A general solution to some plane problems of micropolar elasticity |
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| Institution: | 1. Dept. of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, USA;2. Dept. of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark;1. Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China;2. School of Aerospace, Tsinghua University, Beijing 100083, PR China;1. School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland;2. School of Medicine and Medical Science, University College Dublin, Belfield, Dublin 4, Ireland;3. Health Service Executive, Dublin, Ireland |
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| 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 concentrated forces. |
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