On the geometrically similar expansion of a hole in a thin infinite plate

Abstract

The problem is considered of expanding a central cylindrical hole from zero radius in a thin infinite plate of conical profile such that, initially, thickness is proportional to radius, chosen so that geometrical similarity is maintained. A previously incorrect theory is modified by using a matrix formulation of the equations suitable for iterative solution on the digital computer, and the predicted profile of the plate is compared with that found from an experiment performed on a finite mild steel plate of conical profile. The Prandtl-Reuss relations for the large deformation elastic-plastic flow of a work-hardening material obeying the Maxwell (von Mises) yield criterion are used. Apart from the intrinsic interest of obtaining a complete solution to a problem of this type, the solution will be used to provide a valid model against which to test solutions obtained by finite element methods for large deformation elastic-plastic analysis.