Premium
Solution of bonded bimaterial problem of two interfaces subjected to concentrated forces and couples
Author(s) -
Hasebe Norio,
Kato Seiji
Publication year - 2015
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.201400179
Subject(s) - stress functions , stress (linguistics) , strips , interface (matter) , function (biology) , plane (geometry) , mathematical analysis , mathematics , variable (mathematics) , geometry , materials science , composite material , boundary value problem , philosophy , linguistics , capillary number , evolutionary biology , capillary action , biology
A closed form solution is derived for the bonded bimaterial planes at two interfaces. The bonded planes with two interfaces are symmetric with respect to the interface, which is straight. A rational mapping function and complex stress functions are used for the analysis. The problem is reduced to a Riemann‐Hilbert problem. Two interfaces problem to derive the general solution is more difficult than one interface problem. As a demonstration of geometry, semi‐strips bonded at two parts at the ends of strips are considered. The solution of different geometrical shapes can be obtained by changing the mapping function. Concentrated forces and couples are applied to the each strip. The first derivative of complex stress functions which does not include integral terms with regard to variable of the mapping plane is achieved. Therefore, there is no need of numerical integration to calculate stress components and to determine unknown coefficients in complex stress function. This is very benefit. All elastic constants in complex stress functions are expressed by Dundurs’ parameters. Stress distributions are shown for different lengths of the interface.