Prediction of individual deformation characteristics of structural elements by a ``leader'' product

V. P. Radchenko ; E. A. Afanaseva

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 3, pp. 500-519.

Résumé

We propose a numerical method for predicting the individual deformation characteristics of structural elements by a “leader” product. The basis of this method is generalized one-parameter models. These models relate the integral characteristics of the stress state to the integral characteristics of the deformation state in the “generalized load – generalized displacement” coordinates. The scope of the method is structural elements of the same type, which are under identical conditions of external loading and are characterized by a large spread of deformation characteristics (generalized displacement). It is assumed that the operation of one structural element (prototype) begins some time earlier than the others. A hypothesis on the similarity of all realizations reduced to a single origin by a time shift in the “generalized displacement – time” coordinates is introduced. Using statistical information on the initial sections of “lagging” structural elements and the sample prototype, the statistical characteristics of the similarity parameter of the operated structural element are determined in relation to the “leader” product, and then its deformation characteristics are predicted. In the paper, we investigate friction units and structural elements (rods, threaded connections) under creep conditions. Based on statistical correlation analysis of the experimental information, a verification of the similarity hypothesis usabilty for all implementations of the structural elements studied is carried out. The method was illustrated by an example of predicting the wear of the friction units of the front landing gear of the aircraft depending on the number of take-off and landing cycles. The method was also illustrated with an example of how to calculate the elongation of rods made of a polyvinylchloride compound under uniaxial loading and axial displacement of the screwing area of a threaded joint under creep conditions. The experimental data for the generalized displacement of specific implementations are shown to not exceed the calculated limits of the confidence interval for mathematical expectation for all structural elements considered in prediction time intervals of one to four “basic” intervals, within which estimates of random parameters for specific structural elements were determined.

Détail

Keywords: prediction, generalized displacement, individual deformation characteristics, friction unit, creep, rod, threaded connection.

Bibliographie

[1] Bolotin V. V., Prognozirovanie resursa mashin i konstruktsii [Forecasting Resource Machines and Structures], Mashinostroenie, Moscow, 1984, 312 pp. (In Russian)

[2] Frolov K. V., Metody sovershenstvovaniia mashin i sovremennye problemy mashinostroeniia [Methods for Improving Machines and Modern Problems of Mechanical Engineering], Mashinostroenie, Moscow, 1984, 223 pp. (In Russian)

[3] Frolov K. V., Zubov I. V., Izrailev Yu. L., et al., “Extending the period of safe operation of power-generating equipment between major overhauls”, Strength Mater., 18:5 (1986), 553–563 | DOI

[4] Rebrov I. S., Usilenie sterzhnevykh metallicheskikh konstruktsii. Proektirovanie i raschet [Strengthening of Bar-Metal Structures. Design and Calculation], Stroiizdat, Leningrad, 1988, 288 pp. (In Russian)

[5] Bondarenko V. M., Merkulov S. I., “To the question of the development of the theory of reconstructed reinforced concrete”, Beton Zhelezobeton [Concrete and Reinforced Concrete], 2004, no. 6, 3–11 (In Russian)

[6] Budin A Ya., Chekreneva M. V., Usilenie portovykh sooruzhenii [Strengthening Port Facilities], Transport, Moscow, 1983, 180 pp. (In Russian)

[7] Serazutdinov M. N., Ubaidulloev M. N., Abragim Kh. A., “Increasing the bearing capacity of reinforced loaded structures”, Stroit. Mekh. Inzhen. Konstr. Sooruzh., 2011, no. 3, 23–30 (In Russian)

[8] Serazutdinov M. N., Ubaidulloev M. N., “Amplification of loaded bar structures taking into account the influence of repair and assembly forces”, Inzhenerno-Stroit. Zhurnal, 2012, no. 1(27), 98–100 (In Russian)

[9] Radchenko V. P., Simonov A. V., Dudkin S. A., “Stochastic version of the one-dimensional theory of creep and long-term strength”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2001, no. 12, 73–84 (In Russian) | DOI

[10] Radchenko V. P., Saushkin M. N., Goludin E. P., “Stochastic model of nonisothermal creep and long-term strength of materials”, J. Appl. Mech. Tech. Phys., 53:2 (2012), 292–298 | DOI

[11] Gromakovskii D. G., Radchenko V. P., Averkieva V. I., “Development of a system for diagnosing friction units based on the stiffness method”, Vestn. Mashinostr., 1988, no. 8, 10–14 (In Russian)

[12] Radchenko V. P., Shershneva M. V., Kubyshkina S. N., “Evaluation of the reliability of structures under creep for stochastic generalized models”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, no. 3(28), 53–71 (In Russian) | DOI | Zbl

[13] Radchenko V. P., Popov N. N., “Analytical solution of the stochastic steady-state creep boundary value problem for a thick-walled tube”, J. Appl. Math. Mech., 76:6 (2012), 738–744 | DOI

[14] Radchenko V. P., Shershneva M. V., Tsvetkov V. V., “Generalized stochastic model of creep and creep rupture beams in pure bending and its application to the estimation of reliability”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, no. 4(29), 72–86 (In Russian) | DOI

