接線変位を考慮した二次元弾性接触問題

概要

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For the contact problems in the theory of two-dimemsional elasticity, in which the rigid punch is pressed on the elastic half plane, we usually use the contact condition between the vertical displacement and the punch profile, and ignore the effect of the tangential displacement. However, the surface deformation on the contact area is different from the punch profile because the deformation is given by the vector of both displacements. In the present paper, we analyze the same problem under the more rigorous contact condition in consideration of both displacements, as follows: (v)_<y=0>+kf'(x)・(u)_<y=0>=δ_0-kf(x), |x|≦a where (v)_<y=0> and (u)_<y=0> are the vertical and the tangential displacements on the contact area, respectively, δ_0 the indentation displacement and kf(x) the punch profile. We calculate numerically the two cases of the parabolic and the wedge punches, and discuss the effect of the tangential displacement on the stress state. In the results, we show that all of the contact stresses, the indentation forses and the indentation displacements are smaller than those in the conventional cases.
1990-05-25