Transverse Bending of an Infinite Plate with a Cylindrical Circular Hole by the Three-Dimensional Theory of Elasticity

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  • 円孔をもつ無限板の曲げ : 三次元弾性理論による平面曲げ問題
  • エンコウ オ モツ ムゲンバン ノ マゲ

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In this paper, a three-dimensional solution for an infinite plate with a cylindrical circular hole under transverse bending is given. It is represented by a combination of the solution which is regular in the outside of a hole and the solution which is regular in the infinite plate with finite thickness, and satisfies the boundary conditions on a hole and the surfaces of the plate. Numerical results are given when the ratios of hole diameter (2a) to plate thickness (2h) are about 0.3, 1, and 3. The results show that the smaller a/h becomes, the larger the stress concentration factor becomes as compared with the value obtained by the theory of thin plates, and the more the circumferential stress over the thickness of the plate at the ends of diameter parallel to the axis of the applied bending moment deviates from a linear distribution.

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