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On Airy functions and stresses in nonisotropic heterogeneous 2d‐elasticity
Author(s) -
Kulikov A.,
Nazarov S.A.,
Sweers G.
Publication year - 2008
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.200800094
Subject(s) - elasticity (physics) , displacement field , infinitesimal strain theory , cauchy stress tensor , airy function , mathematics , mathematical analysis , tensor (intrinsic definition) , classical mechanics , physics , pure mathematics , thermodynamics , finite element method
Problems in elasticity are described by relations between the displacement field u , the strain or deformation tensor ε, and the stress tensor σ. In 2D elasticity and if volume forces are absent, one may also consider an elastic potential. We explain these settings for a domain Ω with finitely many holes. On such domains the problem for the displacement and the potential problem are not necessarily equivalent. We will also recall the relation between these quantities. We conclude the paper with the potential setting for some specific problems in semi‐periodic domains with infinite many holes. Also the setting for non‐smooth domains is addressed.