On Cesàro-Volterra Method in Orthotropic Saint-Venant Beam

The linearly elastic and orthotropic Saint-Venant beam model, with a spatially constant Poisson tensor and fiberwise homogeneous elastic moduli, is investigated by a coordinate-free approach. A careful reasoning reveals that the elastic strain, fulfilling the whole set of differential conditions of integrability and a differential condition imposed by equilibrium, is defined on the whole ambient space in which the beam is immersed. At this stage the shape of the beam cross-section is inessential and Cesàro-Volterra formula provides the general integral of the differential conditions of kinematic compatibility. The cross-section geometrical shape comes into play only when differential and boundary equilibrium conditions are imposed to evaluate the warping displacement field. The treatment of an orthotropic Saint-Venant beam is applied to investigate about the locations of the shear and twist centres. It is shown that the position of the shear centre can be expressed in terms of the sole cross-section twist warping. The advantage with respect to treatments in the literature is that the solution of a single Neumann-like problem is required.     

Von Kàrmàn vortices behind a bluff body in a wall-bounded turbulized flow with a turbulized boundary layer

The results of the experimental investigation of vortex formation behind a body set transversely in a highly-turbulized channel flow in the presence of a fixed separation line and a turbulized boundary layer on the body nose are presented. It is shown that the action of the turbulizing factors can lead both to an increase and a decrease in von Kàrmàn vortex formation frequency, depending on the cross-sectional shape of the body. A simplified model explaining the effects established and based on the relation between the transverse dimensions of the wake downstream the body and the velocity at its outer boundary is presented.     

Numerical modeling of the induced vorticity effect on the von Kàrmàn vortex street downstream of a circular cylinder

On the basis of a solution of the time-dependent Navier-Stokes equations on multiblock computational grids, the phenomenon of significant decay of the von Kàrmàn vortex street downstream of a circular cylinder owing to vorticity generation in passive and active vortex cells embedded in the cylinder contour is numerically analyzed. Feodosiya, Sankt-Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 68–74, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

Constructing generalized Cesàro formulas for finite plane strains

The problem of finding the displacement vector from a system of nonlinear differential equations which includes displacement gradient components is studied. Expressions on the right side of this system for certain parameter values have the kinematic sense of Lagrange and Euler finite strain tensors. The task is to construct generalized Cesàro formulas for finite strains. The construction of the solution consists of two stages (algebraic and differential), and the second is performed for space whose dimension is greater than or equal to two. An algorithm for the inversion of the original system is proposed, and analytical constructions for the case of two-dimensional space are performed. The problem is solved at the first (algebraic) stage, i.e., an exact analytical expression for the displacement vector components is derived through the known finite strain tensor and an unknown scalar function having the kinematic sense of rotation. Necessary conditions for the existence of this relationship are formulated.