The possibility for diagnostics of a breathing crack type damage in a long cylindrical shell is examined. The damage is modeled by a notch that alters the cross-sectional geometry. The method of conformal mappings is used to solve the first main boundary-value problem of elasticity for domains in the form of an annular sector with and without a notch. The solutions are analyzed and compared to estimate the relative decrease in the stiffness of the shell because of the opening of the crack
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References
D. I. Anpilogov, “Conformal mapping of annular sectors onto a unit circle,” Vestn. Kharkov. Nats. Univ., Ser. Math. Prikl. Mat. Mekh., 57, No. 790, 146–157 (2007).
N. K. Bari, A Treatise on Trigonometric Series, Pergamon Press, Oxford (1964).
N. S. Bakhvalov, A. V. Lapin, and E. V. Chizhonkov, Numerical Methods in Problems and Exercises [in Russuan], Vyssh. Shk., Moscow (2000).
A. P. Bovsunovskii, “On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 2. Experimental and calculation results,” Strength of Materials, 31, No. 3, 253–259 (1999).
G. V. Galatenko, “Stress state in the plastic zone on the continuation of an elliptic mode I crack under bi- and tri-axial loading,” Int. Appl. Mech., 43, No. 11, 1202–1207 (2007).
A. A. Kaminsky and G. V. Gavrilov, “Subcritical stable growth of a penny-shaped crack in an aging viscoelastic body with cylindrical anisotropy,” Int. Appl. Mech., 43, No. 1, 68–78 (2007).
V. V. Matveev and A. P. Bovsunovskii, “Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 2. Bending vibrations, analytical solution,” Strength of Materials, 30, No. 6, 564–574 (1998).
N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1975).
N. P. Plakhtienko, “Diagnostics of piecewise-constant stiffness at nonlinear resonances,” Prikl. Mekh., 27, No. 10, 112–120 (1991).
A. B. Roitman and D. I. Anpilogov, “Vibration diagnostics of a damaged inclined cylindrical shell,” Strength of Materials, 33, No. 6, 588–597 (2001).
G. S. Pisarenko (ed.), Strength of Materials [in Russian], Vyshcha Shkola, Kyiv (1986).
A. A. Kaminsky and M. F. Selivanov, “Growth of a penny-shaped crack with a nonsmall fracture process zone in a composite,” Int. Appl. Mech., 44, No. 8, 866–871 (2008).
A. A. Kaminsky, L. A. Kipnis, and V. A. Kolmakova, “Model of the fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media,” Int. Appl. Mech., 44, No. 10, 1084–1092 (2008).
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Translated from Prikladnaya Mekhanika, Vol. 46, No. 8, pp. 90–105, August 2010.
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Anpilogov, A.I. Calculation of the relative decrease in the stiffness of a damaged annular sector from analysis of the displacement field. Int Appl Mech 46, 929–941 (2011). https://doi.org/10.1007/s10778-011-0383-z
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DOI: https://doi.org/10.1007/s10778-011-0383-z