539.3 Finite element modeling of temperature fields in thin-walled multilayer anisotropic shells
Dimitrienko Y. I. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University), Koryakov M. N. (Bauman Moscow State Technical University), Maremshaova A. A. (Bauman Moscow State Technical University)
THIN-WALLED SHELLS, TEMPERATURE FIELDS, HEAT CONDUCTION PROBLEM, VARIATIONAL STATEMENT, FINITE ELEMENT MODELING
doi: 10.18698/2309-3684-2023-1-4363
The problem of developing a model for calculating temperature fields in thin-walled multilayer curvilinear-anisotropic thin shells of arbitrary geometric shape, including composite ones, is considered. As a rule, to solve this problem, a specific coordinate notation of the equations of the theory of heat conduction is used, which creates certain difficulties for calculating complex composite shells. In this paper, it is proposed to use an invariant record of the variational formulation of problems in the theory of heat conduction, followed by the application of the finite element algorithm procedure. As a result, a matrix differential equation is derived for determining the temperature field at the nodes of a finite element mesh. A software module has been developed for the finite element solution of the problem of non-stationary thermal conductivity of shells. The module functions as part of the SMCM software package, created at the Scientific and Educational Center for Supercomputer Engineering Modeling and Development of Software Systems, Bauman Moscow State Technical University (REC SIMPLEX). An example of solving the problem of calculating a non-stationary temperature field in a cylindrical shell with longitudinal-transverse reinforcement is given. Comparison of numerical simulation with similar calculations in the ANSYS software was carried out, which showed the high accuracy of the proposed method: the relative deviation of the results does not exceed 0,5%
Dimitrienko Yu.I. Thermomechanics of composite structures under high temperatures. Springer, 2016, 434 p.
Podstrigach Ya.S., Shvets R.N. Termouprugost' tonkih obolochek [Thermoelasticity of thin shells]. Kiev, Naukova dumka Publ., 1983, 343 p.
Kovalenko A.D. Osnovy termouprugosti [Fundamentals of thermoelasticity]. Kiev, Naukova dumka Publ., 1970, 308 s.
Karnaukhov V.G., Kirichok I.F. Svyazannye zadachi teorii vyazkouprugih plastin i obolochek [Related problems of the theory of viscoelastic plates and shells]. Kiev, Naukova dumka Publ., 1986, 223 p.
Novozhilov V.V., Chernykh K.F., Mikhailovsky E.I. Linejnaya teoriya tonkih obolochek [Linear theory of thin shells]. Leningrad, Polytechnic Publ., 1991, 656 p.
Bakulin V.N. Metody optimal'nogo proektirovaniya i raschyota kompozicionnyh konstrukcij [Methods of optimal design and calculation of composite structures. Vol. 1]. Moscow, Fizmatlit Publ., 2008, 256 p.
Ambartsumyan S.A. Teoriya anizotropnyh obolochek [Theory of anisotropic shells]. Moscow, Fizmatgiz Publ., 1961, 384 p.
Alfutov N.A., Zinoviev P.A., Popov B.G. Raschet mnogoslojnyh plastin I obolochek iz kompozicionnyh materialov [Calculation of multilayer plates and shells made of composite materials]. Moscow, Mashinostroenie Publ., 1984, 264 p.
Bolotin V.V., Novikov Yu.N. Mekhanika mnogoslojnyh konstrukcij [Mechanics of multilayer structures]. Moscow, Mashinostroenie Publ., 1980, 375 p.
Vasiliev V.V. Mekhanika konstrukcii iz kompozicionnyh materialov [Mechanics of structures made of composite materials]. Moscow, Mashinostroenie Publ., 1988, 271 p.
Vildeman V.E., Sokolkin Yu.V., Tashkinov A.A. Mekhanika neuprugogo deformirovaniya i razrusheniya kompozitsionnykh materialov [Mechanics of inelastic deformation and destruction of composite materials]. Moscow, Nauka Publ., 1997, 288 p.
Goldenweiser A.L. Teoriya tonkih uprugih obolochek [Theory of thin elastic shells]. Moscow, Nauka Publ., 1976, 512 p.
Zhang D., Luo Zh., Xuan W. Simulation analysis of temperature field in the heat transfer process of shell. Physics Procedia, 2012, vol. 25, pp. 92–98.
Feng X., Liu W., Liu Ch. Thermal-mechanical coupling analysis of functionally graded cylindrical shells. IOP Conference Series: Materials Science and Engineering, 2019, vol. 576, art. no. 012006.
De Sousa Alves B., Laforest M., Sirois F. 3-D finite-element thin-shell model for high-temperature superconducting tapes. IEEE Transactions on Applied Superconductivit, 2022, vol. 32, iss. 2, art. no. 7500411.
Sargsyan S.H. Thermoelasticity of thin shells on the basis of asymmetrical theory of elasticity. Journal of Thermal Stresses, 2009, vol. 32, no. 8, pp. 791–818.
Dimitrienko Yu.I., Yurin Yu.V. Timoshenko-type asymptotic theory for thin multi-layered plates shells. Маthematical Modeling and Computational Methods, 2018, no. 1, pp. 16–40.
Dimitrienko Y. I. Gubareva E.A., Pichugina A.E. Modeling of the stresses in thin composite cylindrical shells based on the asymptotic theory. Маthematical Modeling and Computational Methods, 2018, no. 3, pp. 114–132.
Dimitrienko Yu.I. Mekhanika sploshnoy sredy. Tom 4. Osnovy mekhaniki tverdogo tela [Continuum Mechanics. Vol. 4. Fundamentals of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
Dimitrienko Yu.I. Tenzornoe ischislenie [Tensor calculus]. Moscow, Vysshaya shkola Publ., 2001, 575 p.
Zenkevich O. Metod konechnyh elementov v tekhnike [Finite element method inengineering]. Moscow, Mir Publ., 1975, 542 p.
Certificate no. 2020663790 Programma TermalStressPCM_HT_Manipula dlya konechno-elementnogo rascheta termonapryazhenij v konstrukciyah konicheskogo tipa iz tkanevyh polimernyh kompozicionnyh materialov pri vozdejstvii vysokotemperaturnogo gazovogo potoka, s uchetom krivolinejnoj anizotropii i termodestrukcii materiala [TermalStressPCM_HT_Manipula program for finite element calculation of thermal stresses in conical-type structures made of fabric polymer composite materials under the influence of high-temperature gas flow, taking into account curvilinear anisotropy and thermal degradation of the material] / Yu.I. Dimitrienko, Yu.V. Yurin, M.N. Koryakov, S.V. Sobshchikov, A.A. Zakharov, I.O. Bogdanov; applicant and copyright holder: BMSTU — no. 2020662965; application 26.10.2020; registered in the register of computer programs 02.11.2020 — [1].
Димитриенко Ю.И., Юрин Ю.В., Коряков М.Н., Маремшаова А.В. Конечно-элементное моделирование температурных полей в тонкостенных многослойных оболочечных элементах конструкций. Математическое моделирование и численные методы, 2023, No 1, с. 43–63
Download article
Количество скачиваний: 2