Stiffness Characteristics of a Rotor Shaft with Slant Crack Including Elliptical Front Edge

The stiffness characteristics of a rotating cracked shaft including elliptical front edge between transverse crack and 45° slant crack have been studied here. The strain energy release rate (SERR) method has been used to calculate the stiffness matrix of two types of the crack element. Time-varying characteristics of stiffness of the straight front edge and elliptical front edge of the cracked shaft were studied in a stable rotation cycle. The analytical result of this paper shows that change of the cracked shaft stiffness raises during the increase of the crack depth. The stiffness characteristics of the rotor with slant crack having elliptical front edge vary differently from those of the rotor with transverse crack having elliptical front edge.

Implementation of Crack Problem of Functionally Graded Materials with ABAQUSTM

An implementation method of the virtual crack closure technique (VCCT) for fracture problems of non-homogeneous materials such as functionally graded materials (FGMs) with commercial finite element software ABAQUSTMis introduced in this paper. In order to avoid the complex post proceeding to extract fracture parameters, the interface crack element based on the VCCT is developed. The heterogeneity of FGMs is characterized though user subroutine UMAT and the interface crack element is implemented by user subroutine UEL. Several examples are analyzed to demonstrate the accuracy of the present method.

Development of a Novel Algorithm for a Crack Detection, Localization, and Sizing in a Beam Based on Forced Response Measurements

The present work aims at the development of a method for the crack detection, localization and sizing in a beam based on the transverse force and response signals. The Timoshenko beam theory is applied for transverse vibrations of the beam model. The finite element method is used for the cracked beam forced vibration analysis. An open transverse surface crack is considered for the crack model, which contains standard five flexibility coefficients. The effect of the proportionate damping is also included. A harmonic force of known amplitude with sine-sweep frequency is used to dynamically excite the beam, up to few flexible modes, which could be provided with the help of an exciter. In practice, linear degrees of freedom (DOFs) can be measured quite accurately; however, rotational DOFs are difficult to measure accurately. All rotational DOFs, except at crack element, are eliminated by a dynamic condensation scheme; for elimination of rotational DOFs at the crack element, a new condensation scheme is implemented. The algorithm is iterative in nature and starts with a presumption that a crack is present in the beam. For an assumed crack location, flexibility coefficients are estimated with the help of forced responses. The Tikhonov regularization technique is applied in the estimation of bounded crack flexibility coefficients. These crack flexibility coefficients are used to obtain the crack size by minimizing an objective function. With the help of the estimated crack size and measured natural frequency, the crack location is updated. The procedure iterates till the crack size and location get stabilized up to the desired level of accuracy. The algorithm has a potential to detect no crack condition also. The crack flexibility and damping coefficients are estimated as a by-product. Numerical examples, with the simply supported and cantilevered beams, are given to justify the applicability and versatility of the algorithm in practice. With the numerically simulated forced responses, which have the noise contamination and the error in the natural frequency measurements, the estimated crack parameters (i.e., the crack location and size) are in good agreement.

The whole crack singular element for 2-D boundary element analysis of multiple straight cracks in the general anisotropic solids

We develop a singular crack element for the general anisotropic solids in two dimensions for the mixed mode boundary element analysis of multiple straight cracks. Given a normalized crack along an interval (−1, +1) on the X-axis, we represent the crack opening displacement (COD) by the continuous distribution of dislocation dipoles, which is interpolated by the Chebyshev polynomials with the p1 − X2 weight function. The analytical integration of the dislocation dipole distribution leads to a closed form displacement formula for the crack with the pr COD and the 1/pr stress singularity at its tips. In the BE solution, the stress intensity factors are determined, along with the unknown boundary displacements and tractions, without the post-processing. The proposed crack element, called the whole crack singular element (WCSE), drastically simplifies the mixed mode analysis of multiple straight cracks in the general anisotropic solids with no sacrifice of the accuracy.