Green’s functions for transversely isotropic magnetoelectroelastic media

Hou, Peng; Ding, Hu; Chen, Jiangying

doi:10.1016/j.ijengsci.2004.08.015

Cited by 56 publications

(38 citation statements)

References 31 publications

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“…Liu et al [13] derived two-dimensional Green's functions for anisotropic magnetoelectroelastic solids with a crack. Hou et al [14] obtained the Green's functions for infinite and semi-infinite magnetoelectroelastic media, which are expressed in terms of elementary functions. Rojas-Diaz et al [15] derived two-dimensional (2D) and three-dimensional (3D) time harmonic Green's functions for anisotropic magnetoelectroelasticity by means of Radon-transformation.…”

Section: Introductionmentioning

confidence: 99%

Application of the extended traction boundary element-free method to the fracture of two-dimensional infinite magnetoelectroelastic solid

Feng

Han

et al. 2011

Sci. China Phys. Mech. Astron.

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A novel extended traction boundary element-free method is proposed to analyze the crack problems of two-dimensional infinite magnetoelectroelastic solid. An extended traction boundary integral equation only involving Cauchy singularity is firstly derived. Then, the extended dislocation densities on the crack surface are expressed as the combination of a characteristic term and unknown weight functions, and the radial point interpolation method is adopted to approximate the unknown weight functions. The numerical scheme of the extended traction boundary element-free method is further established, and an effective numerical procedure is used to evaluate the Cauchy singular integrals. Finally, the stress intensity factor, electric displacement intensity factor and magnetic induction intensity factor are computed for some selected crack problems that contain straight, curved and branched cracks, and good numerical results are obtained. At the same time, the fracture properties of these crack problems are discussed. boundary element-free method, boundary integral equation, radial point interpolation method, crack problem, magnetoelectroelastic materials PACS: 02.70.Pt, 46.50.+a, 62.60.Mk, 77.90.+k

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Section: Introductionmentioning

confidence: 99%

Application of the extended traction boundary element-free method to the fracture of two-dimensional infinite magnetoelectroelastic solid

Feng

Han

et al. 2011

Sci. China Phys. Mech. Astron.

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“…Wang and Shen [17] derived the general solution for three-dimensional transversely isotropic magneto-electroelastic media by using five potential functions and determined Green's functions for a half-space and the fundamental solution for a generalized dislocation. Green's functions for the two-dimensional problem have been obtained by Guan and He [18] by means of Almansi's theorem, while Green's functions for infinite, two-phase and semi-infinite magneto-electro-elastic composites have been derived and presented in [19]. The exact solution for the statically loaded three-dimensional multilayered rectangular simply supported plate of magnetoelectro-elastic composites has been computed by Pan [20] by means of the propagator matrix method.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

Milazzo¹,

Orlando²,

Alaimo³

2009

Smart Mater. Struct.

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Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the definition of the bending moment. Moreover, the influences of the electro-mechanic, magneto-mechanic and electromagnetic coupling on the stiffness of the bimorph stem from the computation of the beam equivalent stiffness constants. Free and forced vibration analyses of both multiphase and laminated magneto-electro-elastic composite beams are carried out to check the effectiveness and reliability of the proposed analytic solution.

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“…Jiang and Pan (2004) obtained the 2-D Green's function in terms of the Stroh formalism in an exact closed form for magnetoelectroelastic full-, half-, and bimaterial-planes with general anisotropy. Hou et al (2005) presented 3-D Green's functions of infinite, two-phase and semi-infinite transversely isotropic magnetoelectroelastic media in terms of mono-harmonic displacement functions for all cases of distinct eigenvalues and multiple eigenvalues. Ding et al (2005) obtained Green's functions for two-phase transversely isotropic magnetoelectroelastic media in the case of distinct eigenvalues, including 2-D Green's functions of a two-phase infinite plane and half-plane as well as 3-D counterparts.…”

Section: Introductionmentioning

confidence: 99%

Time-harmonic Green’s functions for anisotropic magnetoelectroelasticity

Rojas-Díaz

Sáez

García-Sánchez

et al. 2008

International Journal of Solids and Structures

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Two-dimensional (2-D) and three-dimensional (3-D) time-harmonic Green's functions for linear magnetoelectroelastic solids are derived in this paper by means of Radon-transform. Displacement field and electric and magnetic potentials in a fully anisotropic magnetoelectroelastic infinite solid due to a time-harmonic point force, point charge and magnetic monopole are obtained in form of line integrals over a unit circle in 2-D case and surface integrals over a unit sphere in 3-D case. This dynamic fundamental solution is then split into the sum of regular dynamic plus singular terms. The singular terms coincide with the Green's functions for the static problem and may be further reduced to closed form expressions. The proposed Green's functions can be used in the corresponding boundary element method (BEM) formulation.

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Green’s functions for transversely isotropic magnetoelectroelastic media

Cited by 56 publications

References 31 publications

Application of the extended traction boundary element-free method to the fracture of two-dimensional infinite magnetoelectroelastic solid

Application of the extended traction boundary element-free method to the fracture of two-dimensional infinite magnetoelectroelastic solid

An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

Time-harmonic Green’s functions for anisotropic magnetoelectroelasticity

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