A New Method of Solution of the Two-Dimensional Isostatical Problem in the Mathematical Theory of Plasticity

Abstract

The author discusses an analogy between the statically determinate state of stress in the perfectly plastic material and the steady irrotational flow of a hypothetical non-viscous fluid introduced by him, the pressure in which is proportional to the logarithm of its density and which has the same local Mach number \sqrt2 throughout the whole field of flow.
The hodograph method for this fluid flow is developed in detail, and besides an application of the W.K.B. method is considered.
Several exact solutions of the fundamental differential equations illustrate the present new method of solving the isostatical problem in the theory of plasticity.