Zastosowanie metody perturbacji do analizy plastycznego płynięcia ośrodka typu Coulomba w stanie osiowej symetrii - IZBICKI, Ryszard (Engineering Transactions, 1970)
Application of the perturbation method to the analysis of the plastic flow of a Coulomb type body in an axially symmetric state This paper is concerned with the plastic f10w of a perfect rigid-plastic medium of the Coulomb type in the case of axial symmetry. The influence of the gravity force and the adjoint law of f10w being assumed as a physical law. The solution is obtained by assuming that the state of stress corresponds to the corners or the Tresca (Coulomb) hexagon for which the Haar-Karman principle is satisfied. Then, the static and kinematic equations are of the hyperbolic type and the characteristics of the two set s of equations coincide. The problems are solved by the perturbation method with reference to the initial characteristics as proposed in Ref. 9 for a Tresca body and adopted for a body of the Coulomb type. The fields of stress and velocity are obtained for the problems under consideration. It is found that in some strain regions the field of velocity does not satisfy the relations resulting from the yield condition and the associate law of f10w for the Haar-Karman corners of the Tresca hexagon, and requiring that the principal strain rates have different signs in an axial plane. Then, the static field gives a lower estimate of the limit lo ad and the kinematic field an upper one. It is also found by numerical computation that the difference between the two estimates of the limit load may be considerable.