Прикладні проблеми механіки неоднорідних тіл: сучасний стан та перспективи розвитку
За матеріалами доповіді на засіданні Президії НАН України 12 липня 2023 року
DOI:
https://doi.org/10.15407/visn2023.09.070Ключові слова:
структурно неоднорідні тіла, багатошарові та волокнисті композити, багатошарові покриття, функціонально-градієнтні тіла, метаматеріали, напружено-деформований стан, прямі та обернені задачіАнотація
Структурно неоднорідні тіла, для яких характерною є залежність усіх або деяких властивостей матеріалу від просторових координат, становлять інтерес як для науковців в академічних колах, так і для інженерів-виробничників. Більш як 100-річний період досліджень механічної поведінки неоднорідних тіл спонукає до спроб математичного моделювання та розроблення адекватних методів аналізу. У доповіді простежено основні етапи розвитку досліджень з механіки неоднорідних структур, виокремлено найголовніші напрацювання та проаналізовано сучасні виклики. Розглянуто отримані в Інституті прикладних проблем механіки і математики ім. Я.С. Підстригача НАН України найвагоміші результати за цим напрямом та окреслено перспективи розвитку цих досліджень.
Посилання
Timoshenko S.P. History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures. McGraw-Hill, New York, 1953.
Todhunter I., Pearson K. A History of the Theory of Elasticity and of the Strength of Materials: from Galilei to Lord Kelvin. V. 1. Galilei to Saint-Venant, 1639—1850. Dover Pub., New York, 1960.
Maugin G.A. Material Inhomogeneities in Elasticity. Chapman and Hall, London, 1993. https://doi.org/10.1201/9781003059882
Olszak W. (ed.) Non-Homogeneity in Elasticity and Plasticity. Pergamon Press, New York, 1959.
Suresh S., Mortensen A. Fundamentals of Functionally Graded Materials: Processing and Thermomechanical Behaviour of Graded Metals and Metal-Ceramic Composites. Ashgate Publishing, London, 1998.
Tanigawa Y. Some Basic Thermoelastic Problems for Nonhomogeneous Structural Materials. Applied Mechanics Reviews. 1995. 48(6): 287—300. https://doi.org/10.1115/1.3005103
Tokovyy Y., Ma C.-C. The Direct Integration Method for Elastic Analysis of Nonhomogeneous Solids. Cambridge Scholars Publishing, Newcastle, 2021.
Tokovyy Y., Ma C.-C. Elastic Analysis of Inhomogeneous Solids: History and Development in Brief. J. Mechanics. 2019. 35(5): 613—626. https://doi.org/10.1017/jmech.2018.57
Ewing W.M., Jardetzki W.S., Press F. Elastic Waves in Layered Media. New York, Toronto, London: McGraw Hill Book Company Inc., 1957.
Muravskii B.G. Mechanics of Non-Homogeneous and Anisotropic Foundations. Springer, Berlin, 2001.
Fröhlich O.K. Druckverteilung im Baugrunde mit Besonderer Berücksichtigung der Plastischen Erscheinungen. Springer, Wien, 1934.
Föppl A. Versuche über die Elastizität des Erdbodens. Zentralblatt der Bauverwaltung. 1897. 17: 276—278.
Gibson R.E. Some results concerning displacements and stresses in a non-homogeneous elastic half space. Géotechnique. 1967. 17: 58—67.
Cristescu N.D., Craciun E.M., Soós E. Mechanics of Elastic Composites. Chapman & Hall, CRC Press, New York, 2004.
Gibson R.F. Principles of Composite Material Mechanics. CRC Press, Boca Raton, London, New York, 2016.
Guz A.N., Khoroshun L.P., Vanin G.A. et al. Mekhanika kompozitnykh materialov i elementov konstruktsiy (Mechanics of Composite Materials and Structural Elements). Vol. 1. Kyiv, Naukova Dumka, 1982 (in Russian).
Sam M., Jojith R., Radhika N. Progression in manufacturing of functionally graded materials and impact of thermal treatment. A critical review. Journal of Manufacturing Processes. 2021. 68A: 1339—1377. https://doi.org/10.1016/j.jmapro.2021.06.062
Birman V., Byrd L.W. Modeling and analysis of functionally graded materials and structures. Applied Mechanics Reviews. 2007. 60(5): 195—216.
Plevako V.P. Equilibrium of a nonhomogeneous half-plane under the action of forces applied to the boundary. Journal of Applied Mathematics and Mechanics. 1973. 37(5): 858—866.
