Study of residual stresses in the annular plates used in the aerial vehicles

Using the round plates with inserts made of various materials in the aircraft requires considering alterations in the residual stress fields and an ability to compute them. The paper analyzes a bimetallic annular plate with the rigidly fixed internal contour. It develops an algorithm for computing the residual stress fields of a bimetallic annular plate taking into account properties of the materials used, geometric parameters and conditions of its fixation. The paper provides examples of computing stresses with an alteration in the plate size and the material elasticity modulus. The developed algorithm could be used for tubular structures and intersections of pipes with the rectangular plates. The algorithm allows engineering methods to carry out preliminary computation with a sufficient degree of accuracy at the design stage of structures that could be represented in a computation scheme as the bimetallic annular plate.
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References

[1] Balabukh L.I., Alfutov N.A., Usyukin V.I. Stroitelnaya mekhanika raket [Construction mechanics of rockets]. Moscow, Vysshaya shkola Publ., 1984. 391 p. (In Russ.).

[2] Baranov D.A., Elenev V.D. Tipovye resheniya v proektirovanii i konstruirovanii elementov raket-nositeley [Typical solutions in design and construction of rocket-carrier elements]. Samara, SamGU Publ., 2020. 112 p. (In Russ.).

[3] Zhitomirskiy G.I. Konstruktsiya samoletov [Design of aeroplanes]. Moscow, Mashinostroenie Publ., 2005. 406 p. (In Russ.).

[4] Sapozhnikov V.M., Lagosyuk G.S. Prochnost i ispytaniya truboprovodov gidrosistem samoletov i vertoletov [Durability and testing of pipelines of hydraulic systems of aeroplanes and helicopters]. Moscow, Mashinostroenie Publ., 1973. 248 p. (In Russ.).

[5] Akhmedzyanov A.M., ed. Proektirovanie aviatsionnykh gazoturbinnykh dvigateley [Designing of aviation gas-turbine engines]. Moscow, Mashinostroenie Publ., 2000. 453 p. (In Russ.).

[6] Voskoboynik M.S., Lagosyuk G.S., Mirtov K.D. et al. Konstruktsiya i prochnost samoletov i vertoletov [Design and strength of aeroplanes and helicopters]. Moscow, Transport Publ., 1972. 440 p. (In Russ.).

[7] Vikulin A.V., Kruzhalov A.G. Prospects for improvement modern gas turbine engines due to application bimetal blisks in cooled turbines. Aviatsionnaya promyshlennost [Aviation Industry], 2021, no. 2, pp. 20–25. (In Russ.).

[8] Altenbach H., Bauer S., Eremeyev V.A. et al. Recent approaches in the theory of plates and plate-like structures. Springer, 2022. 305 p.

[9] Reddy J.N. Theory and analysis of elastic plates and shells. CRC Press, 2006. 568 p.

[10] Makaeva R.Kh., Tsareva A.M., Karimov A.Kh. Determination of natural frequencies and vibration modes of a constant thickness centrally secured disk. Izvestiya vysshikh uchebnykh zavedeniy. Aviatsionnaya tekhnika, 2008, no. 1, pp. 41–45. (In Russ.). (Eng. version: Russ. Aeronaut., 2008, vol. 51, no. 1, pp. 53–59, doi: https://doi.org/10.3103/S1068799808010091)

[11] Boyarshinov S.V. Osnovy stroitelnoy mekhaniki mashin [Fundamentals of construction mechanics of machines.]. Moscow, Mashinostroenie Publ., 1973. 456 p. (In Russ.).

[12] Chizhevskiy K.G. Raschet kruglykh i koltsevykh plastin [Calculation of circular and ring plates]. Leningrad, Mashinostroenie Publ., 1977. 182 p. (In Russ.).

[13] Bazarenko N.A. Interaction of a hollow cylinder of finite length and a plate with a cylindrical cavity with a rigid insert. Journal of Applied Mathematics and Mechanics, 2010, vol. 74, no. 3, pp. 323–333.

[14] Nemirovskiy Yu.V., Romanova T.P. Dynamic deformation of a curved plate with a rigid insert. Prikladnaya mekhanika i tekhnicheskaya fizika, 2006, vol. 47, no. 2, pp. 126–138. (In Russ.). (Eng. version: J. Appl. Mech. Tech. Phys., 2006, vol. 47, no. 2, pp. 254–265, doi: https://doi.org/10.1007/s10808-006-0051-y)

[15] Filippov S.B. Buckling of the cylindrical shell joint with annular plates under external pressure. Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya [Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy], 2021, vol. 8, no. 2, c. 282–294, doi: https://doi.org/10.21638/spbu01.2021.208 (in Russ.).

[16] Evgenyev S.S., Petrosyan G.G., Futin V.A. Calculation of axial gasodynamic forces, disk friction losses and overflow in semiopen impellers of centrifugal compressors. Izvestiya vysshikh uchebnykh zavedeniy. Aviatsionnaya tekhnika, 2009, no. 3, pp. 17–23. (In Russ.). (Eng. version: Russ. Aeronaut., 2009, vol. 52, no. 3, pp. 319–326, doi: https://doi.org/10.3103/S1068799809030106)

[17] Makhutov N.A. Deformatsionnye kriterii razrusheniya i raschet elementov konstruktsiy na prochnost [Deformation criteria of failure and strength calculation of structural elements]. Moscow, Mashinostroenie Publ., 1981. 272 p. (In Russ.).

