Couple-Stresses Elastic Solution of a Plate Bounded by an Elliptical Hole and Subject to Uniform Tension along the Minor Axis
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概要
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Couple-stresses solutions are obtained for an infinite tension plate bounded at the interior by an elliptical hole with the static equilibrating tractions. The normal tension tension in the plate is uniform along the minor axis. Elliptical coordinates are used in order that the boundary may be described by a coordinate and all equations for the couple-stresses theory of elasticity are derived in such coordinates. The selection of the Mathieu's functions and the form of weighting functions in the boundary conditions match a particular class of boundary values which reduces upon limiting processes to three special cases. The first two cases are ones with free stresses on the interior boundary: the couple-stresses solution for the degenerate circle and the classical solution for the elliptical hole. The third one is the degenerate crack with vanishing values of normal stress and couple-stress, but with nonvanishing shear stress on the interior boundary. Of particular interest is the problem of a crack as a degenerated ellipse for its immediate practical value in the study of fracture strength in the presence of couple-stresses. The couple-stresses solutions may be obtained for an infinite elastic plate with static equilibrating traction prescribed elliptical hole under various biaxial fields of stresses at infinity, by means of the superposition principle of solution in the cited reference and in this paper, Due to the similarity in the method of solution in this paper and in the reference, only the relevant results are listed in this paper.
- 社団法人日本材料学会の論文
- 1974-01-15
著者
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Hsu Y.c.
Department Of Mechanical Engineering The University Of New Mexico
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WANG W.J.
Brown and Root, Inc.
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JU F.D.
Department of Mechanical Engineering, the University of New Mexico
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Wang W.j.
Brown And Root Inc.