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Analytical solutions of uniform extended dislocations and tractions over a circular area in anisotropic magnetoelectroelastic bimaterials

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Abstract

In this paper, we derive the analytical solutions in a three-dimensional anisotropic magnetoelectroelastic bimaterial space subject to uniform extended dislocations and tractions within a horizontal circular area. By virtue of the Stroh formalism and Fourier transformation, the final expression of solutions in the physical domain contains only line integrals over [0, 2π] rather than infinite integrals. As the reduced cases, the half-space and homogeneous full-space solutions can be directly derived from the present solutions. Also, in terms of material domains, the present solutions can be reduced to the piezoelectric, piezomagnetic, purely elastic materials with different symmetries of material property. To carry out numerical calculations, Gauss quadrature is adopted. In the numerical examples, the effect of different loading locations on the response at the interface is analyzed. It is shown that, when the magnetic traction or electric dislocation is applied, the physical quantities on the interface may not decrease monotonically as the loading area moves away from the interface. The distributions of different in-plane physical quantities on the upper and lower interfaces under various extended horizontal loadings are compared and the differences are discussed. The work presented in this paper can serve as benchmarks for future numerical studies in related research fields.

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Authors and Affiliations

  1. Dept. of Civil Engineering, University of Akron, Akron, OH, 44325, USA

    Y. -F. Zhao & E. Pan

  2. Dept. of Applied Mechanics, University of Science and Technology, 100083, Beijing, China

    X. -C. Shang

Authors
  1. Y. -F. Zhao
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  2. X. -C. Shang
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  3. E. Pan
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Corresponding author

Correspondence to E. Pan.

Additional information

The project was partially supported by the National Natural Science Foundation of China (10772024).

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Zhao, Y.F., Shang, X.C. & Pan, E. Analytical solutions of uniform extended dislocations and tractions over a circular area in anisotropic magnetoelectroelastic bimaterials. Acta Mech Sin 29, 73–84 (2013). https://doi.org/10.1007/s10409-013-0056-8

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  • DOI: https://doi.org/10.1007/s10409-013-0056-8

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