Conservative numerical method for solving static linear boundary value problems of elastic shells of revolution
DOI:
https://doi.org/10.7242/1999-6691/2012.5.1.11Keywords:
elasticity, theory of shells, Hamiltonian systemAbstract
In this paper, we propose an algorithm for constructing a conservative numerical scheme for solving boundary value problems for linear Hamiltonian systems with an arbitrary finite-order approximation to the exact solution. Application of the algorithm expressed in high-level languages allowed us to develop the program for calculating the stress-strain state of a thin multilayered anisotropic shell of revolution. The results of calculations of real shells made of composite materials are presented.
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Kireev I.V., Nemirovskij U.V. APؐʾߑdؑiC’Pڐؐՠmetody issledovania linejnyh gamil’tonovyh sistem uravnenij statiki uprugih obolocek vrasenia // Vycisl. meh. splos. sred. - 2011. - T. 4, No 2. - S. 35-60.
Kantorovic L.V., Akilov G.P. Funkcional’nyj analiz. - M.: Nauka, 1984. - 750 s.
Krylov V.I., Sul’gina L.T. Spravocnaa kniga po cislennomu integrirovaniu. - M.: Nauka, 1966. - 372 s.
Kireev I.V. Simmetricnye cislennye metody resenia kraevyh zadac dla sistem obyknovennyh differencial’nyh uravnenij // Modelirovanie v mehanike splosnyh sred: Mezvuz. sb. naucnyh statej. / Krasnoarsk, 1992. - S. 81-91.
Samarskij A.A., Popov U.P. Raznostnye metody resenia zadac gazovoj dinamiki. - M.: Nauka, 1992. - 424 s.
Kireev I.V., Nemirovskij U.V. Gamil’tonova formalizacia opredelausih sootnosenij linejnoj teorii obolocek vrasenia // Vycisl. meh. splos. sred. - 2010. - T. 3, No 4. - S. 29-52.
Kireev I.V. Kraevye zadaci dla gamil’tonovyh sistem obyknovennyh differencial’nyh uravnenij: Prepr. No 11 / VC SO AN SSSR. - Krasnoarsk, 1990. - 31 c.
Bucy R.S. Two-point boundary value problems of linear Hamiltonian system // SIAM J. Appl. Math. - 1967. - V. 15, N. 6, - P. 1385-1389. DOI
Il’in V.A., Sadovnicij V.A., Sendov B.H. Matematiceskij analiz. - M.: Nauka, 1979. - 720 s.
Gantmaher F.R. Teoria matric. - M.: Nauka, 1988. - 538 s.
Suetin P.K. Klassiceskie ortogonal’nye mnogocleny. - M.: Nauka, 1979. - 416 s.
Voevodin V.V., Kuznecov U.A. Matricy i vycislenia. - M.: Nauka, 1984. - 320 s.
Cernyseva A.A, Kireev I.V. Modifikacia kriteria Uilkinsona ostanovki iteracij v metode soprazennyh gradientov // Vestnik KrasGU. Seria <> / KrasGU, 2005. - No 4.- C. 173-177.
Sajdurov V.V. Mnogosetocnye metody konecnyh elementov. - M.: Nauka, 1989. - 288 s.
Vanin G.A. Mikromehanika kompozicionnyh materialov. - Kiev: Nauk. dumka, 1985. - 304 s.
Alfutov N.A, Zinov’ev P.A., Popov B.G. Rascet mnogoslojnyh plastin i obolocek iz kompozicionnyh materialov. - M.: Masinostroenie, 1984. - 264 s.
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