[15] Venttsel' E. S., Ovcharov L. A., Teoriia veroiatnostei [Theory of Probability], Nauka, Moscow, 1969, 368 pp. (In Russian)

[16] Granovskii V. A., Siraia T. N., Metody obrabotki eksperimental'nykh dannykh pri izmereniiakh [Methods for Processing Experimental Data During Measurements], Energoatomizdat, Leningrad, 1990, 288 pp. (In Russian)

[17] Chizhik A. A., “Individual methods for predicting the resource of the main elements of power equipment”, J. Mach. Manuf. Reliab., 1990, no. 5, 3–11 (In Russian)

[18] Samarin Yu. P., “Stochastic mechanical characteristics and reliability of structures with rheological properties”, Polzuchest' i dlitel'naia prochnost' konstruktsii [Creep and Long-Term Strength of Structures], Kuybyshev Aviation Inst., Kuybyshev, 1986, 8–17 (In Russian)

[19] Radchenko V. P., Pavlova G. A., “Methods for evaluating the individual reliability of structural elements, taking into account information on deformations and displacements at the initial stage of operation”, Nadezhnost' i prochnost' mashinostroitel'nykh konstruktsii [Reliability and Strength of Engineering Structures], Kuybyshev Aviation Inst., Kuybyshev, 1988, 124–138 (In Russian)

[20] Radchenko V. P., Khrenov S. M., “Method to calculate the third stage of tensile creep taking into account the individual deformation properties”, Polzuchest' i dlitel'naia prochnost' konstruktsii [Creep and Long-Term Strength of Structures], Kuybyshev Aviation Inst., Kuybyshev, 1986, 56–65 (In Russian)

[21] Radchenko V. P., Pavlova G. A., “Prediction of individual reliability of structural elements during creep at the operating stage according to the leader”, Izv. Vuzov. Mashinostroenie, 1989, no. 11, 23–27 (In Russian)

[22] Samarin Yu. P., Maklakov V. N., “Individual prediction of material behavior under high-cycle fatigue using inelastic deformation problems”, J. Mach. Manuf. Reliab., 1991, no. 6, 107–112 (In Russian)

[23] Eremin Yu. A., Radchenko V. P., Samarin Yu. P., “Calculation of individual deformation properties of structural elements under creep conditions”, Mashinovedenie, 1984, no. 1, 67–72 (In Russian)

[24] Eremin Yu. A., Kaidalova L. V., Konson E. D., “Individual prediction of residual deflections of the welded diaphragms under operating conditions”, Izv. Vuzov. Mashinovedenie, 1988, no. 1, 12–16 (In Russian)

[25] Eremin Yu. A., Kaidalova L. V., Radchenko V. P., “Investigation of beam creep based on the analogy of the structure of the equation of state of the material and structural elements”, Mashinovedenie, 1983, no. 2, 64–67 (In Russian)

[26] Samarin Yu. P., Eremin Yu. A., “Method of investigating component creep”, Strength Mater., 17:4 (1985), 487–493 | DOI

[27] Radchenko V. P., Dudkin S. A., Timofeev M. I., “Experimental study and analysis of the inelastic micro- and macro-inhomogeneity fields of AD-1 alloy”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2002, no. 16, 111–117 (In Russian) | DOI

[28] Katanaha N. A., Semenov A. S., Getsov L. B., “Unified model of steady-state and transient creep and identification of its parameters”, Strength Mater., 45:4 (2013), 145-156 | DOI

[29] Zoteev V. E., “Mathematical modeling and numerical method for estimating the characteristics of non-isothermal creep based on the experimental data”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 25:3 (2021), 531–555 (In Russian) | DOI | Zbl

[30] Zoteev V. E., “A numerical method of nonlinear estimation based on difference equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:4 (2018), 669–701 (In Russian) | DOI

[31] Seber G. A. F., Lee A. J., Linear Regression Analysis, Wiley Series in Probability and Statistics, Wiley, Hoboken, NJ, 2003, 565 pp. | DOI

[32] Pronikov A. S., Nadezhnost' mashin [Reliability of Machines], Mashinostroenie, Moscow, 1978, 592 pp. (In Russian)

[33] Ungarova L. G., Methods of mathematical modeling of hereditarily elastic media based on fractional calculus, Cand. Disser. (Phys. Math. Sci.), Samara, 2020, 199 pp. (In Russian)

[34] Ivanov D. V., Dol' A. V., Biomekhanicheskoe modelirovanie [Biomechanical Modeling], Amirit, Saratov, 2021, 250 pp. (In Russian)

[35] Beskrovny A. S., Bessonov L. V., Golyadkina A. A., et all., “Development of a decision support system in traumatology and orthopedics. Biomechanics as a tool for preoperative planning”, Rus. J. Biomech., 25:2 (2021), 99–112 (In Russian) | DOI

[36] Ivanov D. V., “Biomechanical support for the physician's decision when choosing a treatment option based on quantitative success criteria”, Izv. Saratov Univ. Math. Mech. Inform., 22:1 (2022), 62–89 (In Russian) | DOI