A general solution to some plane problems of micropolar elasticity

William E. Warren, Esben Byskov

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    14 Citationer (Scopus)

    Abstract

    We obtain a general solution to the field equations of plane micropolar elasticity for materials characterized by a hexagonal or equilateral triangular structure. These materials exhibit 3-fold symmetry in the plane and the elastic response is isotropic. Utilizing two displacement potential functions, the solution is obtained in terms of two analytic functions and a third function satisfying the modified homogeneous Helmholtz equation. Expressions for the two-dimensional components of displacement, stress, and couple stress, along with the resultant force on a contour, are presented.We observe that micropolar effects are most significant in material regions subjected to large deformation gradients. Specific results are presented for the classical crack problem, the half plane loaded uniformly on the surface, Flamant's problem, and the circular cylinder compressed by equal and opposite oncentrated forces.
    OriginalsprogEngelsk
    TidsskriftEuropean Journal of Mechanics A - Solids
    Vol/bind27
    Udgave nummer1
    Sider (fra-til)18-27
    Antal sider10
    ISSN0997-7538
    DOI
    StatusUdgivet - 2008
    BegivenhedThe American Academy of Mechanics Conference - New Orleans, Louisiana, USA
    Varighed: 17 jun. 200820 jun. 2008
    Konferencens nummer: 1

    Konference

    KonferenceThe American Academy of Mechanics Conference
    Nummer1
    Land/OmrådeUSA
    ByNew Orleans, Louisiana
    Periode17/06/200820/06/2008

    Bibliografisk note

    Udgivelsesdato: January 2008
    Volumne: 27

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