Please use this identifier to cite or link to this item: https://scholarhub.balamand.edu.lb/handle/uob/1804
Title: A correspondence between compressible and incompressible plane elastostatics
Authors: Honein, Tanios
Honein, Elie 
Najjar, Michel
Rai, Habib 
Affiliations: Department of Mechanical Engineering 
Department of Mechanical Engineering 
Department of Mechanical Engineering 
Department of Mechanical Engineering 
Issue Date: 2019
Part of: Journal of acta mechanica
Volume: 230
Issue: 7
Start page: 2549
End page: 2562
Abstract: 
It is shown that a heretofore seemingly unnoticed correspondence (or analogy) exists between the traction boundary value problem for compressible media and the displacement boundary value problem for incompressible media occupying the same domain, in plane, isotropic, linear elastostatics. The Airy stress function, which satisfies equilibrium identically, has to be biharmonic in order to satisfy the compatibility condition in a compressible body. Correspondingly, a displacement potential function, which satisfies the incompressibility condition identically, has to be biharmonic in order to satisfy equilibrium. Since Stokes flow is governed by identical relations as incompressible plane elasticity, if displacement is interpreted as velocity and the shear modulus as dynamic viscosity, the correspondence extends to that between compressible elasticity and Stokes flow for boundary value problems indicated above. This analogy provides a rare example of a constrained system which is equivalent to the same system without the constraint.
URI: https://scholarhub.balamand.edu.lb/handle/uob/1804
Ezproxy URL: Link to full text
Type: Journal Article
Appears in Collections:Department of Mechanical Engineering

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