The calculation of the thermal stressed state of multilayer platesofa non-canonical shape
Abstract
A method for solving the problem of stationary thermoelasticity of multilayer plates of non-canonical shape in plan is proposed, which is based on the method of immersing a complex domain into the domain of a canonical form. A non-canonical plate with arbitrary boundary conditions "immerses" into a canonical plate. To ensure that the specified boundary conditions are met, additional compensating loads are added to the auxiliary structure, distributed along the contour of the initial structure. The intensities of compensating loads are determined from a system of integral equations. Deformation of the layers of the plates are described within the framework of the first-order theory, taking into account the transverse shear strains in each layer. The field of temperature loads is obtained by solving the non-stationary problem of thermal conductivity of a multilayer plate. The temperature stresses in a five-layer plate when heated by a film heat source are investigated.
Downloads
References
/References
N. Noda, R. B. Hetnarski, Y. Tanigawa, Thermal Stress, 2nd ed. Taylor and Francis, London, 2004.
O. Hachkevych, R. Terlets'kyi, O. Turii. The formulation and development of methods of solving thermomechanics problems for irradiated layered solids MMC, Vol. 4, No 1, 2017, P. 21-36. DOI: https://doi.org/10.23939/mmc2017.01.021.
C.H. Hsueh, Thermal stresses in elastic multilayer systems. Thin Solid Films. Vol. 418, No 2, 2002, Pages 182-188 DOI: https://doi.org/10.1016/S0040-6090(02)00699-5.
N.V. Smetankina. Non-stationary deformation, thermal elasticity and optimisation of laminated plates and cylindrical shells. Miskdruk Publishers, Kharkiv, 2011, 376 p. [in Russian]
Thermal Stresses V, edited by R. B. Hetnarski. Lastran Corporation, Rochester, NY, 1999. 542 pages.
T.-M. Shih, M. Arie, D. Ko. Literature Survey of Numerical Heat Transfer (2000–2009): Part II, Numerical Heat Transfer, Part A: Applications, Vol. 60, No 11-12, 2011, 883-1096, DOI: 10.1080/10407782.2011.636720.
A. Barut, E. Madenci, Non-linear analysis of composite panels under non-uniform temperature distribution, Int. J. Solids and Struct. Vol. 37. No 27, 2000, P. 3681–3713. DOI: https://doi.org/10.1016/S0020-7683(99)00119-5
S. Brischetto, E. Carrera Thermal Stress Analysis by refined multilayered composite shell theories, J. of Thermal Stresses, Vol. 32, No 1-2, 2008, 165-186, DOI: 10.1080/01495730802540882
J.F. Silva, J.P. Nunes, J.C. Velosa. Using Thermoplastic (HDPE) Liners and Glass Fiber Reinforced Thermosetting and Thermoplastic Structural Wall Matrices to Produce Filament Wound Pressure Vessels. Proceedings of the ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASME 2010 Pressure Vessels and Piping Conference: Volume 6, Parts A and B. Bellevue, Washington, USA. July 18–22, 2010. P. 275-281. ASME. DOI: https://doi.org/10.1115/PVP2010-25826
Neng-Hui Zhang. Thermoelastic stresses in multilayered beams. Thin Solid Films Vol. 515, Issue 23, 2007, P. 8402-8406, DOI: https://doi.org/10.1016/j.tsf.2007.05.003
G. Chunxue, Z. Zhiwei, L. Xuehua Modeling of thermal stresses in elastic multilayer coating systems Journal of Applied Physics 117, 055305, 2015, DOI: https://doi.org/10.1063/1.4907572
N.V. Smetankina, O.V. Postnyi. Calculation of the thermal stress state of layered shells of complex shape. Dynamics, Strength and Modelling in Mechanical Engineering: Abstracts of reports of the IІ International Scientific and Technical Conference (05–08 October 2020 р., Kharkiv). Kharkiv: A. Pidhornyi Institute of Mechanical Engineering Problems of the NAS of Ukraine, 2020. P. 285 [in Ukrainian]
H.A. Sheludko, O.M. Shupikov, N.V. Smetankina, S.V. Ugrimov. Applied adaptive search. Kharkiv, Oko, 2001, 191 p. [in Ukrainian]
A. I. Malykhina, D. O. Merkulov, O. V. Postnyi, N. V. Smetankina. Stationary problem of heat conductivity for complex-shape multilayer plates. Bulletin of V.N. Karazin Kharkiv National University, series «Mathematical modeling. Information technology. Automated control systems». 2019. Vol. 41. P. 46–54.