Grigorenko Ya.M., Vasilenko A.T., Pankratova N.D. On the calculation of the stress state of thick-walled inhomogeneous anisotropic shells. Prykladnaya Mekhanika. 1974. 10(5): 86—93.
Lekhnitskii S.G. Radial distribution of stresses in a wedge and in a half-plane with variable modulus of elasticity. Journal of Applied Mathematics and Mechanics. 1962. 16(1): 146—151
Podstrigach Ya.S., Lomakin V.A., Kolyano Yu.M. Termouprugost' tel neodnorodnoy struktury (Thermoelasticity of bodies of inhomogeneous structure). Moscow, 1984 (in Russian).
Plevako V.P. Obshchiye resheniya v zadachakh teorii uprugosti neodnorodnykh sred (General solutions in problems of the theory of elasticity of inhomogeneous media). Kharkov, 1997 (in Russian).
Guo L.-C., Nodа N. Modeling method for a crack problem of functionally graded materials with arbitrary properties – piecewise-exponential model. Int. J. Sol. Struc. 2007. 44(21): 6768—6790. https://doi.org/10.1016/j.ijsolstr.2007.03.012
Sakharov A.S. et al. Metod konechnykh elementov v mekhanike tverdykh tel (Finite element method in solid mechanics). Kyiv, 1982 (in Russian).
Gontarovskii V.P., Kozlov I.A., Gontarovskaya T.N. Stress and strain calculations on inhomogeneous bodies of rotation by finite-element methods. Strength Mater. 1975. 7: 991—995. https://doi.org/10.1007/BF01522403
Pobedrya B.Ye., Gorbachev V.I. O staticheskikh zadachakh uprugikh kompozitov (On static problems of elastic composites). Vestnik Moskovskogo Universiteta. Seriya Matematika. Mekhanika. 1977. 5: 101—111.
Kuharchuk Yu., Sulym G., Shevchuk S. Pruzhna rivnovaha dvovymirnykh til z kutovymy tochkamy ta tonkymy vklyuchennyamy (Elastic equilibrium of two-dimensional bodies with corner points and thin inclusions). Mechanical engineering. 1997. 1: 14—20.
Kushnir R.M., Popovych V. Stress state of a thermosensitive plate in a central symmetric temperature field. Physico-chemical mechanics of materials. 2006. 42(2): 5—12.
Abovsky N.P., Andreev N.P., Deruga A.P. Variatsionnyye printsipy teorii uprugosti i teorii obolochek (Variational principles of the theory of elasticity and the theory of shells). Moscow, 1978 (in Russian).
Luciano R., Sacco E. Variational methods for the homogenization of periodic heterogeneous media. Europ. J. Mech. A/Solids. 1998. 17(4): 599—617. https://doi.org/10.1016/S0997-7538(99)80024-2
Zhang N.H., Wang M.L. A mathematical model of thermoviscoelastic FGM thin plates and Ritz approximate solutions. Acta Mechanica. 2006. 181(3-4): 153—167. https://doi.org/10.1007/s00707-005-0300-9
Aleksandrov A.Ya., Solovyov Yu.I. Prostranstvennyye zadachi teorii uprugosti (Spatial problems of the theory of elasticity). Moscow, 1978 (in Russian).
Mishiku M., Teodosiu K. Solution of an elastic static plane problem for nonhomogeneous isotropic bodies by means of the theory of complex variables. Journal of Applied Mathematics and Mechanics. 1966. 30(2): 459—468. https://doi.org/10.1016/0021-8928(67)90195-5
Кheinloo M.L. Optimization of material properties of inhomogeneous circular discs subjected to pressure. Int. Appl. Mech. 1987. 23(8): 777—782. https://doi.org/10.1007/BF00886667
Nadeau J.C., Ferrari M. Microstructural optimization of a functionally graded transverselly isotropic layer. Mechanics of Materials. 1999. 31(10): 637—651. https://doi.org/10.1016/S0167-6636(99)00023-X
Vigak V.M. Upravleniye temperaturnymi napryazheniyami i peremeshcheniyami (Control of thermal stresses and displacements). Kyiv: Naukova Dumka, 1988 (in Russian).
Dai H.L., Rao Y.N., Dai T. A review of recent researches on FGM cylindrical structures under coupled physical interactions. Composite Structures. 2016. 152: 199—225. https://doi.org/10.1016/j.compstruct.2016.05.042
Thai H.T., Kim S.E. A review of theories for the modeling and analysis of functionally graded plates and shells. Composite Structures. 2015. 128: 70—86.
