Identification of crack in functionally graded material beams using the p-version of finite element method

Abstract

The detection of cracks in functionally graded material (FGM) structural members has been a significant subject due to their increasing applications in various important engineering industries. A model-based approach is developed in this paper to determine the location and size of an open edge crack in an FGM beam. The p-version of finite element method is employed to estimate the transverse vibration characteristics of a cracked FGM beam. A rational approximation function of the stress intensity factor (SIF) with crack depth and material gradient as independent variables is presented in order to overcome the cumbersomeness and inaccurateness caused by the complicated expression of the analytical SIF solution in crack modeling. Subsequently the crack is represented by a massless rotational spring and its stiffness is obtained from fracture mechanics approach and the aforementioned SIF function. The proposed p-version finite element formulation and crack modeling are validated by analytical literature results of intact FGM beams and two-dimensional finite element analysis of cracked FGM beams with different supporting conditions and material gradients. The influences of crack size, crack location and material gradient on the natural frequencies of a cracked cantilever FGM beam are studied. To identify the crack parameters, the frequency contours with respect to crack location and size are plotted and the intersection of contours from different modes indicates the predicted crack location and size. Numerical experiments have demonstrated that the proposed method has excellent computational efficiency and satisfactory identification performance.