Construction of green's function in terms of green's function of lower dimension

Indenbom, V. L.; Orlov, S.S.

doi:10.1016/0021-8928(68)90059-2

Cited by 14 publications

(4 citation statements)

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“…It should also be pointed out that the new closed-form expression for the tractions originated by a unit point force in the infinite transversal isotropic space, T ik , can also be used in the context of the theory of dislocations [26,38,41,42], where T ik has a work-conjugated interpretation of the displacements originated by a unit infinitesimal dislocation loop in this space.…”

Section: Távara Et Almentioning

confidence: 99%

“…In fact, such a decomposition is related to the Burgers formula [41], giving a displacement field originated by a unit dislocation loop. A generalization of the Burgers formula to general anisotropic materials was developed by Indenbom and Orlov [42], see also Lothe [38], and introduced in the framework of the symmetric Galerkin BEM by Rungamornrat [43] recently. According to these works, T ik can be decomposed as…”

Section: Somigliana Displacement Identitymentioning

confidence: 99%

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Unique real‐variable expressions of displacement and traction fundamental solutions covering all transversely isotropic elastic materials for 3D BEM

Távara

Ortiz

Mantič

et al. 2007

Numerical Meth Engineering

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SUMMARYA general, efficient and robust boundary element method (BEM) formulation for the numerical solution of three-dimensional linear elastic problems in transversely isotropic solids is developed in the present work. The BEM formulation is based on the closed-form real-variable expressions of the fundamental solution in displacements U ik and in tractions T ik , originated by a unit point force, valid for any combination of material properties and for any orientation of the radius vector between the source and field points. A compact expression of this kind for U ik was introduced by Ting and Lee (Q. J. Mech. Appl. Math. 1997; 50:407-426) in terms of the Stroh eigenvalues on the oblique plane normal to the radius vector. Working from this expression of U ik , and after a revision of their final formula, a new approach (based on the application of the rotational symmetry of the material) for deducing the derivative kernel U ik, j and the corresponding stress kernel i jk and traction kernel T ik has been developed in the present work. These expressions of U ik , U ik, j , i jk and T ik do not suffer from the difficulties of some previous expressions, obtained by other authors in different ways, with complex-valued functions appearing for some combinations of material parameters and/or with division by zero for the radius vector at the rotational-symmetry axis. The expressions of U ik , U ik, j , i jk and T ik have been presented in a form suitable for an efficient computational implementation. The correctness of these expressions and of their implementation in a three-dimensional collocational BEM code has been tested numerically by solving problems with known analytical solutions for different classes of transversely isotropic materials.

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Section: Távara Et Almentioning

confidence: 99%

Section: Somigliana Displacement Identitymentioning

confidence: 99%

Unique real‐variable expressions of displacement and traction fundamental solutions covering all transversely isotropic elastic materials for 3D BEM

Távara

Ortiz

Mantič

et al. 2007

Numerical Meth Engineering

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“…Since then, Mura (1963Mura ( , 1987, Kro¨ner (1972Kro¨ner ( , 1990, and Mazilu (1972) have done extensive work in this field. Willis (1965), Indenbom and Orlov (1968), Mura and Kinoshita (1971), and Pan and Chou (1976) have extended Green's functions to anisotropic materials. Recently, Wang (1992), Chen (1993), Nan (1994), Dunn (1994), Michelitsch (1997, Huang et al (1998), Gao andFan (1998), andLi (2002) have obtained Green's functions for piezomagnetic and piezoelectric solids.…”

Section: Basic Theories Of Micromechanicsmentioning

confidence: 99%

Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles

Yin

Sun

Chen

2006

Journal of the Mechanics and Physics of Solids

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“…The ring integral solution was also derived by Lifshitz & Rozenzweig (1947), and has been used to develop series solutions for the Green's function (Mura & Kinoshita, 1971). There are, of course, many indirectly related works, of which we mention only Indenbom & Orlov (1968), who obtained the Green's function in terms of lower dimensional Green's functions. This paper describes a related procedure to generate Green's functions for the time harmonic equations of theories with extra field variables.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and poroelastic solids

Norris

1994

Proc. R. Soc. Lond. A

105

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A procedure is described to generate fundamental solutions or Green’s functions for time harmonic point forces and sources. The linearity of the field equations permits the Green’s function to be represented as an integral over the surface of a unit sphere, where the integrand is the solution of a one-dimensional impulse response problem. The method is demonstrated for the theories of piezoelectricity, thermoelasticity, and poroelasticity. Time domain analogues are discussed and compared with known expressions for anisotropic elasticity.

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Construction of green's function in terms of green's function of lower dimension

Cited by 14 publications

References 1 publication

Unique real‐variable expressions of displacement and traction fundamental solutions covering all transversely isotropic elastic materials for 3D BEM

Unique real‐variable expressions of displacement and traction fundamental solutions covering all transversely isotropic elastic materials for 3D BEM

Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles

Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and poroelastic solids

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