Acta Mechanica Solida Sinica

, Volume 30, Issue 2, pp 145–153 | Cite as

Static response of a layered magneto-electro-elastic half-space structure under circular surface loading

  • Jiangyi Chen
  • Junhong Guo


A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic, layered magneto-electro-elastic (MEE) structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coefficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coefficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading, are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.


Magneto-electro-elastic material Layered and half-space structure Stiffness matrix method System of vector functions Surface loading 


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  1. 1.
    S.J. Singh, Static deformation of a transversely isotropic multilayered half-space by surface loads, Phys. Earth Planet. Inter. 42 (1986) 263–273.CrossRefGoogle Scholar
  2. 2.
    K. Wang, Analysis and calculation of stresses and displacements in layered elastic systems, Acta Mech. Sin. 3 (1987) 251–260.CrossRefGoogle Scholar
  3. 3.
    E. Pan, M. Bevis, F. Han, et al., Surface deformation due to loading of a layered elastic half-space: a rapid numerical kernel based on a circular loading element, Geophys. J. Int. 171 (2007) 11–24.CrossRefGoogle Scholar
  4. 4.
    C.W. Nan, M.I. Bichurin, S.X. Dong, et al., Multiferroic magnetoelectric composites: historical perspective, status, and future directions, J. Appl. Phys. 103 (2008) 031101.CrossRefGoogle Scholar
  5. 5.
    A.A. Semenov, S.F. Karmanenko, B.A. Kalinikos, et al., Dual-tunable hybrid wave ferrite-ferroelectric microwave resonator, Electron. Lett. 42 (2006) 641–642.CrossRefGoogle Scholar
  6. 6.
    H.M. Wang, E. Pan, A. Sangghaleh, et al., Circular loadings on the surface of an anisotropic and magnetoelectroelastic half-space, Smart Mater. Struct. 21 (2012) 075003–075014.CrossRefGoogle Scholar
  7. 7.
    H.J. Chu, Y. Zhang, E. Pan, et al., Circular surface loading on a layered multiferroic half-space, Smart Mater. Struct. 20 (2011) 035020.Google Scholar
  8. 8.
    J. Ma, LL. Ke, Y.S. Wang, Frictionless contact of a functionally graded magneto-electro-elastic layered half-plane under a conducting punch, Int. J. Solids Struct. 51 (2014) 2791–2806.CrossRefGoogle Scholar
  9. 9.
    J. Ma, L.L. Ke, Y.S. Wang, Sliding frictional contact of functionally graded magneto- electro-elastic materials under a conducting flat punch, J. Appl. Mech. 82 (2015) 011009.CrossRefGoogle Scholar
  10. 10.
    J. Ma, S. EI-Borgi, L.L. Ke, et al., Frictional contact problem between a functionally graded magneto-electro-elastic layer and a rigid conducting flat punch with frictional heat generation, J. Thermal Stress. 39 (2016) 245–277.CrossRefGoogle Scholar
  11. 11.
    E. Pan, Static Green’s functions in multilayered half-spaces, Appl. Math. Model. 21 (1997) 509–521.CrossRefGoogle Scholar
  12. 12.
    J.Y. Chen, E. Pan, P.R. Heyliger, Static deformation of a spherically anisotropic and multilayered magneto-electro-elastic hollow sphere, Int. J. Solids Struct. 60–61 (2015) 66–74.Google Scholar
  13. 13.
    E. Pan, J.Y. Chen, M. Bevis, et al., An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth, Geophys. J. Int. 203 (2015) 2150–2181.CrossRefGoogle Scholar
  14. 14.
    L. Wang, I. Rokhlin S, Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media, Ultrasonics 39 (2001) 413–424.CrossRefGoogle Scholar
  15. 15.
    S.I. Rokhlin, L. Wang, Stable recursive algorithm for elastic wave propagation in layered anisotropic media: stiffness matrix method, J. Acoust. Soc. Am. 112 (2002) 822–834.CrossRefGoogle Scholar
  16. 16.
    J.T. Ratnanather, J.H. Kim, S.R. Zhang, et al., Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions, ACM Trans. Math. Softw. 40 (2014) 131–162.MathSciNetCrossRefGoogle Scholar
  17. 17.
    E. Pan, Exact solution for simply supported and multilayered magneto-electro-elastic plates, J. Appl. Mech. 68 (2001) 608–618.CrossRefGoogle Scholar
  18. 18.
    F. Ramirez, P.R. Heyliger, E. Pan, Free vibration response of two-dimensional magneto-electro-elastic laminated plates, J. Sound Vib. 292 (2006) 626–644.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2017

Authors and Affiliations

  1. 1.School of Mechanical EngineeringZhengzhou UniversityZhengzhouChina
  2. 2.Department of MechanicsInner Mongolia University of TechnologyHohhotChina

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