| Назва | Presentation of a general 3D solution of equations of elasticity theory for a wide class of orthotropic materials |
| Назва англійською | Presentation of a general 3D solution of equations of elasticity theory for a wide class of orthotropic materials |
| Автори | Victor Revenko (https://orcid.org/0000-0002-2616-8747) |
| Принадлежність | The Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the NAS of Ukraine, Lviv, Ukraine |
| Бібліографічний опис | Presentation of a general 3D solution of equations of elasticity theory for a wide class of orthotropic materials / Victor Revenko // Scientific Journal of TNTU. — Tern. : TNTU, 2019. — Vol 95. — No 3. — P. 49–54. |
| Bibliographic description: | Revenko V. (2019) Presentation of a general 3D solution of equations of elasticity theory for a wide class of orthotropic materialsg. Scientific Journal of TNTU (Tern.), vol 95, no 3, pp. 49–54. |
| DOI: | https://doi.org/10.33108/visnyk_tntu2019.03.049 |
| УДК |
539.3 |
| Ключові слова |
Cartesian coordinate system, displacement function, orthotropic body, solution of equilibrium equations. |
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A mathematical model of the statically loaded three-dimensional orthotropic body was used. The broadest class of orthotropic materials in the Cartesian coordinate system is considered. We find a general representation of the solution of equilibrium equations in displacements for orthotropic materials. The expression of displacements, strains and stresses is obtained through the introduced displacement function, which satisfies the sixth-order equation for partial derivatives.
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| ISSN: | 2522-4433 |
| Перелік літератури |
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Ambartsumyan S. A. Obshchaya teoryyi anizotropnykh obolochek. Moskva: Nauka, 1974. 446 p. [Іn Russian].
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Lekhnytskyy S. H. Teoryyi upruhosti anizotropnoho tela. M.: Nauka, 1977. 415 p. [Іn Russian].
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Sen-Venan B. Memuar o kruchenyi pryzm. Memuar ob izhibe pryzm. M.: Fyzmathyz, 1961. 518 p. [іn Russian].
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Spravochnik po kompozitnym materialam: v 2-kh kn. / рod red. Dzh. Liubyna. M.: Mashynostroenye, 1988. Kn. 1. 448 р.; Kn. 2. 584 p. [In Russian].
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Revenko V. P. Three-Dimensional Stress State of an Orthotropic Rectangular Prism under a Transverse Force Applied at its End. Int. Appl. Mech. 2005. 43. № 4. P. 367–373.
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Papkovich P. F. Predstavlenie obshcheho intehrala osnovnykh differentsyal'nykh uravneniy teoriy upruhosti cherez harmonycheskie funktsiy. Yzv. AN SSSR. Ser. 7. 1932. № 10. Р. 1425–1435. [Іn Russian].
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Revenko V. P. Solving the three-dimensional equations of the linear theory of elasticity. Int. Appl. Mech. 2009. 45. № 7. P. 730–741.
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Elliot H. A. Axial symmetric stress distributions in aelotropic hexagonal crystals. The problem of the plane and related problems. Math. Proc. Cambridge Phil. Soc. 1949. 45. № 4. P. 621–630.
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Hu H. C. On the the three-dimenssional problems of elasticity of a transversely isotropic body. Data Sci. Sinica. 1953. 2. P. 145–151.
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Sylovanyuk V. P. Ruynuvannya poperedn'o napruzhenykh i transversal'no-izotropnykh til iz defektamy. L'viv.: NAN Ukrayiny. FMI im. H. V. Karpenka, 2000. 300 p. [Іn Ukraine].
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| References: |
-
Ambartsumyan S. A. Obshchaya teoryyi anizotropnykh obolochek. Moskva: Nauka, 1974. 446 p. [Іn Russian].
-
Lekhnytskyy S. H. Teoryyi upruhosti anizotropnoho tela. M.: Nauka, 1977. 415 p. [Іn Russian].
-
Sen-Venan B. Memuar o kruchenyi pryzm. Memuar ob izhibe pryzm. M.: Fyzmathyz, 1961. 518 p. [іn Russian].
-
Spravochnik po kompozitnym materialam: v 2-kh kn. / рod red. Dzh. Liubyna. M.: Mashynostroenye, 1988. Kn. 1. 448 р.; Kn. 2. 584 p. [In Russian].
-
Revenko V. P. Three-Dimensional Stress State of an Orthotropic Rectangular Prism under a Transverse Force Applied at its End. Int. Appl. Mech. 2005. 43. № 4. P. 367–373.
-
Papkovich P. F. Predstavlenie obshcheho intehrala osnovnykh differentsyal'nykh uravneniy teoriy upruhosti cherez harmonycheskie funktsiy. Yzv. AN SSSR. Ser. 7. 1932. № 10. Р. 1425–1435. [Іn Russian].
-
Revenko V. P. Solving the three-dimensional equations of the linear theory of elasticity. Int. Appl. Mech. 2009. 45. № 7. P. 730–741.
-
Elliot H. A. Axial symmetric stress distributions in aelotropic hexagonal crystals. The problem of the plane and related problems. Math. Proc. Cambridge Phil. Soc. 1949. 45. № 4. P. 621–630.
-
Hu H. C. On the the three-dimenssional problems of elasticity of a transversely isotropic body. Data Sci. Sinica. 1953. 2. P. 145–151.
-
Sylovanyuk V. P. Ruynuvannya poperedn'o napruzhenykh i transversal'no-izotropnykh til iz defektamy. L'viv.: NAN Ukrayiny. FMI im. H. V. Karpenka, 2000. 300 p. [Іn Ukraine].
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