Certain cases of elastic equilibrium of a composed wedge with an interface crack

Problems of interface cracks starting from the common corner points of pairs of perfectly glued wedges of different isotropic elastic materials are addressed. It is demonstrated that for a few particular configurations and a restrictive condition imposed on values of elastic constants (corresponding to vanishing of the second Dundurs parameter), the problem of elastic equilibrium may be solved by Khrapkov’s method. These configurations are: (i) the wedges forming a half-plane; (ii) the wedges forming a plane; (iii) one of the wedges being a half-plane. In all cases, the external boundaries are supposed to be free of stresses. By applying Mellin’s transform for all three configurations the problem has been reduced to vector Riemann’s problem, and the matrix coefficient has been factorized for the case of the mentioned restrictive condition. The first configuration, i.e. the problem of an inclined edge crack located along the boundary separating two wedges of different elastic isotropic materials forming a half-plane is considered in more detail. The solution has been obtained for both uniform (corresponding to remote loading) and non-uniform (loading applied at the crack faces) problems. Numerical results are presented and compared with the available results obtained by other authors for particular cases. The obtained solutions appear especially valuable for analysing extreme cases of parameters.

A New Reactive Hybrid Membership Function in Fuzzy Approach for Identification of Inclined Edge Crack in Cantilever Beam Using Vibration Signatures

In this paper, the crack identification using smart technique (by several hybrid membership functions in a fuzzy controller) has been developed for inverse analysis of the vibration signatures (like modal frequencies, mode shapes) and crack parameters (like crack depth, crack location and crack inclination) of an inclined edge crack cantilever beam. The modal frequencies are obtained from finite element (using ANSYS) and experimental analysis which are used as inputs to the hybrid fuzzy controller. The hybrid fuzzy system is designed by taking different types of membership functions (MF) to determine the crack parameters. The calculated first three modal frequencies are used to create number of fuzzy rules with the three output crack parameters. Finally, the proposed hybrid technique is validated by comparing the results obtained from trapezoidal and Gaussian fuzzy controllers, FEA and experimental results. The outcomes obtained from hybrid fuzzy controller are in good agreement with experimental results. Nomenclature