Numerical modeling of the shearing of irradiated fuel assemblies

The stress-strain state of layered bodies is studied numerically taking into account features of the loading devices used in the technological shearing processes of irradiated fuel assemblies. The effect of the localization of the hold-down clamp on the shear stress intensity and the shear stress value is studied. The dependence of the stress-strain state of the layers on the value of the gap between the blades is obtained. It is shown that the nature of the failure changes in the process of wearing of the shear blade edges. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 134–140, May–June, 2006.     

Dynamics of flexible multibody systems with tree topologies

The dynamic equations of flexible multibody systems with tree topological configuration are derived by using the Jourdain's principle. The independent joint coordinates are introduced to describe the large displacements of the bodies, and the modal coordinates are used to describe small deformations of flexible bodies based on the consistent mass finite element method and normal vibration mode analysis. The minimum differential equations are developed, which are compatible with the equations of multi-rigid body systems or structural dynamics. The stiff problem in the numerical integration is thus alleviated effectively. The method used in this paper can be extended to deal with systems with other topological configurations. Finally, the validity and feasibility of the presented mathematical model are demonstrated by a numerical example of a manipulator with two elastic links. The project supported by National Natural Science Foundation of China     

Resistance distance in graphs and random walks

We study the resistance distance on connected undirected graphs, linking this concept to the fruitful area of random walks on graphs. We provide two short proofs of a general lower bound for the resistance, or Kirchhoff index, of graphs on N vertices, as well as an upper bound and a general formula to compute it exactly, whose complexity is that of inverting an N×N matrix. We argue that the formulas for the resistance in the case of the Platonic solids can be generalized to all distance‐transitive graphs. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 29–33, 2001     

Dipole-dipole minimum energy configuration for Platonic,Archimedean and Catalan solid structures

Several magnetic materials consisting of dipoles owe their properties to the specific nature of the dipole-dipole interaction. In the present work, we study systems of dipoles where the particles are arranged on various types of three-dimensional structures. However, these solids are not arbitrary. They constitute the well-known Platonic, Archimedean and Catalan solids. We systematically study them in order to fill a gap in the literature that does not contemplate this interaction in the previous solids, despite the fact that they are encountered in many different physical systems. In particular, in the regime of strong dipole moments where a classical treatment is possible, we shall provide not only the minimum energy but also the precise orientations of all their dipoles. We will numerically obtain the minimum energy configuration where all vertices possess the same classic dipole, either electric or magnetic.     

On the Impact of Elastic Bodies with Adhesive Forces

We analyze the problem of an elastic sphere impacting against another elastic body for the case when adhesive forces act between the bodies. Depending on the parameter describing the (relative) influence of the adhesive forces, the bodies will either separate or continue to be in contact and perform an oscillatory motion after the rebound. The value of the adhesive forces parameter defining separation and capture is calculated. This revised version was published online in July 2006 with corrections to the Cover Date.     

A new affine invariant for polytopes and Schneider's projection problem

New affine invariant functionals for convex polytopes are introduced. Some sharp affine isoperimetric inequalities are established for the new functionals. These new inequalities lead to fairly strong volume estimates for projection bodies. Two of the new affine isoperimetric inequalities are extensions of Ball's reverse isoperimetric inequalities.

     

Aerodynamic Characteristics of Slender Star-Shaped Bodies with Supersonic Leading Edges

A theory of the flow around slender conical bodies with a star-shaped cross-section in regimes with shock attachment along the length of the leading edges is developed. The aerodynamic characteristics of the slender star body, a single cycle of which represents a V-shaped wing, are obtained for different numbers of reflections of the disturbances proceeding from the leading edges of the cycles from the wing cantilevers, using superposition of the solutions of linear problems of flow around the V-wing.     

Helly-Type Theorems on Common Supporting Lines for Nonoverlapping Families of Convex Bodies in the Plane

Helly-type results are established relating to the existence of a line supporting a family of nonoverlapping convex bodies in the plane.