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Existence and integral representation of solutions for plane deformations of a micropolar elastic solid with surface elasticity
Author(s) -
Gharahi Alireza,
Schiavone Peter
Publication year - 2020
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.201900228
Subject(s) - mathematics , boundary value problem , mathematical analysis , uniqueness , elasticity (physics) , robin boundary condition , free boundary problem , materials science , composite material
We consider a linear theory of elastic boundary reinforcement of a micropolar elastic solid subjected to plane‐strain deformations. The reinforcement consists of a thin micropolar elastic coating bonded to part of the boundary of the solid. The elastic properties of the coating incorporate both classical and micropolar bending, extension and twisting effects. Interior and exterior mixed boundary problems are formulated and analyzed using the boundary integral equation method. The boundary value problems are reduced to systems of singular integro‐differential equations to which Noether‐type theorems are shown to apply. We consider also the corresponding boundary value problems based on an alternative lower‐order shell model of the reinforcement. Finally, existence and uniqueness results are presented for the corresponding interior and exterior boundary value problems in the appropriate classical function spaces.