軸方向に6個の半円切欠きを有する丸棒の弾塑性ねじりについて : 第1報, 応力および弾塑性境界

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タイトル別名
  • On the Elastic-Plastic Torsion of a Shaft with Six Semi-Circular Longitudinal Grooves : 1st Report, Stress and Elastic-Plastic Boundary
  • ジク ホウコウ ニ 6コ ノ ハンエン キリカキ オ ユウスル マルボウ ノ ダン ソセイネジリ ニ ツイテ 1

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This problem seems to present great difficulties to an orthodox approach. To obtain the approximate solution the fundamental partial differential equation of the torsion can be transformed into the finite-difference equation. By placing the triangular net over the cross-section of the shaft, the suthor seeks to obtain the resultant shearing stress within elastic limit by Relaxation Method and describes various forms of the elastic-plastic boundary and the relation between the twisting moment and the twisting angle, when a plastic deformation takes place somewhere in its cross-section. The boundary thus described is compared with the one which Trefftz obtained in case of an infinite plate with a circular hole strained by a uniform shearing stress at infinity. Finally, it may be observed, these two boundaries almost coincide at the initial stage of appearance of plastic regions, but they are not in accordance any more with eath other as the area of plastic regions expands.

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