A method of solution of the ornstein-zernike equation in one and three dimensions

An elegant analytic method is presented to derive a modified form of the Ornstein-Zernike equation which not only solves the statistical mechanical problem for hard rods and spheres but can be used to find solutions for arbitrary non-vanishing direct correlation functions.     

A finite element approach to the chaotic motion of geometrically exact rods undergoing in-plane deformations

The paper is concerned with a hybrid finite element formulation for the geometrically exact dynamics of rods with applications to chaotic motion. The rod theory is developed for in-plane motions using the direct approach where the rod is treated as a one-dimensional Cosserat line. Shear deformation is included in the formulation. Within the elements, a linear distribution of the kinematical fields is combined with a constant distribution of the normal and shear forces. For time integration, the mid-point rule is employed. Various numerical examples of chaotic motion of straight and initially curved rods are presented proving the powerfulness and applicability of the finite element formulation.     

杆系结构弹性波传播的实验研究

利用ＳＨＰＢ装置，用空气枪加载就３５ＣｒＭｎＳｉ钢组成的杆系结构（平面Ｌ型、空间直角坐标Ｙ型）受冲击载荷作用的弹性波传播进行了实验研究，给出了一些力学现象，并利用广义特征线法给出了理论与实验的比较曲线，得到了一些有益的结论。     

Kirchhoff’s Problem of Helical Equilibria of Uniform Rods

It is demonstrated that a uniform and hyperelastic, but otherwise arbitrary, nonlinear Cosserat rod subject to appropriate end loadings has equilibria whose center lines form two-parameter families of helices. The absolute energy minimizer that arises in the absence of any end loading is a helical equilibrium by the assumption of uniformity, but more generally the helical equilibria arise for non-vanishing end loads. For inextensible, unshearable rods the two parameters correspond to arbitrary values of the curvature and torsion of the helix. For non-isotropic rods, each member of the two-dimensional family of helical center lines has at least two possible equilibrium orientations of the director frame. The possible orientations are characterized by a pair of finite-dimensional, dual variational principles involving pointwise values of the strain-energy density and its conjugate function. For isotropic rods, the characterization of possible equilibrium configurations degenerates, and in place of a discrete number of two-parameter families of helical equilibria, typically a single four-parameter family arises. The four continuous parameters correspond to the two of the helical center lines, a one-parameter family of possible angular phases, and a one-parameter family of imposed excess twists. Mathematics Subject Classifications (2000) 74K10.     

Post-buckling analysis of slender elastic vertical rods subjected to terminal forces and self-weight

This article presents the behavior of slender elastic rods subjected to axial terminal forces and self-weight. The mathematical formulation is presented, a solution is sought for a double-hinged boundary condition and the analysis is carried out for different values of non-dimensional weight. The formulation derives from geometrical compatibility, equilibrium of forces and moments and constitutive relations yielding a set of six first order non-linear ordinary differential equations with boundary conditions specified at both ends, which characterizes a complex two-point boundary value problem. Furthermore, a perturbation method is used to find the critical buckling loads and initial post-buckling solutions. A numerical integration scheme based on a three parameter shooting method is employed in the post-buckling solutions.     

Stability of n-covered Circles for Elastic Rods with Constant Planar Intrinsic Curvature

A stability index is computed for the n-covered circular equilibria of inextensible-unshearable elastic rods with constant planar intrinsic curvature û and constant values for the twisting stiffness and two bending stiffnesses. A simple expression is derived for the index as a function of û, (the ratio of bending stiffness out of the plane of curvature to bending stiffness in the plane of curvature), and (the ratio of twisting stiffness to bending stiffness in the plane of curvature). In particular, for intrinsically straight rods (û = 0) we prove that the 1-covered circle is stable if and only if 1, and the n-covered circle (n>1) is stable if and only if >1, >1, and

Dendrimers with Oligospiroketal (OSK) Building Blocks: Synthesis and Properties

The development of novel dendrimers containing oligospiroketal (OSK) rods as building blocks is described. The linkage between the core unit (CU), branching units (BU), and OSK rods relies on the CuAAC reaction between terminal alkynes and azides. Two different strategies of dendrimer synthesis were investigated and it was found that the convergent approach is clearly superior to the divergent one. SAXS measurements and MD simulations indicate that the obtained dendrimer features a globular structure with very low density. Obviously, the OSK rods stabilize a rather loose mass‐fractal structure.     

Subspace variational principle of rods and shells

This paper builds the general forms of subspace variational principles of rods andshells which are taken as the controlled equations of the constitutive theories developedfrom the three-dimensional (non-polar) continuum mechanics. And the constitutiveequations of rods and shells using the principles are satisfactory.     

Monolayer properties of a fuzzy rod polymer: Poly(γ-stearyl α, L-glutamate)

Static and dynamic properties, and surface morphologies of monolayers at the air-water interface of a fuzzy rod polymer, poly(γ-stearyl α, L-glutamate), PSLG, have been examined by the Wilhelmy plate method for surface pressure, electrically induced capillary wave diffraction (ECWD), epi-fluorescence microscopy, and atomic force microscopy (AFM). The monolayers were first formed by spreading polymer solutions at the air-water interface and allowing the solvent to evaporate to obtain polymer films, i.e., spread monolayers. The surface mass density was varied by either successive additions of more solutions on a given surface area or step-wise compression of the surface barrier on a Langmuir trough. Surface pressure isotherms at 23–;60°C were confirmed to be reversible and reproducible, and an abrupt change at approximately 60°C was observed, which is reported as the melting point of crystalline stearyl side chains. By AFM, the monolayer director n by surface alignment was confirmed as perpendicular to the compression direction and certain islands of departure from the monolayer state were visualized upon transferring the monolayers horizontally to silicon wafers. Macroscopic anisotropy in the surface alignment was probed by the electrocapillary waves propagated perpendicular (⟂) and parallel (∥) to the director n; the surface tension anisotropy amount to about 7% difference, σ_⟂/σ_⟂ < 0.07, where σ is the surface tension deduced from the wave propagation characteristics. Multidomain morphologies of the monolayers were imaged by epi-fluorescence microscopy and they were found to differ according to the method of monolayer mass density variation, i.e., the successive addition and step-wise compression. © 1996 John Wiley & Sons, Inc.     

Spatial braiding of cylindrical articles

The effective deformative characteristics of spatially reinforced composites made by spatial braiding along the generatrices of a one-sheet hyperboloid are analyzed. The geometrical relationships determining the structure of a unit cell of a braided composite are derived. The effective thermoelastic characteristics are calculated by the method of orientational averaging. The dependences of the bending and torsional stiffnesses of thick-walled cylindrical rods — made by the method suggested and by winding — on the braiding/winding angle are compared. The numerical estimations are given for rods made of carbon (CFRP) and aramid (AFRP) epoxy plastics. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompzitnykh Materialov, Vol. 36, No. 3, pp. 341–354, May–June, 2000.