##
**Problem of thermoelasticity for a cylinder with thin multilayer coating.**
*(English.
Russian original)*
Zbl 1435.35380

J. Math. Sci., New York 243, No. 1, 145-161 (2019); translation from Mat. Metody Fiz.-Mekh. Polya 60, No. 2, 117-129 (2017).

Summary: On the basis of the obtained analytic solution of the one-dimensional problem of thermoelasticity for a cylinder with multilayer coating under the conditions of convective heat exchange with the environment, we study the thermal stressed state of the system.

### MSC:

35Q74 | PDEs in connection with mechanics of deformable solids |

74F05 | Thermal effects in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

74B10 | Linear elasticity with initial stresses |

PDF
BibTeX
XML
Cite

\textit{V. A. Shevchuk}, J. Math. Sci., New York 243, No. 1, 145--161 (2019; Zbl 1435.35380); translation from Mat. Metody Fiz.-Mekh. Polya 60, No. 2, 117--129 (2017)

Full Text:
DOI

### References:

[1] | G. M. Bartenev and A. I. Zhornik, “Temperature stresses in glass coatings on metal pipes,” Fiz. Khim. Obrab. Mat., No. 3, 100-108 (1972). |

[2] | V. M. Vigak and A. M. Rigin, “Temperature stresses in a multilayer piecewise homogeneous cylinder,” Mat. Met. Fiz.-Mekh. Polya, Issue 15, 63-67 (1982). · Zbl 0481.73013 |

[3] | Vigak, V. M., Solutions of one-dimensional problems of elasticity and thermoelasticity for cylindrical piecewise-homogeneous bodies, Journal of Mathematical Sciences, 96, 3057-3064 (1999) |

[4] | V. A. Kudinov, A. V. Eremin, and E. V. Kotova, “Construction of exact analytic solutions of the problems of thermoelasticity for multilayer cylindrical structures,” Vest. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauk., No. 2(27), 188-191 (2012). · Zbl 1326.74043 |

[5] | Kudinov, V. A.; Eremin, A. V.; Kuznetsova, A. E.; Stefanyuk, E. V., Thermal stresses in a multilayer hollow cylinder under thermal shock on its external surface, Russian Aeronautics (Iz VUZ), 57, 37-44 (2014) |

[6] | O. G. Kutsenko, O. M. Kharytonov, and G. M. Zrazhens’kyi, “Analytic solution of a nonstationary problem of thermoelasticity corresponding to the thermal shock of a two-layer cylinder,” Visn. Kyiv. Nats. Univ. im. T. Shevchenka, Ser. Fiz.-Mat. Nauk., Issue 2, 65-70 (2009). · Zbl 1187.74049 |

[7] | Kushnir, R. M.; Protsyuk, B. V.; Synyuta, V. M., Quasistatic temperature stresses in a multilayer thermally sensitive cylinder, Materials Science, 40, 433-445 (2004) |

[8] | Ya. S. Podstrigach and P. R. Shevchuk, “Temperature fields and stresses in bodies with thin coatings,” Tepl. Napryazh. Élem. Konstr., Issue 7, 227-233 (1967). |

[9] | Podstrigach, Ya. S.; Shevchuk, P. R.; Ivashchuk, D. V., Stressed state of the material in diffusion saturation of a cylinder with a thin coating, Strength of Materials, 6, 787-792 (1974) |

[10] | V. S. Popovych, H. Yu. Harmatii, and K. S. Ivankiv, “Nonstationary problem of heat conduction for a thermosensitive cylinder with coating,” Visn. L’viv. Univ., Ser. Mekh.-Mat., Issue 46, 83-88 (1997). |

[11] | V. S. Popovych, K. S. Ivankiv, and H. Yu. Harmatii, “Axisymmetric quasistatic problem of thermoelasticity for a thermosensitive cylinder with thin coating,” Visn. L’viv. Univ., Ser. Mekh.-Mat., Issue 46, 89-96 (1997). |

[12] | Popovych, V. S.; Kalynyak, B. M., Mathematical Modeling and Methods for the Determination of the Static Thermoelastic State of Multilayer Thermally Sensitive Cylinders, Journal of Mathematical Sciences, 215, 218-242 (2016) · Zbl 1349.74224 |

[13] | Prokopenko, YA, Mathematical simulation of thermally loaded two-layer cylinders, Vest. Tambov. Gos. Tekh. Univ., 15, 806-813 (2009) |

[14] | B. V. Protsyuk, “Determination of the thermal stressed state of a piecewise inhomogeneous thermosensitive hollow cylinder,” Prykl. Probl. Mekh. Mat., Issue 13, 101-110 (2015). |

