Author(s)

G. B. Sinclair, X. Chi & T. I-P. Shih

Abstract

Essential for meaningful design for structural integrity is an appreciation of when stress singularities are present in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier- Stokes equations are locally governed by Stokes flow in angular corners. Findings are confirmed by developing and using an analogy with solid mechanics, and by applying divergence checks to global numerical results. These flow-induced singularities render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone. Keywords: incompressible viscous fluids, Navier-Stokes equations, flow-induced stress singularities. 1 Introduction As an introductory example, we consider the steady two-dimensional flow of an incompressible viscous fluid over a step (fig. 1). The issue of concern is what stress singularities, if any, are induced by the fluid flow at the corners C and C΄. Such singularities can in turn lead to stress singularities within the solid comprising the boundary. When a stress singularity occurs at location of concern within a structure, there are three approaches that may be adopted to try and ensure structural integrity: to dispense with any detailed stress analysis

Keywords

incompressible viscous fluids, Navier-Stokes equations, flow-induced stress singularities.