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

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.