Stress concentration occurs near the crack tip under the loading, strain energy release can cause the change of structural local flexibility, which leads to the change of structure response. Among these models, the crack model based on local flexibility has been widely used during the past three decades. Well-known current models include the crack model by means of an equivalent reduced section (Petroski et al., ), the continuous crack model theory (Chondros et al, ), and the crack model by virtue of local flexibility of the cracked element (Papadopoulos et al., ). It is provided that a reasonable mathematical model is generally needed. A comprehensive review of the state of vibration-based methods for cracked structures has been published by Dimarogonas and Papadopoulos. Therefore, dynamic analysis and crack detection for cracked structures have received more attention from many investigators. If a potential structural destruction or collapse can be predicted in time, the cost of reproduction and maintenance will be minimized greatly. The presence of the crack is inevitable in the most engineering structure due to material defects and external load, it degrades structural safety at some extent. Keywords: vibration analysis, local flexibility, cracked pipe, open crack, closed crack. The results demonstrate that the proposed method is accurate for calculating local flexibility and can be applied for vibration analysis in a pipe-like structure. The results of testing by Naniwadekar’s and Authors’ are used to validate the proposed method. An adaptive Simpson method is used to calculate the local flexibility coefficients of a cracked pipe. The proposed equations consider the influence of the crack orientation on the local flexibility coefficient. In this paper, the general solution of the local flexibility equations of a pipe with a part through-crack subjected to axial force, shearing force, and bending moment is deduced with respect to an arbitrary angled crack. However, few reports exist on the local flexibility of pipes with an arbitrary angled crack.
Mechanical analysis of cracked pipe structures based on local flexibility has received increased attention in the last three decades. But cracks inevitably appear in the pipe body due to various factors. Pipeline is an important transportation facility in the oil and gas industries.
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