Three-dimensional Stress Concentration Around a Cylindrical Hole in a Semi- Infinite Elastic Body
Year: 1965
Type: report
Abstract: We present a three-dimensional solution, exact with- in classicalelastostatics, for the stresses and deformations arising in a halfspace with a semi-infinite transverse cylindrical hole; if the body--at infinite distances from its cylindrical boundary--is subjected to anarbitrary, uniformplane field of stress that is parallel to the bounding plane.The solution in integral form was deduced with the aid of the Papkovich stress functions bymeans of an especially adapted, unconventional, integral-transform technique.Numerical results for the nonvanishing stresses along the boundary of the hole and for the normal displacement at the plane bounda- ry, corresponding to several values of Poisson's ratio, are also inc luded.These results exhibit in detail the three- dimensional stress boundary layer that emerges near the edges of the hole in the analogous problem for a plate of finite thickness, as the ratio of the plate thickness to the di- ameter of the hole grows beyond bounds.The results obtained illustrate the limitations inherent in the two-dimensional plane-strain treatment of the spatial plane problem; in addition, they are relevant to failure considerations and are of interest in connection with experimental stress analysis. I. THEORETICAL ANALYSIS' .. WR.(P, C) = 3(y) -C(7) 7Kz(.yp)sin •y< + 73D(7) 02(7, p) e-•Y< d.y.(53) ,--X-.
DOI: 10.2172/4585663
Authors: C.K. Youngdahl, E. Sternberg
Institution: Argonne National Laboratory
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4237480748