Free Streamline Hydrodynamic Analogy for a Linear Elastic Antiplane Slot Problem with Perfectly Plastic Ligaments at Its Ends

Abstract

It is shown that a two-dimensional analogy exists between an inviscid incompressible fluid flow around two finite-length flat plates (Riabouchinsky problem) and that of a straight slot cut in a linear elastic plate having rounded ends that are on the verge of yielding plastically. For the plates, a uniform flow at infinity is assumed in a direction perpendicular to the side-by-side parallel lines that constitute the two-dimensional geometry of the plates. Correspondingly, the slot has a boundary condition at infinity of a uniform shear traction in the antiplane direction. In the fluid flow problem, two free streamlines form at both ends of the flat plates, while in the slotted plate problem, the rounded ends of the traction-free slot surfaces constitute ligaments of perfectly plastic material. The specific shape of the rounded ends of the slot problem can be inferred by analogy with the fluid flow problem.