Exact and asymptotic stability analyses of a coated elastic half-space

Authors
Citation
Zx. Cai et Yb. Fu, Exact and asymptotic stability analyses of a coated elastic half-space, INT J SOL S, 37(22), 2000, pp. 3101-3119
Citations number
9
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanical Engineering
Journal title
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
ISSN journal
0020-7683 → ACNP
Volume
37
Issue
22
Year of publication
2000
Pages
3101 - 3119
Database
ISI
SICI code
0020-7683(200005)37:22<3101:EAASAO>2.0.ZU;2-V
Abstract
We study the buckling of a pre-stressed coated elastic half-space with the aid of the exact theory of nonlinear elasticity, treating the coating as an elastic layer and using its thickness as a small parameter. Two asymptotic limits are identified: A(jilk) = O(khA(jilk)) and A(jilk) = O(k(3)h(3)A(ji lk)), where A(jilk) and A(jilk) are the elastic moduli for the half-space a nd the coating, respectively, k is a mode number and h the thickness of coa ting. The first limit corresponds to the case when the coating and half-spa ce exert maximum effect on each other and the second limit corresponds to t he classical model equation for a plate supported by an elastic foundation. For each limit the leading order bifurcation condition is derived using tw o different methods. In the first method we derive the leading order govern ing equations first and then obtain from them the bifurcation condition. In the second method we derive the exact bifurcation condition first and then take the thin-layer limit. The two methods are found to yield the same res ults, assuring us that the leading order governing equations are asymptotic ally consistent. These leading order governing equations in the thin-layer limit are then compared with those assumed or derived by previous researche rs. (C) 2000 Elsevier Science Ltd. All rights reserved.