Fractal geometry and topology abstracted from hair fibers

Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2）-circle fractal sets as subsets. As far as the （9＋2） topological patterns are concerned, the following propositions are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.     

分形理论在煤层气非平衡吸附模型中的应用

传统的煤层气动力学模型均是建立在欧几里得几何基础上的,难以描述煤层孔隙结构的复杂性及形状的不规则性。本文以分形理论为基础,通过引入分形维数来刻画煤层孔隙结构的复杂性并考虑煤层的吸附特性、双重介质特征及介质的变形,建立基于Fick第二定律的分形介质煤层气非稳态渗流数学模型。由于流动方程的强非线性,结合各类边界条件用正则摄动法和Laplace变换得到模型在拉氏空间上的近似解析解,再利用Laplace数值反演求得实空间上的数值解。对参数进行敏感性分析并绘制了典型压力曲线,这些结果为煤层气开采提供了理论依据和试井方法。     

Low Mach number prediction of the acoustic signature of fractal-generated turbulence

In this work, we compare the acoustic properties of a fractal square grid with those of a regular grid by means of a hybrid approach based on Lighthill’s analogy and Direct Numerical Simulation (DNS). Our results show that the sound levels corresponding to our fractal square grid of three fractal iterations are significantly reduced by comparison to a regular grid of same porosity and mesh-based Reynolds number. We also find a well-defined peak at a Strouhal number between 0.2 and 0.3 in the acoustic spectrum of our fractal square grid which is absent in the case of our regular grid. We explain this effect in terms of a new criterion for quasi-periodic vortex shedding from a regular or fractal grid.     

Properties of Chaotic and Regular Boundary Crisis in Dissipative Driven Nonlinear Oscillators

The phenomenon of the chaotic boundary crisis and the related concept of the chaotic destroyer saddle has become recently a new problem in the studies of the destruction of chaotic attractors in nonlinear oscillators. As it is known, in the case of regular boundary crisis, the homoclinic bifurcation of the destroyer saddle defines the parameters of the annihilation of the chaotic attractor. In contrast, at the chaotic boundary crisis, the outset of the destroyer saddle which branches away from the chaotic attractor is tangled prior to the crisis. In our paper, the main point of interest is the problem of a relation, if any, between the homoclinic tangling of the destroyer saddle and the other properties of the system which may accompany the chaotic as well as the regular boundary crisis. In particular, the question if the phenomena of fractal basin boundary, indeterminate outcome, and a period of the destroyer saddle, are directly implied by the structure of the destroyer saddle invariant manifolds, is examined for some examples of the boundary crisis that occur in the mathematical models of the twin-well and the single-well potential nonlinear oscillators.     

Solution set on the natural satellite formation orbits under first-order earth＇s non-spherical perturbation

Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.     

考虑变形耦合的几何非线性空间梁单元

以"精确几何模型梁单元"为代表的很多几何非线性梁单元,在构造过程中分别对描述截面转动的转角和描述截面形心位置的位移进行了独立插值,由此引起了诸如运动学描述冗余和剪切闭锁等困难。其根本原因在于单元形函数没能体现细长梁中的变形耦合关系。本文对这类传统单元进行了改造,通过深入研究单元变形之间的内在联系,提出了一种变形场完全满足Bernoulli梁变形耦合关系的新单元,避免了构造过程中对转动矢量的插值,并通过数值算例检验了单元的有效性。     

Finite Element Analysis of Elasto-plastic Plate Bending Problems using Transition Rectangular Plate Elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.The English text was polished by Keren Wang.     

基于改进遗传算法主动柔性结构压电元件位置优化

基于改进的遗传算法提出了一种解决多压电片布置在柔性结构上以实现振动主动控制的有效方法.本文采用D优化设计准则,即把Fisher信息矩阵行列式最大值作为目标函数的一种优化方法.通过对结构模态振型和动力特性的研究,使用一种简单的方法将所选择的低阶模态振型转化为归一化形式,最后通过结构模态振型可确定压电片最优位置.为了达到更好的振动控制效果,压电片布置在结构模态应变最大位置处.当在结构不同位置上布置压电片时,结构各阶模态振型也将随之发生不同程度的变化.本文建立了ANSYS软件和遗传算法的接口来实现对结构的模态重分析,从而提取各阶模态振型.     

