Asymptotic investigation into linear hamiltonian differencial systems of the statics of elastic shells of revolution
DOI:
https://doi.org/10.7242/1999-6691/2011.4.2.13Keywords:
elasticity, theory of shells, Hamiltonian system, asymptotic analysisAbstract
We propose a method of constructing the asymptotic approximations to the solution of the governing equations of linear theory of shells of revolution in complex Hamiltonian form. Based on the Wasow approach, an algorithm for constructing symplectic transformations of the original system of linear differential equations in the canonical form is developed. Asymptotic expansions for the solutions of linear Hamiltonian differential systems of the statics of the shell of revolution are constructed.
Downloads
References
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.
Arnol’d V.I. Matematiceskie metody klassiceskoj mehaniki. - M. Nauka, 1989. - 472 s.
Grebennikov E.A. Metod usrednenia v prikladnyh zadacah. - M.: Nauka, 1986. - 256 s.
Vazov V. Asimptoticeskie razlozenia resenij obyknovennyh differencial’nyh uravnenij. - M.: Mir, 1968. - 464 s.
Dubrovin B.A., Novikov S.P., Fomenko A.T. Sovremennaa geometria: Metody i prilozenia. - M.: Nauka, 1979. - 760 s.
Gantmaher F.R. Teoria matric. - M.: Nauka, 1988. - 538 s.
Belman R. Vvedenie v teoriu matric. - M.: Nauka, 1976. - 352 s.
Kantorovic L.V., Akilov G.P. Funkcional’nyj analiz. - M.: Nauka, 1977. - 742 s.
Stenger F. Error Bounds for Asymptotic Solutions of Differential Equations, I. The Distinct Eigenvalue Case // J. Res. NBS, Math. and Math. Phys. - 1966. - V. 70B. - P. 167-186.
Stenger F. Error Bounds for Asymptotic Solutions of Differential Equations, II The General Case // J. Res. NBS, Math. and Math. Phys. - 1976. - V. 70B. - P. 187-210.
Kireev I.V, Nemirovskij U.V. Asimptoticeskij analiz uprugogo osesimmetricnogo sostoania tonkoj mnogoslojnoj ortotropnoj obolocki vrasenia: Prepr. No 5 / VC SO AN SSSR. Krasnoarsk, 1985. - 29 c.
Vasil’eva A.B. Asimptoticeskie metody v teorii obyknovennyh differencial’nyh uravnenij s malymi parametrami pri starsih proizvodnyh // UMN. - 1962. - T. 17, No 4. - S. 225-231.
Lizarev A.D., Klenov V.I. Analiticeskie resenia odnogo klassa uravnenij s polinomial’nymi koefficientami // Differencial’nye uravnenia. - 1978. - T. 14, No 12. - S. 2158-2173.
Biderman V.L. Mehanika tonkostennyh konstrukcij. - M.: Masinostroenie, 1977. - 488 s.
Cernyh K.F. Linejnaa teoria obolocek. - L.: Izd. LGU, 1962. - C. 1. - 274 s.
Cernyh K.F. Linejnaa teoria obolocek. - L.: Izd. LGU, 1964. - C. 2. - 296 s.
Friedrics K.O., Dressler R.F. Boundary-layer theory for elastic plates // Comm. Pure & Appl. Math. - 1961. - V. 14. - P. 1-33. DOI
Downloads
Published
Issue
Section
License
Copyright (c) 2011 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.