Abstract
This paper presents an asymmetric solution for the stress distributions around a hemispherical pit at a plane surface of a semi-infinite body under uniaxial tension. In this analysis, eight stress functions were chosen so as to fulfill the boundary conditions automatically, both at the plane surface and at infinity. On the other hand, the remaining boundary conditions at the surface of the pit were satisfied with the aid of the “half-range expansion” technique. Numerical results are given for the variations around the pit and along the z-axis and compared with the corresponding results under biaxial tension.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Eubanks, R. E., Stress concentration due to a hemispherical pit at a free surface. J. Appl. Mech. 21 (1954) 57–62.
Ling, C. B., On the stresses in a simi-infinite solid having a hemispherical pit. Annals of Academia Sinica. (Taiwan, China) 2 (1955) 39–44.
Fujita, T., et al., On the stress concentration due to a hemispherical pit. Scientific and Engineering Reports of the Defense Academy (in Japanese) 13 (1975) 599–619.
Atsumi, A. and Itou, S., On the stress concentration due to a hemispherical pit. Preprint of Japan Soc. Mech. Engr. (in Japanese) 761–1 (1976) 343–346.
Tsuchida, E. and Nakahara, I., On the stresses in a semi-infinite solid having a hemispherical pit subjected to an axisymmetric pressure. Trans. Japan Soc. Mech. Engr. (in Japansese) 33 (1967) 696–705.
Fujita, T., et al., Stresses in a thick plate having a hemispherical pit under circular bending. Proc. 25th Japan Nat. Congr. Appl. Mech. (1975) 715–727.
Fujita, T., et al., Stress concentration due to a hemispherical pit at a free surface of a thick plate under all-around tension. Bull. Japan Soc. Mech. Engr. 21 (1978) 561–565.
Saito, K. and Nakahara, I., Stresses in a semi-infinite body having a hemispherical pit under uniaxial tension. Trans. Japan Soc. Mech. Engr. (in Japanese) 33 (1967) 343–350.
Todohunter, I. and Pearson, K., A History of the Theory of Elasticity and of the Strength of Materials, Vol. 2 Part II, Dover Publications, New York 1960, p. 242.
Sadowsky, M. A. and Sternberg, E., Stress concentration around an ellipsoidal cavity in an infinite body under arbitrary plane stress perpendicular to the axis of revolution of cavity. J. Appl. Mech. 14 (1947) 191–201.
Hobson E. W., The Theory of Spherical and Ellipsoidal Harmonics. Chelsea, New York 1965, p. 98.
Tsuchida, E. and Nakahara, I., Stress concentration around a spherical cavity in a semi-infinite elastic body under uniaxial tension. Bull. Japan Soc. Mech. Engr. 17 (1974) 1207–1217.
Tsuchida, E. and Nakahara, I., Three-dimensional stress concentration around a spherical cavity in a thick plate under uniaxial tension. Bull. Japan Soc. Mech. Engr. 19 (1976) 1107–1114.
Tsuchida, E., et al., Stresses in a thick plate containing an eccentric spherical cavity under uniaxial tension. Bull. Japan Soc. Mech. Engr. 19 (1976) 838–848.
Tsuchida, E., et al., On the asymmetric problem of elastic theory for an infinite elastic solid containing some spherical cavities. (1st report—an infinite solid containing two spherical cavities). Bull. Japan Soc. Mech. Engr. 19 (1976) 993–1000 and 22 (1979) 141–147.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fujita, T., Tsuchida, E. & Nakahara, I. Asymmetric problem of a semi-infinite body having a hemispherical pit under uniaxial tension. J Elasticity 12, 177–192 (1982). https://doi.org/10.1007/BF00042214
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00042214