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A general solution to some plane problems of micropolar elasticity

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Authors:
  • Warren, William E. ;
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    Dept. of Mechanical Engineering, University of New Mexico
  • Byskov, Esben
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    Department of Civil Engineering, The Faculty of Engineering and Science, Aalborg University
DOI:
10.1016/j.euromechsol.2007.05.006
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.
Type:
Conference paper
Language:
English
Published in:
European Journal of Mechanics a - Solids, 2008, Vol 27, Issue 1, p. 18-27
Keywords:
Micropolarity; Complex functions; Helmholtz equation
Main Research Area:
Science/technology
Publication Status:
Published
Review type:
Peer Review
Conference:
The American Academy of Mechanics Conference, 2008
Submission year:
2008
Scientific Level:
Scientific
ID:
2167733582

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