二次計画法を用いた平面弾塑性問題の一解析　（続）　　偏差応力テンソルの第３不変量Ｊ′３を含む７次の降伏関数を用いた場合

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  • An analysis of the two-dimensional elastic-plastic stress problem using quadratic programming. Second report. The case of adopting the seventh-degree yield function containing the third invariant of the deviatoric stress tensor.
  • 2ジ ケイカクホウ オ モチイタ ヘイメン ダンソセイ モンダイ ノ イチカイ

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An application of the finite element method to the elastic-plastic analysis is presented using the quadratic programing technique with bounded variables. A yield function in the theory of plasticity is given in terms of not only the second invariant of the deviatoric stress tensor J'2 but also of the third J'3. Two numerical examples are shown for the stress concentration problem under the plane stress state. The result obtained by the yield function with J'3 is compared with that obtained by the conventional J2 theory. The difference of the distribution of stresses and strains between two theories depends on the stress ratio. The magnitude of the stresses and strains obtained by the theory with J'3 is larger than that by the conventional one. The distribution of the larger effective plastic strain in a cross-section is calculated by the present theory compared with that obtained by using J2 theory especially in the range of the large plastic deformation.

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