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Determining the stress state in a circular ring has been a classical topic in the stress analysis literature. Based on the principle of superposition, the results may be obtained by adding known solutions to an associated ring problem, where the boundary stresses on the inner and outer walls of the ring are represented in Fourier series. In this work, the coefficients of the Fourier series are generated through an algorithm based on the fast Fourier transform (FFT). In the case of concentrated loading, the required additional fundamental solutions are derived in closed-form. The presented numerical method allows for accurate and efficient computations of the stress distributions in a circular ring in static equilibrium under arbitrary in-plane loading; and generally, the FFT-based algorithm provides a convenient and versatile tool for handing some two-dimensional problems involving circular boundaries. [ABSTRACT FROM AUTHOR]

The windings of the power transformers are prone to deformation or displacement as a result of huge electromagnetic forces. Regular monitoring of transformers for detecting minor winding movements is crucial for preventing them from developing into major faults and eventually, causing an outage. In this study, a novel procedure is proposed to determine the location and severity of the disk space variation, a frequently occurring mechanical damage in transformers, by developing a two‐level method. At the first level, an accurate model of the winding is determined from sweep frequency response analysis measured data corresponding to the healthy status. Analysis and interpretation of the obtained results by the proposed fault detector algorithm lead to locating the position and severity of the fault, in the next level. The process of determining the winding model from the frequency response analysis data is achieved by a multistage method utilising an enhanced version of magnetic optimisation algorithm, which comprises of utilising Fourier series coefficients and phase functions, and fast calculation of coupled network matrices. Experimental results of two 64 kV transformer windings verify the effectiveness of the proposed method in detecting the winding faults. [ABSTRACT FROM AUTHOR]