N. Smetankina, O. Postnyi. Nonstationary heat conduction in multilayer glazing subjected to distributed heat sources. Informatyka, Automatyka, Pomiary w Gospodarce i Ochromie Srodowiska., 2020., Vol. 10, No 2, P. 28-31. DOI: https://doi.org/10.35784/iapgos.930
N.V. Smetankina, O.V. Postnyi, A.I. Merkulova, D.O. Merkulov. Modeling of non-stationary temperature fields in multilayer shells with film heat sources. Conference Proceedings: 2020 IEEE KhPI Week on Advanced Technology (KhPIWeek) IEEE (5-10 Oct. 2020)., IEEE: Kharkiv, 2020., P. 242–246. DOI: https://doi.org/10.1109/KhPIWeek51551.2020.9250139
Boley, B. A., Weiner, J. H. Theory of Thermal Stresses Quantum, New York, 1974.
Noda N., Hetnarski, R. B., Tanigawa, Y. Thermal Stress, 2nd ed. Taylor and Francis, London, 2004.
Hachkevych O., Terlets'kyi R., Turii O. The formulation and development of methods of solving thermomechanics problems for irradiated layered solids MMC. 2017; Vol. 4, No 1, 2017, P. 21-36. DOI: https://doi.org/10.23939/mmc2017.01.021.
Hsueh C.H. Thermal stresses in elastic multilayer systems. Thin Solid Films Vol. 418, No 2, 2002, Pages 182-188 DOI: https://doi.org/10.1016/S0040-6090(02)00699-5.
Smetankina, N.V.: Non-stationary deformation, thermal elasticity and optimisation of laminated plates and cylindrical shells. Miskdruk Publishers, Kharkiv, 2011, 376 p.
Thermal Stresses V, edited by R. B. Hetnarski. Lastran Corporation, Rochester, NY, 1999. 542 pages.
Shih T.-M., Arie M., Ko D. Literature Survey of Numerical Heat Transfer (2000–2009): Part II, Numerical Heat Transfer, Part A: Applications, Vol. 60, No 11-12, 2011, 883-1096, DOI: https://doi.org/10.1080/10407782.2011.636720
Barut A., Madenci E. Non-linear analysis of composite panels under non-uniform temperature distribution, Int. J. Solids and Struct. Vol. 37. No 27, 2000, P. 3681–3713. https://doi.org/10.1016/S0020-7683(99)00119-5
Brischetto S., Carrera E. Thermal stress analysis by refined multilayered composite shell theories, J. of Thermal Stresses, Vol. 32, No 1-2, 2008, 165-186, DOI: https://doi.org/10.1080/01495730802540882
Silva J.F., Nunes J.P., Velosa, J.C. Using Thermoplastic (HDPE) Liners and Glass Fiber Reinforced Thermosetting and Thermoplastic Structural Wall Matrices to Produce Filament Wound Pressure Vessels. Proceedings of the ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASME 2010 Pressure Vessels and Piping Conference: Volume 6, Parts A and B. Bellevue, Washington, USA. July 18–22, 2010. P. 275-281. ASME. DOI: https://doi.org/10.1115/PVP2010-25826
Neng-HuiZhang, Thin Solid Films Vol. 515, Issue 23, 14 September 2007, P. 8402-8406 Thermoelastic stresses in multilayered beams, DOI: https://doi.org/10.1016/j.tsf.2007.05.003
Chunxue G., Zhiwei Z., Xuehua L. Modeling of thermal stresses in elastic multilayer coating systems Journal of Applied Physics 117, 055305, 2015, DOI: https://doi.org/10.1063/1.4907572
Сметанкіна Н. В., Постний О. В. Розрахунок термонапруженого стану шаруватих оболонок складної форми. Динаміка, міцність та моделювання в машинобудуванні: тези доповідей IІ Міжнародної науково-технічної конференції (05–08 жовтня 2020 р., Харків). Харків: Інститут проблем машинобудування ім. А. М. Підгорного НАН України, 2020. C. 285.
Шелудько Г.А., Шупіков О.М., Сметанкіна Н.В., Угрімов С.В. Прикладний адаптивний пошук.- Харків: Око, 2001.-191 с.
Malykhina A. I., Merkulov D. O., Postnyi O. V., Smetankina N. V. Stationary problem of heat conductivity for complex-shape multilayer plates. Вісник Харківського національного університету імені В. Н. Каразіна, серія «Математичне моделювання. Інформаційні технології. Автоматизовані системи управління». 2019. Вип. 41. С. 46–54.
Smetankina N., Postnyi O. Nonstationary heat conduction in multilayer glazing subjected to distributed heat sources. Informatyka, Automatyka, Pomiary w Gospodarce i Ochromie Srodowiska., 2020., Vol. 10, No 2, P. 28-31. DOI: https://doi.org/10.35784/iapgos.930
Smetankina N. V., Merkulova A.I., Merkulov D. O., Postnyi O. V. Modeling of non-stationary temperature fields in multilayer shells with film heat sources. Conference Proceedings: 2020 IEEE KhPI Week on Advanced Technology (KhPIWeek) IEEE (5-10 Oct. 2020)., IEEE: Kharkiv, 2020., P. 242–246. DOI: https://doi.org/10.1109/KhPIWeek51551.2020.9250139
