In memory of Professor Alexander A. Amosov (1939–2009).
A Vekua-type linear theory of thick elastic shells†
Article first published online: 2 JUL 2013
Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Special Issue: Refined theories of plates and shells
Volume 94, Issue 1-2, pages 164–184, January 2014
How to Cite
Zhavoronok, S. (2014), A Vekua-type linear theory of thick elastic shells. Z. angew. Math. Mech., 94: 164–184. doi: 10.1002/zamm.201200197
- Issue published online: 7 JAN 2014
- Article first published online: 2 JUL 2013
- Manuscript Accepted: 9 JUN 2013
- Manuscript Revised: 3 MAY 2013
- Manuscript Received: 30 SEP 2012
- Russian Foundation for Basic Researches. Grant Number: No.13-01-00446-a
- Thick shells;
- theory of Vekua type;
- variational formalism;
- Lagrange equations of the second kind.
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.