based on the new beam element and genetic algorithms is solved to search the solution.