分布した不適合度による応力について : 平面問題(昭和25年11月造船協会秋季講演会)

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Stress distribution due to the distributed incompatibility is studied. Total strain (s_x, s_y, γ_s) which satisfies the condition of compatibility consists of two strains, the elastic strain (s_x', s_y', γ_s') and the additional strain (s_x", s_y", γ_s"). The elastic or the additional strain does not satisfy the condition of compatibility by itself. Fundamental relations are as follows : - (1) Strain [numerical formula] (1) (2) Condition of compatibility [numerical formula] (2) (3) Stress-strain relations [numerical formula] (3) where σ_x, σ_y, σ_s : stress components E : Young's modulus G : modulus of rigidity ν : Poisson's ratio (4) Condition of equilibrium of stress [numerical formula] (4) The stress function F must satiafy the next equstion, ∇^4F (x, y)=E・R (x, y) (5) where, [numerical formula] (5)'R (x, y) will be called the incompatibility at the point (x, y). The relation between the stress function and the stress components are, [numerical formula] (6) The general solution of Eq. (5) is, [numerical formula] (7) where [numerical formula] B.H. : Biharmonic function The integration is performed over the domain S where the incompatibility exists. (7) will be changed to, [numerical formula] (8) where [numerical formula] (8) Thus the stress distribution due to distributed incompatibility can be calculated by the expression (7) or (8). The distributed incompatibility is equal to the distributed rotational dislocation and also equal to the combination of the distributed dilatation and the two displacemental dislocations. Next the special solution convenient for the problem of axial symmetry is obtained. Some applications of this theorem for the thermal stress and plasticity are also carried out.
社団法人日本船舶海洋工学会の論文

分布した不適合度による応力について : 平面問題(昭和25年11月造船協会秋季講演会)

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