The Application of an Orthogonal Net of Circles to the Problem of Plane Strain in Plasticity

Abstract

A geometric proof of Ringleb’s theorem is indicated. Several geometric considerations as they relate to the application of this theorem to the plane-strain problem of plasticity are derived. Two distinct methods of numerical solution, which are direct outgrowths of this analysis, are thoroughly discussed. The ease of their application and the accuracy of the results are discussed with reference to the standard straight-line approximation. The existence of Hencky’s second theorem for problems of plane strain in plasticity is shown to imply certain features which permit absolute estimates of the accuracy of the results.