[18] Potapov S.D., Perepelitsa D.D. Research of influence of residual tension in the zone of the arrangement of the crack on the rate of its growth at cyclic loading. Vestnik MAI [Aerospace MAI Journal], 2014, vol. 21, no. 1, pp. 104–110. (In Russ.).

[19] Vasserman N.N., Ratchiev A.M. Distinctive features of predicting the crack propagation kinetics in basic GTE parts. Izvestiya vysshikh uchebnykh zavedeniy. Aviatsionnaya tekhnika, 2011, no. 2, pp. 8–11. (In Russ.).

[20] Normy prochnosti aviatsionnykh gazoturbinnykh dvigateley grazhdanskoy aviatsii [Strength standards for civil aviation gas turbine engines]. Moscow, TsIAM Publ., 2004. 260 p. (In Russ.).

[21] Banshchikova I.A. The stress-strain state and duration to fracture of ring plates under creep conditions. Vychislitelnaya mekhanika sploshnykh sred [Computational Continuum Mechanics], 2015, vol. 8, no. 4, pp. 359–368. (In Russ.).

[22] Konev S.V., Mikhaylets V.F., Teftelev I.E. et al. Analysis of the characteristic stress state of the coil flange as a circular plate. Vestnik Magnitogorskogo gosudarstvennogo tekhnicheskogo universiteta im. G.I. Nosova [Vestnik of Nosov Magnitogorsk State Technical University], 2018, vol. 16, no. 3, pp. 98–102, doi: https://doi.org/10.18503/1995-2732-2018-16-3-98-102 (in Russ.).

[23] Skorokhod A.Z. Assessment of internal voltage distribution of ring plates in calculation of heat pipe boilers. Vestnik BelGUTa: Nauka i transport [Bulletin of BSUT: Science and Transport], 2020, no. 1, pp. 64–67. (In Russ.).

[24] Gerasimov S.I., Zhilkin V.A., Kosenyuk V.K. Determination of residual stresses in thin plates using the combined methods of boundary integral equations and holographic interferometry. Izvestiya Akademii nauk SSSR. MTT, 1991, no. 1, pp. 185–191. (In Russ.).

[25] You L.H., Wang J.X., Tang B.P. Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure. Meccanica, 2009, vol. 44, no. 3, pp. 283–292, doi: https://doi.org/10.1007/s11012-008-9174-y

[26] Tokovyy Y., Hung K.-M., Ma C.-C. Determination of stresses and displacements in a thin annular disk subjected to diametral compression. J. Math. Sci., 2010, vol. 165, no. 3, pp. 342–354, doi: https://doi.org/10.1007/s10958-010-9803-6

[27] Saadatfar M., Zarandi M.H. Deformations and stresses of an exponentially graded magneto-electro-elastic non-uniform thickness annular plate which rotates with variable angular speed. Int. J. Appl. Mech., 2020, vol. 12, no. 5, art. 2050050, doi: https://doi.org/10.1142/S1758825120500507

[28] Lebedev A.E., Kapranova A.B., Gudanov I.S. et al. Study of the influence of annular plate size on the stress-strain state of a vertical steel tank. Chem. Petrol. Eng., 2021, vol. 57, no. 3-4, pp. 239–245, doi: https://doi.org//10.1007/s10556-021-00924-x

[29] Zaydes S.A. Numeric definition of residual voltage at surface covering plastic deformation. Sovremennye tekhnologii. Sistemnyy analiz. Modelirovanie [Modern Technologies. System Analysis. Modeling], 2011, no. S-4, pp. 76–82. (In Russ.).

[30] Ryspaev T.A., Chynybaev M.K., Nikishov D.S. et al. Determination of residual stresses in welded joints by finite element method. Materialovedenie, 2013, no. 2, pp. 52–57. (In Russ.).

[31] Efimov A.V., Chebotarevskiy Yu.V., Pavlov D.G. Residual tension determination in a solid thin round dialectical plate at locally heating from no stationary external heat resource. Vestnik Saratovskogo gosudarstvennogo tekhnicheskogo universiteta [Bulletin of Saratov State Technical University], 2005, no. 3, pp. 28–32. (In Russ.).

[32] Mattikalli A.C., Kurahatti R.V. Numerical method based parametric investigation of isotropic annular plate. Mater. Today: Proc., 2020, vol. 27, no. 1, pp. 376–381, doi: https://doi.org/10.1016/j.matpr.2019.11.161

[33] Al-Abbas B.H., Hemzah S.A., Alyhya W.S. Finite difference derivation and finite element technique of annular plate buckling under axial and shear loads. Int. J. Civ. Eng. Technol., 2018, vol. 9, no. 10, pp. 32–41.

[34] Velikanov N.L., Koryagin S.I., Sharkov O.V. Stresses in circular plates with rigid elements. J. Phys.: Conf. Ser., 2018, vol. 1015, no. 5, art. 052028, doi: https://doi.org/10.1088/1742-6596/1015/5/052028

[35] Muskhelishvili N.I. Nekotorye osnovnye zadachi matematicheskoy teorii uprugosti [Some basic problems in the mathematical theory of elasticity]. Moscow, Nauka Publ., 1966. 707 p. (In Russ.).