岩体结构要素分形几何研究

本文研究了岩体结构诸要素, 包括结构面形态、结构面厚度、结构面分布、产状分布、孔隙分布颗粒表面形态等的分形表征, 目的是提高岩体结构的定量描述程度, 为岩体工程的定量评价提供新的途径。     

Two-dimensional lattice gases for regular binary mixtures

This paper reports on the development of two-dimensional lattice gas models for regular binary mixtures. In particular, results are reproduced concerning equilibrium solutions and an expression for the diffusion coefficient. In our model, a volume force is incorporated, and the system of macroscopic evolution equations resembles the Boussinesq approximation in convection theory. As an example, a lattice gas Rayleigh-Bénard system is considered. We conclude with a few remarks on implementation and optimisation of the program using a SIMD parallel computer.     

Intermittency and multiscale dynamics in milling of fiber reinforced composites

We have analyzed the variations in cutting force during milling of a fiber-reinforced composite material. In particular, we have investigated the multiscale dynamics of the cutting force measured at different spindle speeds using multifractals and wavelets. The multifractal analysis revealed the changes in complexity with varying spindle speeds. The wavelet analysis identified the coexistence of important periodicities related to the natural frequency of the system and its multiple harmonics. Their nonlinear superposition leads to the specific intermittent behavior. The workpiece used in the experiment was prepared from an epoxy-polymer matrix composite reinforced by carbon fibers.     

DNS of Fractal-Generated Turbulence

An innovative approach which combines high order compact schemes, Immersed Boundary Method and an efficient domain decomposition method is used to perform high fidelity Direct Numerical Simulations (DNS) of four spatially evolving turbulent flows, one generated by a regular grid and three generated by fractal square grids. The main results which we have been able to obtain from these simulations are the following: the vorticity field appears more clustered when generated by fractal square grids compared to a regular grid; fractal square grids generate higher vorticities and turbulence intensities than a regular grid; the flow holds clear geometrical imprints of the fractal grids far downstream, a property which could be used in the future for flow design, management and passive control; the DNS obtained with fractal grids confirmed the existence of two turbulent regions, one where the turbulence progressively amplifies closer to the grid (the production region) followed by one where the turbulence decays; the energy spectra of fluctuating turbulent velocities at various locations in the production region of the flow provide some information on how the turbulence is generated at the smallest scales first near the grid where the smallest wakes are dominant, followed by progressively smaller turbulent frequencies further downstream where progressively larger wakes interact.     

Instability of binary nanofluids with magnetic field

The present paper investigates the effects of a vertical magnetic field on the double diffusive nanofluid convection. The effects of the Brownian motion and thermophoresis due to the presence of nanoparticles and the effects of the Dufour and Soret parameters due to the presence of solute are included in the investigated model. The normal mode technique is used to solve the conservation equations. For the analytical study, valid approximations are made in the complex expression for the Rayleigh number to get useful and interesting results. The bottom heavy binary nanofluids are more stable than the regular binary fluids, while the top heavy binary nanofluids are less stable than the regular binary fluids. The critical wave number and the critical Rayleigh number increase whereas the frequency of oscillation (for the bottom heavy configuration) decreases when the Chandrasekhar number increases. The numerical results for the alumina-water nanofluid are studied by use of the MATHEMATICA software.     

Coupled experiments and simulations of microstructural damage in wood

In this paper, we explore ways to couple experimental measurements with the numerical simulations of the mechanical properties of wood. For our numerical simulations, we have adopted a lattice approach, where wood fibers or bundles of wood fibers are modeled as discrete structural elements connected by a lattice of spring elements. Element strength and stiffness properties are determined from bulk material properties. Damage is represented by broken lattice elements, which cause both stiffness and strength degradation. The modeling approach was applied to small specimens of spruce subjected to transverse uniaxial tension, and mode I transverse splitting. The model was found to be good at predicting the load-deformation response of both notched and unnotched specimens, including the post-peak softening response. In addition, the damage patterns predicted by the model are consistent with those observed in the experiments.     

Creep-rupture lifetime simulation of unidirectional metal matrix composites with and without time-dependent fiber breakage

A numerical simulation for predicting the axial creep-rupture lifetime of continuous fiber-reinforced metal matrix composites is proposed, based on the finite element method. The simulation model is composed of line elements representing the fibers and four-node isoparametric plane elements representing the matrix. While the fibers behave as an elastic body at all times, the matrix behaves as an elasto-plastic body at the loading process and an elasto-plastic creep body at the creep process. It is further assumed in the simulation that the fibers are fractured not only in stress criterion but time-dependently with random nature. Simulation results were compared with the creep-rupture lifetime data of a boron-aluminum composite with 10% fiber volume fraction experimentally obtained. The simulated creep-rupture lifetimes agreed well with the averages of the experimental data. The proposed simulation is further carried out to predict a possibility of creep-rupture for the composite without time-dependent fiber breakage. It is finally concluded that the creep-rupture of a boron-aluminum composite is closely related with the shear stress relaxation occurring in the matrix as well as time-dependent fiber breakage.     

