### Abstract

The three-dimensional Navier's equations are solved analytically for the case of a cylindrical inclusion of radius "a" which is embedded in a plate of arbitrary thickness 2 h. Both the plate and the inclusion are assumed to be of homogeneous and isotropic materials with different material properties. Perfect bonding is assumed to prevail at the interface. As to loading, a uniform tension is applied in the plane of the plate at points remote from the inclusion. The analysis shows all stresses including the octahedral shear stress to be sensitive to the radius to half thickness ratio (a/h) as well as the material properties. In the limit, as (μ_{2}/μ_{1})→ 0 and as μ_{2}μ_{1}→ 1 (where μ_{2} and μ_{1} are, respectively, the shear moduli of the inclusion and of the plate) the results for a cylindrical hole and a continuous plate are recovered. Similarly as (a/h) → ∞ (very thin plate) the plane stress solution is recovered. Moreover, for (μ_{2}/μ_{1})>1.0 the presence of a stress singularity near the point of intersection of the inclusion and the free surface of the plate is confirmed by the numerical results.

Original language | English (US) |
---|---|

Pages (from-to) | 129-146 |

Number of pages | 18 |

Journal | International Journal of Fracture |

Volume | 39 |

Issue number | 1-3 |

DOIs | |

State | Published - Mar 1989 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics

### Cite this

*International Journal of Fracture*,

*39*(1-3), 129-146. https://doi.org/10.1007/BF00047446

**The three-dimensional stress field around a cylindrical inclusion in a plate of arbitrary thickness.** / Penado, F E; Folias, E. S.

Research output: Contribution to journal › Article

*International Journal of Fracture*, vol. 39, no. 1-3, pp. 129-146. https://doi.org/10.1007/BF00047446

}

TY - JOUR

T1 - The three-dimensional stress field around a cylindrical inclusion in a plate of arbitrary thickness

AU - Penado, F E

AU - Folias, E. S.

PY - 1989/3

Y1 - 1989/3

N2 - The three-dimensional Navier's equations are solved analytically for the case of a cylindrical inclusion of radius "a" which is embedded in a plate of arbitrary thickness 2 h. Both the plate and the inclusion are assumed to be of homogeneous and isotropic materials with different material properties. Perfect bonding is assumed to prevail at the interface. As to loading, a uniform tension is applied in the plane of the plate at points remote from the inclusion. The analysis shows all stresses including the octahedral shear stress to be sensitive to the radius to half thickness ratio (a/h) as well as the material properties. In the limit, as (μ2/μ1)→ 0 and as μ2μ1→ 1 (where μ2 and μ1 are, respectively, the shear moduli of the inclusion and of the plate) the results for a cylindrical hole and a continuous plate are recovered. Similarly as (a/h) → ∞ (very thin plate) the plane stress solution is recovered. Moreover, for (μ2/μ1)>1.0 the presence of a stress singularity near the point of intersection of the inclusion and the free surface of the plate is confirmed by the numerical results.

AB - The three-dimensional Navier's equations are solved analytically for the case of a cylindrical inclusion of radius "a" which is embedded in a plate of arbitrary thickness 2 h. Both the plate and the inclusion are assumed to be of homogeneous and isotropic materials with different material properties. Perfect bonding is assumed to prevail at the interface. As to loading, a uniform tension is applied in the plane of the plate at points remote from the inclusion. The analysis shows all stresses including the octahedral shear stress to be sensitive to the radius to half thickness ratio (a/h) as well as the material properties. In the limit, as (μ2/μ1)→ 0 and as μ2μ1→ 1 (where μ2 and μ1 are, respectively, the shear moduli of the inclusion and of the plate) the results for a cylindrical hole and a continuous plate are recovered. Similarly as (a/h) → ∞ (very thin plate) the plane stress solution is recovered. Moreover, for (μ2/μ1)>1.0 the presence of a stress singularity near the point of intersection of the inclusion and the free surface of the plate is confirmed by the numerical results.

UR - http://www.scopus.com/inward/record.url?scp=0024630054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024630054&partnerID=8YFLogxK

U2 - 10.1007/BF00047446

DO - 10.1007/BF00047446

M3 - Article

AN - SCOPUS:0024630054

VL - 39

SP - 129

EP - 146

JO - International Journal of Fracture

JF - International Journal of Fracture

SN - 0376-9429

IS - 1-3

ER -