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A Vekua‐type linear theory of thick elastic shells
Author(s) -
Zhavoronok S.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200197
Subject(s) - formalism (music) , mathematics , type (biology) , tensor (intrinsic definition) , cauchy stress tensor , anisotropy , algebra over a field , mathematical analysis , geometry , pure mathematics , physics , art , musical , ecology , quantum mechanics , visual arts , biology
This paper presents an effective variational formalism of construction of the thick anisotropic linear shell theory of Vekua‐type of an arbitrary order. The dynamic equations are formulated as the Lagrange equations of the second kind, independent from expansion functions. The asymmetric stress tensor is used to obtain the compact form of the dynamic equations similar to the classical shell theories. The proposed approach allows one for computer‐aided derivation of all equations using computer algebra software supporting main tensor operations. Some solutions of test problems are presented.