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The Transmission of Force through a Fluid‐Solid Interface
Author(s) -
Aderogba K.,
Adeboye E. A.
Publication year - 1978
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.19780580208
Subject(s) - isotropy , fluid pressure , mechanics , elasticity (physics) , compressibility , herschel–bulkley fluid , displacement (psychology) , body force , harmonic function , traction (geology) , poromechanics , classical mechanics , mathematical analysis , displacement field , physics , elementary function , mathematics , fluid mechanics , materials science , geology , finite element method , thermodynamics , psychology , porous medium , quantum mechanics , geomorphology , porosity , composite material , psychotherapist
Consideration is given to a fluid‐solid system consisting of a semi‐infinite incompressible viscous fluid overlying an isotropic semi‐infinite elastic solid. A uniform force is operative within a subregion of the fluid or the solid. It is shown within the limits of the linear theories of elasticity and hydrodynamics that the fields in the two phases may be easily expressed in terms of the corresponding fields in the homogeneous infinite media. In particular, the interface value of the displacement of the solid due to a force operative in the overlying fluid depends on both the velocity and pressure fields of the same force in an infinite fluid, the former proportionally, and the latter through integration. In contrast, the associated interface traction is always proportional to the infinite‐fluid result, regardless of the geometry of the region of application of the force, and for any force distribution. This multiplicative property can however be shown to exhibit itself in the displacement field also, provided that the infinite‐fluid velocity is derivable by differentiation from a harmonic potential. A uniformity of method is maintained by initially representing the solutions for both the fluid and the solid in terms of Papkovitch‐Neuber functions, which are known to be superior to other stress functions, because of their completeness and harmonicity.