Open AccessExtraction of consistent shell theory equations from 3D theory of elasticity
Author(s) -
Evgeny M. Zveryaev
Publication year - 2019
Publication title -
stroitelʹnaâ mehanika inženernyh konstrukcij i sooruženij
Language(s) - English
Resource type - Journals
eISSN - 2587-8700
pISSN - 1815-5235
DOI - 10.22363/1815-5235-2019-15-2-135-148
Subject(s) - curvilinear coordinates , elasticity (physics) , mathematics , operator (biology) , banach space , integrable system , mathematical analysis , geometry , physics , biochemistry , chemistry , repressor , gene , transcription factor , thermodynamics
Aims of research. Derivation of consistent equations of the theory of thin elastic shells without hypotheses and stress averaging over the shell thickness. Methods. Using the iterative method of Saint-Venant - Picard - Banach, the three-dimensional problem of the theory of elasticity is solved without any hypotheses. By the principle of compressed mappings, the solution converges asymptotically, regardless of the choice of the values of the initial approximation. Results. A method has been developed for integrating the spatial equations of the theory of elasticity in curvilinear coordinates for a thin shell. The presence of a small parameter allows the integration of the system of equations in such a way that the output data of the first operator is input to the next operator, etc., dividing the original complex operator into a sequence of simple integrable Picard type operators. Each equation contains terms of only one asymptotic order.