Hamiltonian formalization of constitutive relations of the linear theory of elastic shells of revolution
DOI:
https://doi.org/10.7242/1999-6691/2010.3.4.35Keywords:
elasticity, theory of shells, Hamiltonian systemAbstract
We propose a method to construct constitutive relations of the linear theory of shells of revolution in the complex Hamiltonian form. Based on Lagrange's variational principle, a model of an elastic multilayer orthotropic shell of revolution has been constructed. In this model, kinematic assumptions are made separately for each of the amplitudes of the harmonics in expansion of the field functions of the mechanical problem in a complex Fourier series. Explicit expressions have been obtained for the coefficients and right-hand sides of the complex Hamiltonian system of equations of the statics of the shell of revolution using its rigidity characteristics and acting forces.
Downloads
References
Biderman V.L. Mehanika tonkostennyh konstrukcij. - M.: Masinostroenie, 1977. - 488 s.
Arnol’d V.I. Matematiceskie metody klassiceskoj mehaniki. - M. Nauka, 1989. - 472 s.
Kireev I.V., Nemirovskij U.V. Gamil’tonov podhod k reseniu linejnyh zadac uprugih obolocek vrasenia // Cislennye metody resenia zadac teorii uprugosti i plasticnosti: Tr. X Vsesosuz. konf. - Novosibirsk, 1988. - S. 115-121.
Kireev I.V. Simmetricnye cislennye metody resenia kraevyh zadac dla sistem obyknovennyh differencial’nyh uravnenij // Modelirovanie v mehanike splosnyh sred: Mezvuz. sb. naucn. statej. - Krasnoarsk, 1992. - S. 81-91.
Kireev I.V. Kraevye zadaci dla gamil’tonovyh sistem obyknovennyh differencial’nyh uravnenij: Prepr. No 11 / VC SO AN SSSR. - Krasnoarsk, 1990. - 31 c.
Andreev A.N., Nemirovskij U.V. K teorii uprugih mnogoslojnyh anizotropnyh obolocek // Izv. RAN. MTT. - 1977, No 5. - S. 87-96.
Cernyh K.F. Linejnaa teoria obolocek: V 2-h c. - Izd. LGU, 1962. - C. 1. - 274 s.
Cernyh K.F. Linejnaa teoria obolocek: V 2-h c. - Izd. LGU, 1964. - C. 2. - 296 s.
Parton V.Z., Perlin P.I. Metody matematiceskoj teorii uprugosti. - M.: Nauka, 1981. - 688 s.
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.
Galeev E.M., Tihomirov V.M. Optimizacia. - M.: Elitorial URSS, 2000. - 320 s.
Kantorovic L.V., Akilov G.P. Funkcional’nyj analiz. - M.: Nauka, 1977. - 742 s.
Downloads
Published
Issue
Section
License
Copyright (c) 2010 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