[15] | S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1970). · Zbl 0266.73008 |

[16] | M. Shvorak, “Analytic solution of a nonstationary problem of thermoelasticity for a two-layer cylinder,” Visn. Kyiv. Nats. Univ. im. T. Shevchenka, Ser. Fiz.-Mat. Nauk., Issue 26, 51-55 (2011). · Zbl 1249.74037 |

[17] | V. A. Shevchuk, “Determination of residual stresses in a cylinder with thin multilayer coating,” Prykl. Probl. Mekh. Mat., Issue 10, 159-167 (2012). |

[18] | Shevchuk, V. A., Nonstationary one-dimensional problem of heat conduction for a cylinder with a thin multilayer coating, Journal of Mathematical Sciences, 184, 215-223 (2012) |

[19] | V. A. Shevchuk, “Numerical analysis of thermal stresses in bodies with thin multilayer coatings,” Visn. Dnipropetr. Univ., Ser. Mekh., 19, Issue 15(1), 129-139 (2011). |

[20] | Shevchuk, V. A.; Kalynyak, B. M., Stressed state of cylindrical bodies with multilayer inhomogeneous coatings, Materials Science, 46, 747-756 (2011) |

[21] | O. I. Yatskiv, R. M. Shvets’, and B. Ya. Bobyk, “Some approaches to the solution of the problem of heating of a solid elastic cylinder with nonstationary boundary conditions,” Prykl. Probl. Mekh. Mat., Issue 5, 186-194 (2007). |

[22] | Carpinteri, A.; Lorenzini, E., Thermal shock in a nuclear fuel element with cladding, Nucl. Eng. Design., 61, 1-12 (1980) |

[23] | Ciavarella, M.; Decuzzi, P.; Tagarielli, VL; Demelio, GP, Simple formulas for thermoelastic stresses in TBC coatings, J. Therm. Stresses, 26, 409-422 (2003) |

[24] | B. Kalynyak and V. Popovych, “Thermal stresses in multilayer thermal sensitive cylinder at asymptotic thermal conditions,” in: F. Ziegler, R. Heuer, and C. Adam (Eds.), Proc. of the Sixth Internat. Congr. on Thermal Stresses (May 26-29, 2005, Vienna, Austria), Vienna Univ. of Technology, Vienna (2005), Vol. 2, pp. 119-122. |

[25] | Kroupa, F., Stresses in coatings on cylindrical surfaces, Acta Tech. CSAV, 39, 243-274 (1994) |

[26] | Lee, Z-Y; Chen, CK; Hung, C-I, Transient thermal stress analysis of multilayered hollow cylinder, Acta Mechanica, 151, 75-88 (2001) · Zbl 0996.74028 |

[27] | Men, X.; Tao, F.; Gan, L.; Du, W. (ed.); Zhou, X. (ed.), Analysis of the coating interfacial stress in thick walled cylinder, 1355-1358 (2015), Paris |

[28] | Nied, HF, Thermal shock in a circumferentially cracked hollow cylinder with cladding, Eng. Fract. Mech., 20, 113-137 (1984) |

[29] | Nusier, SQ; Newaz, GM, Transient residual stresses in thermal barrier coatings: analytical and numerical results, Trans. ASME. J. Appl. Mech., 65, 346-353 (1998) |

[30] | Ootao, Y.; Tanigawa, Y.; Fukuda, T., Axisymmetric transient thermal stress analysis of a multilayered composite hollow cylinder, J. Therm. Stresses, 14, 201-213 (1991) |

[31] | Shevchuk, VA; Hetnarski, RB (ed.), Generalized boundary conditions to solving thermal stress problems for bodies with thin coatings, No. 4, 1942-1953 (2014), Dordrecht |

[32] | Shevchuk, VA, Modeling and computation of heat transfer in a system “body-multilayer coating”, Heat Transfer Res., 37, 421-433 (2006) |

[33] | Sollund, HA; Vedeld, K.; Hellesland, J., Efficient analytical solutions for heated and pressurized multilayer cylinders, Ocean Eng., 92, 285-295 (2014) |

[34] | Vedeld, K.; Sollund, HA; Hellesland, J., Closed analytical expressions for stress distributions in two-layer cylinders and their application to offshore lined and clad pipes, Trans. ASME J. Offshore Mech. Arct. Eng., 137, 021702.1-9 (2015) |

[35] | Zhang, Q.; Wang, ZW; Tang, CY; Hu, DP; Liu, PQ; Xia, LZ, Analytical solution of the thermo-mechanical stresses in a multilayered composite pressure vessel considering the influence of the closed ends, Int. J. Pres. Ves. Pip., 98, 102-110 (2012) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.