Jojith R., Sam М., Radhika N. Recent advances in tribological behavior of functionally graded composites: A review. Engineering Science and Technology, an International Journal. 2022. 25: 100999. https://doi.org/10.1016/j.jestch.2021.05.003
Drobenko B.D., Klymenko D.V., Kushnir R.M., Marchuk M.V., Sirenko V.M., Kharchenko V.M. Methodology for researching the strength of rocket technology structures. Kosmicheskaia tehnika. Raketnoe vooruzhenie (Space technology. Missile armaments). 2020. (2): 120.
Marchuk M.V., Sirenko V.M., Drobenko B.D. Methodology for determining destructive loads on large-sized thin-walled structures taking into account the results of non-destructive tests. Applied problems of mechanics and mathematics. 2020. 18: 133—138. https://doi.org/10.15407/apmm2020.18.133-138
Stankevich V.Z., Mykhaskiv V.V. Intensity of dynamic stresses of longitudinal shear mode in a periodically layered composite with penny-shaped cracks. Matematychni metody ta fizyko-mekhanichni polya. 2020. 63(3): 46—54.
Kunets Ya.I., Matus V.V. Asymptotic approach in dynamic problems of the theory of elasticity for bodies with thin elastic inclusions. Matematychni metody ta fizyko-mekhanichni polya. 2020. 63(1): 75—93.
Kunets Ya.I., Matus V.V., Maksimiv Yu.I., Rabosh R.V. Influence of a thin metal layer on the propagation of Blyushtein-Gulyaev type waves in a piezoelectric body. Matematychni metody ta fizyko-mekhanichni polya. 2020. 63(3): 40—45.
Mykhas’kiv V.V., Stasyuk B.M. Effective elastic moduli of short-fiber composite with sliding contact at interfaces. Mechanics of Composite Materials. 2021. 57(5): 635—646. https://doi.org/10.1007/s11029-021-09985-8
Kushch V.I., Shmegera S.V., Mykhas’kiv V.V. Multiple spheroidal cavities with surface stress as a model of nanoporous solid. International Journal of Solids and Structures. 2018. 152-153: 261—271. https://doi.org/10.1016/j.ijsolstr.2018.07.001
Zhbadynskyi I.Y., Mykhas’kiv V.V. Acoustic Filtering Properties of 3D Elastic Metamaterials Structured by Crack-Like Inclusions. 2018 XXIII International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), Tbilisi, Georgia, 2018. P. 145—148. https://doi.org/10.1109/DIPED.2018.8543137
Shevchuk V.A. Study of the thermal stress state of a half-space with a multilayer coating during cyclic convective heat exchange with the external environment. Matematychni metody ta fizyko-mekhanichni polya. 2022. 65(3-4): 136—145.
Tokovyy Y.V. Direct integration method. In: Hetnarski R.B. (ed.) Encyclopedia of Thermal Stresses. Springer, Dordrecht, 2014. P. 951—960. https://doi.org/10.1007/978-94-007-2739-7
Yuzvyak M., Tokovyy Y. Thermal stresses in an elastic parallelepiped. Journal of Thermal Stresses. 2022. 45(12): 1009—1028. https://doi.org/10.1080/01495739.2022.2120940
Kushnir R.M., Yasinskyy A.V., Tokovyy Y.V. Effect of Material Properties in the Direct and Inverse Thermomechanical Analyses of Multilayer Functionally Graded Solids. Adv. Eng. Mater. 2022. 24: 2100875. https://doi.org/10.1002/adem.202100875
Kushnir R.M., Yasinskyi A.V., Tokovy Yu.V. Reconstruction of the thermal load of a functional graded hollow sphere by surface displacements. Matematychni metody ta fizyko-mekhanichni polya. 2020. 63(1): 149—160.
Tokova L., Yasinskyy A., Ma C.C. Effect of the layer inhomogeneity on the distribution of stresses and displacements in an elastic multilayer cylinder. Acta Mech. 2017. 228: 2865—2877. https://doi.org/10.1007/s00707-015-1519-8
Tokovyy Y. Elastic and thermoelastic response of multilayer inhomogeneous hollow cylinders. Mechanics of Advanced Materials and Structures. 2023. https://doi.org/10.1080/15376494.2023.2186548