Experimental investigation of Faraday waves of maximum height

The profiles of standing gravity waves of maximum height, parametrically excited on the free surface of a deep fluid in a vertically oscillating rectangular vessel (Faraday waves), are investigated experimentally. For a small modulation index of the excitation parameter, waves of three types are distinguished: regular, temporally periodic and symmetric about the vertical line passing through their crest; irregular but retaining the connectivity of the liquid volume; and breaking waves with drops separating from the free surface of the fluid. It is established that the profile of the maximum-height regular waves is smooth with a steepness of 0.255 and a limiting angle at the crest of less than 80°. Certain realizations of irregular and breaking waves, with profiles similar to those of regular waves but with much smaller steepnesses, 0288 and 0.429, respectively, are detected.     

The theory of fractal interpolated surface and its applications

I.IntroductionFI.actillilltcrpolationwastlrstpEltforwardbyunA]ncrica1llathematician,M.F.Barllsley.in1986.ItgivesanewInethodologytardataf'ittillg,whichnotonlyopedsupanewresearch11eldfol'tilnctiollappl'oachingtheory,butalsoprovidespowerfultoolsforcolnptltcrgraphicsThistool'sapplicabilityisnowfilllyappreciated.Theuseoflinearfunctions,polynomialfunctionsandSurtllcespringfunctionstoestablishvariousmeterialobjectmodelsinreallifefi-omtraditionalEuclideangeometryisnowcommonpractice.Theavailabilit…     

Analyzing the orientation dependence of stresses in polycrystals using vertices of the single crystal yield surface and crystallographic fibers of orientation space

The influence of the polygonal geometry of the restricted slip-associated yield surface on the distribution of stresses over a polycrystalline aggregate is examined. The vertices of the yield surface (stress states corresponding to polyslip) are grouped according to symmetries imposed by crystal structure. A measure of coaxiality between crystal stresses and yield surface vertex stresses is used to quantify the proximity of the stress in each crystal to a yield surface vertex. It is shown that for prescribed stress states, crystal stresses align more closely with certain families of vertices than with others and this relation between crystal and vertex stresses is found to depend on crystallographic fibers. Using this information, the stress distributions from finite element simulations of face centered cubic polycrystals are analyzed for different stress states ranging from uniaxial to balanced biaxial. Over the fundamental region of orientations, the propensity for the stress to align with a vertex is demonstrated. Further, the stresses in elements contributing to certain crystallographic fibers are shown to favor the vertex families aligned with those fibers. The implications of these results on mechanical behaviors, especially with respect to those observed in diffraction experiments, are discussed.     

磨合过程摩擦力单重分形和多重分形的研究

分别在CD40润滑油和加入添加剂的CD40润滑油润滑条件下,通过销-盘摩擦磨损试验机对船用柴油机活塞环和缸套进行磨合磨损试验,提取摩擦力的时间序列信号,应用分形维数和多重分形谱研究了摩擦力的分形行为.结果表明:摩擦力信号具有分形特征;随着磨合磨损过程的进行,信号的分形维数和多重分形谱出现规律性的变化;不同阶段信号的分形维数趋于减小,与磨损表面粗糙度的变化规律一致;不同阶段信号的多重分形谱呈现出递增或递减趋势,反映了磨损表面的动态变化过程.因此,摩擦力信号的分形维数和多重分形谱可以对磨合磨损过程进行定量分析.     

Influence of softening on fracture propagation in large-scale shell structures

In this study, fracture propagation in large shell elements is modelled with the softening law. This law is given in a general form, enabling investigations of different softening behaviours to be conducted. The final fracture is simulated by removing elements. The softening parameters are derived using the energy-based representative volume element (RVE) approach. Tracing crack propagation through the RVE defines the physically justified softening parameters for the current model. The softening model is implemented into ABAQUS using VUMAT subroutines for the shell elements. A large-scale tearing experiment is simulated with the current model and RVE-based softening parameters. In addition, the softening laws from the literature have been used. The fracture propagation is assessed in terms of plastic energy dissipation in the RVE and the whole structure, load–displacement, and crack growth. The RVE-based model is shown to have better performance compared with other models from the literature.