Crack detection using finite element method

Other than the classical methods the finite element methods is also applied by various researchers for crack detection in damaged structures, those have been described in this section.

Saavedra et al. [66] have presented a theoretical and experimental vibration analysis of a multibeams structure containing transverse crack. They have derived a new cracked finite element stiffness matrix to analyse the vibrational behavior of crack systems with different boundary conditions. Qian et al. [67] have developed a finite element model for crack detection in a damaged beam using stress intensity factors. They have also validated their model with the experimental results obtained for a cantilever beam. According to them their method is also applicable to complex structures with crack. Andreausa et al. [68] have investigated the features of non-linear response of a crack beam using two dimensional finite element model (FEM). They have considered the behavior of the breathing crack as a frictionless contact problem. They have compared the linear dynamic response with the non- linear dynamic response of the cantilever beam and presented a non-linear technique for

crack identification. Viola et al. [69] have developed a finite element model for a cracked Timoshenko beam for crack identification based on the changes in the dynamic behavior of the structure. They have derived the stiffness matrix and consistent mass matrix for developing the crack identification technique. Chondros et al. [70] have studied the torsional vibrational behavior of a circumferentially cracked cylindrical shaft using analytical and numerical finite element analysis; they have used HU-WASHIZU-BARR variational formulation to develop the analytical method for the cracked shaft. Ariaei et al. [71] have presented an analytical approach for determining the dynamic response of the undamped Euler-Bernoulli beams with breathing crack and subjected to the moving mass using discrete element technique and finite element method. They have observed that the presence of cracks alters the beam response patterns. Potirniche et al. [72] have developed a two dimensional finite element method to study the influence of local flexibility on the dynamic response of a structure. Narkis [73] has detected the crack by using inverse technique, that is, through the measurement of frequency of first two natural frequencies of a simply supported uniform beam. He has validated the developed method by comparing the results with the results from numerical finite element calculations. Ostachowicz et al. [74] have analyzed the forced vibrations of the beam and find out the impact of crack parameters such as crack position and its severity on the vibrational characteristics and discussed a basis for crack diagnosis. They have modeled the beam with triangular disk finite elements and assumed the crack to be a breathing crack. Zheng et al. [75] have analyzed the natural frequencies and mode shapes of a cracked and undamaged beam by developing an overall additional flexibility matrix using finite element method. They have also developed a shape function to compute the vibrational characteristics of the cracked beam. The gauss quadrature and least square method has been used by them to compute the overall additional flexibility matrix. The authors have constructed the shape function which can very well satisfy the local flexibility conditions of the crack locations. Kisa et al. [76] have used finite element and component mode synthesis methods to analyze the free vibration of uniform and stepped cracked beam of circular cross section. They have used stress intensity factor and strain energy release rate functions to calculate the flexibility matrix and inverse of the compliance matrix taking into account inertia forces. According to them, crack depth and crack location have considerable affect on the natural frequencies and mode shapes of the cracked beam with non propagating open

cracks. Karthikeyan et al. [77] have proposed a technique for estimation of crack location and size in beam structure from the free and forced response of the beam. They have used finite element method to analyze the modal response for the beam structure with transverse open crack.. In this work they have included the effect of proportionate damping and used an external unit to harmonically excite the beam. They have used an iterative algorithm and regularization technique for locating the crack positions and size on the cracked beam and the results are in good agreement with other methods even in presence of error and noise. Hearndon et al. [78] have formulated a methodology using Euler-Bernoulli and Timo- shenko theories to analyze the affect of crack on dynamic properties of a cantilever beam subjected to bending. To evaluate the influence of crack location and size on the structural stiffness and calculation of transfer function a finite element model has been proposed by them. According to them the reduction in global component stiffness due to the crack is used to determine its dynamic response by a modal analysis computational model. In this work they have revealed that the natural frequencies decreases with increasing crack length. Al- Said [79] has proposed an algorithm based on a mathematical model to identify crack location and depth in an Euler-Bernoulli beam carrying a rigid disk. He has applied Lagrange’s equation to develop the mathematical model for analyzing the lateral vibration of the beam model. The proposed method utilizes mode shapes of two uniform beams connected by mass less torsional spring to establish the trial function. The presented method utilizes the first three natural frequencies to estimate the crack parameters. Results from the presented technique have been authenticated using the finite element software. Shekhar et al. [80] has derived a method to calculate the vibration characteristics using model based on finite element analysis. Panigrahi [81] have performed a three dimensional non-linear finite element analysis to evaluate the normal and shear stress along the overlap zone in a fiber reinforced composite material.

Excepting the classical, wavelet analysis and finite element methods, Artificial Intelligence Techniques are also being adapted by authors for damage identification.