### Abstract

Original language | English |
---|---|

Pages (from-to) | 3463-3470 |

Number of pages | 8 |

Journal | International Journal of Solids and Structures |

Volume | 46 |

Issue number | 18-19 |

DOIs | |

Publication status | Published - Sep 2009 |

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### Keywords

- elasticity
- linear elasticity
- three-dimensional elasticity solution
- analytical solutions
- functionally graded materials
- transversely isotropic material

### Cite this

*International Journal of Solids and Structures*,

*46*(18-19), 3463-3470. https://doi.org/10.1016/j.ijsolstr.2009.06.001

**Revisiting displacement functions in three-dimensional elasticity of inhomogeneous media.** / Kashtalyan, M.; Rushchitsky, J. J.

Research output: Contribution to journal › Article

*International Journal of Solids and Structures*, vol. 46, no. 18-19, pp. 3463-3470. https://doi.org/10.1016/j.ijsolstr.2009.06.001

}

TY - JOUR

T1 - Revisiting displacement functions in three-dimensional elasticity of inhomogeneous media

AU - Kashtalyan, M.

AU - Rushchitsky, J. J.

PY - 2009/9

Y1 - 2009/9

N2 - The paper presents a three-dimensional solution to the equilibrium equations for linear elastic transversely isotropic inhomogeneous media. We assume that the material has constant Poisson’s ratios, and its Young’s and shear moduli have the same functional form of dependence on the co-ordinate normal to the plane of isotropy. We show, apparently for the first time, that stresses and displacements in such an inhomogeneous transversely isotropic elastic solid can be represented in terms of two displacement functions which satisfy the second- and fourth-order partial differential equations. We examine and discuss key aspects of the new representation; they include the relationship between the new displacement functions and Plevako’s solution for isotropic inhomogeneous material with constant Poisson’s ratio as well as the application of the new representation to some important classes of three-dimensional elasticity problems. As an example, the displacement function is derived that can be used to determine stresses and displacements in an inhomogeneous transversely isotropic half-space which is subjected to a concentrated force normal to a free surface and applied at the origin (Boussinesq’s problem).

AB - The paper presents a three-dimensional solution to the equilibrium equations for linear elastic transversely isotropic inhomogeneous media. We assume that the material has constant Poisson’s ratios, and its Young’s and shear moduli have the same functional form of dependence on the co-ordinate normal to the plane of isotropy. We show, apparently for the first time, that stresses and displacements in such an inhomogeneous transversely isotropic elastic solid can be represented in terms of two displacement functions which satisfy the second- and fourth-order partial differential equations. We examine and discuss key aspects of the new representation; they include the relationship between the new displacement functions and Plevako’s solution for isotropic inhomogeneous material with constant Poisson’s ratio as well as the application of the new representation to some important classes of three-dimensional elasticity problems. As an example, the displacement function is derived that can be used to determine stresses and displacements in an inhomogeneous transversely isotropic half-space which is subjected to a concentrated force normal to a free surface and applied at the origin (Boussinesq’s problem).

KW - elasticity

KW - linear elasticity

KW - three-dimensional elasticity solution

KW - analytical solutions

KW - functionally graded materials

KW - transversely isotropic material

U2 - 10.1016/j.ijsolstr.2009.06.001

DO - 10.1016/j.ijsolstr.2009.06.001

M3 - Article

VL - 46

SP - 3463

EP - 3470

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 18-19

ER -