Stress distributions are evaluated for a semi-infinite elastic body having a spheroidal inhomogeneity under an all-around tension (axisymmetric uniform tension) at infinity. Boussinesq’s potential functions are used for the analysis. A special technique is employed for the traction-free condition on the free surface, where the ordinary Legendre functions are expressed in terms of the Bessel functions in cylindrical coordinates. A closed-form expression for the stress concentration factor is found for a special case of a needlelike inhomogeneity.

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