Stokes flow in a rectangular cavity by rotlet forcing

The Stokes flow inside a two-dimensional rectangular cavity |x|a, |y|b is analyzed for a highly viscous, incompressible fluid flow, driven by a single rotlet placed at position (0,c). Specifically, a rigorous solution of the governing two-dimensional biharmonic equation for the stream function is constructed analytically by means of the superposition principle. With this solution, multicellular flow patterns can be described for narrow cavities, in which the number of flow cells is directly related to the value of the aspect ratio A=b/a. The solution also shows that for a certain rotlet position (0,c0), which depends on a and b, the flow has a stagnation point (0,-c0) symmetrically placed inside the rectangle. As the flow would not be affected by placing a second (inactive) rotlet in this stagnation point, this allows us to construct a blinking rotlet model for the rectangular cavity, with the inactive rotlet in the stagnation point of the flow induced by the active rotlet. For rectangular cavities, it holds that more than one of these special rotlet positions can be found for cavities that are elongated to sufficiently large aspect ratios. The blinking rotlet model is applied to illustrate several aspects of stirring in a Stokes flow in a rectangular domain

A unified energy formulation for the stability analysis of open and closed thin-walled members in the framework of the generalized beam theory

Generalized beam theory--GBT--is among the most adequate tools for the analysis of thin-walled prismatic elements. It enables the analysis of the distortion of the element cross-section and local buckling of individual walls in a unified manner that incorporates the results from classical bending theory. The basis of this theory was developed in the 1960s by Schardt for first and second order elastic behaviour of thin-walled members.http://www.sciencedirect.com/science/article/B6V59-4CDHH8M-2/1/0dc966f0e6162a1c782229da7969d09