A Yield Surface Linearization Procedure in Limit Analysis∗

ABSTRACT

Within the framework of discretized structural models and piecewise linear yield polyhedra, a heuristic is presented to iteratively improve the limit load estimation by approaching locally the plastic admissibility domain. For the two-dimensional active stress situation, the scheme requires the generation of at the most three vertices, in addition to the initial four, to describe the improved inscribed yield polygon. Two examples are given to illustrate the procedure and to clarify various aspects of the algorithm presented.     

On the Spectral Representation of Stretch and Rotation

By means of Sylvester's spectral representation of tensor-valued functions, a representation is derived for the finite stretch and rotation associated with the polar decomposition of a given deformation gradient. This revised version was published online in August 2006 with corrections to the Cover Date.     

Some Observations of Vortex Breakdown in a Confined Flow with Solid Body Rotation

The occurrence of breakdown in slender vortex flows as a ``bubble'' or ``spiral'' pattern depends on the degree of radial deflection of the vortex core from its original axis as shown in [1]. A smooth transition from a bubble to a spiral-type ``mode'' can be forced by inducing a small asymmetric disturbance which led to the conclusion, that the patterns do not represent different fundamental modes of breakdown. The subject presented herein addresses the following question: how does breakdown evolve in a swirling flow in which the vortex core is forced on a straight axis? In addition, what is the effect of turbulent inflow conditions? This type of vortex conditions is achieved in a spinning tube flow. The swirl is introduced at the entrance of the rotating tube with a honeycomb package and maintained by the viscous action in the boundary layer of the spinning tube. A diffuser at the end induces an adverse pressure gradient to force the breakdown. Flow visualization experiments are carried out to characterize the nature of breakdown over a range of different flow conditions. For some selected characteristic stages, detailed velocity fields were obtained using the method of Digital Particle-Image-Velocimetry (DPIV). The results show, that for the range of parameters investigated, breakdown is initiated at Rossby-numbers below a critical value of Ro ≈ 0.6 similar to those observed in other experiments. The bursted part of the vortex has a near axi-symmetric slender conical shape containing approximately stagnant flow. Its downstream end is characterized by a jump-like contraction where the flow evolves into a jet with enhanced swirl on the axis. It is only in this region downstream of the jump-like contraction that asymmetric instabilities and wavy flow patterns could be observed. Perturbations caused by them travel upstream but do not change the near-axisymmetric shape of the bursted part of the vortex.     

Mechanical Properties of Ballistic Gelatin at High Deformation Rates

The characterization of soft or low impedance materials is of increasing importance since these materials are commonly used in impact and energy absorbing applications. The increasing role of numerical modeling in understanding impact events requires high-rate material properties, where the mode of loading is predominantly compressive and large deformations may occur at high rates of deformation. The primary challenge in measuring the mechanical properties of soft materials is balancing the competing effects of material impedance, specimen size, and rate of loading. The traditional Split Hopkinson Pressure Bar approach has been enhanced through the implementation of polymeric bars to allow for improved signal to noise ratios and a longer pulse onset to ensure uniform specimen deformation. The Polymeric Split Hopkinson Pressure Bar approach, including the required viscoelastic bar analysis, has been validated using independent measurement techniques including bar-end displacement measurement and high speed video. High deformation rate characterization of 10% and 20% ballistic gelatin, commonly used as a soft tissue simulant, has been undertaken at nominal strain rates ranging from 1,000 to 4,000/s. The mechanical properties of both formulations of gelatin exhibited significant strain rate dependency. The results for 20% gelatin are in good agreement with previously reported values at lower strain rates, and provide important mechanical properties required for this material.     

Vortex Cell with a Cylinder Rotating inside it on the Surface of an Airfoil Section at High Reynolds Numbers

An algorithm for eliminating flow separation in the nose region of a symmetric airfoil section at nonzero angle of incidence is proposed. Below the separation-prone region of the section, to increase the critical angle of incidence, a vortex cell with a cylinder rotating inside is located. The shape of the vortex cell and the precise location of the cylinder are so chosen as to create the same pressure gradient in the mixing layer as in the external flow.     

Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as → 0 is obtained.     

双咪唑离子液体的合成及其高温摩擦学性能研究

合成了3种不同连接链的双咪唑离子液体;采用核磁共振谱仪表征了其结构,采用SRV-IV型摩擦磨损试验机评价了其在变温及250 ℃恒温下的摩擦学性能;并采用扫描电镜(SEM)和X射线光电子能谱仪(XPS)分析了磨斑表面形貌和主要元素的化学状态.结果显示:同变温摩擦磨损试验相比,恒温摩擦磨损试验能更为有效地体现不同双咪唑离子液体的高温摩擦学性能差异;与此同时,烷基链连接的双咪唑离子液体的减摩抗磨性能明显优于醚链连接的双咪唑离子液体,且缩短双咪唑离子液体的连接链长度有利于提高其摩擦学性能.     

AlCoCrFeNi高熵合金的高温摩擦磨损性能

AlCoCrFeNi高熵合金因其优异的综合力学性能而有望成为新一代高温结构材料,但对其高温摩擦磨损性能的研究还较为少见.本文中应用放电等离子烧结(SPS)技术制备了AlCoCrFeNi高熵合金,研究了其显微组织和力学性能,系统地考察了其在室温至800℃时的摩擦磨损性能.结果表明:应用SPS技术制备的AlCoCrFeNi高熵合金主要由FCC相、无序BCC相和少量有序BCC相组成;呈网格状分布的FCC相使高熵合金具有良好的塑性和韧性,而呈等轴状分布的BCC相赋予了高熵合金优异的强度;高熵合金室温至800℃时的摩擦系数在0.43~0.51之间,磨损率低于10–5mm3/(N·m).室温至中温阶段主要为磨粒磨损,中温至高温阶段的磨损机制为磨粒磨损、黏着磨损和塑性变形综合作用.高温下高熵合金表面形成了一层主要由为Al2O3和Cr2O3组成的氧化物膜,在一定程度上起到抗磨作用.     

Stability of the Burgers shock wave

This paper considers the stability of the Burgers shock wave solution with respect to infinitesimal disturbance.It is found that the Burgers shock wave is asymptotically stable in the Liapunov sense.     

Fe-Ni基高温自润滑复合材料摩擦磨损特性研究

本文中采用滑动磨损试验方法研究了以PbO和WS2为润滑组元的复合材料与440C不锈钢配副在25～600℃温度范围内的摩擦磨损特性.通过X射线衍射仪分析发现复合材料中含有铬的硫化物等高温润滑物质生成.使用扫描电镜和金相显微镜进一步分析了材料摩擦表面形貌.结果表明:在500 ～ 600℃范围内,PbWO4、CrxSx+1等各种金属化合物在摩擦表面形成了较完整的润滑膜,产生了自润滑能力,具有优良的减摩耐磨性能.润滑膜材料可向摩擦对偶表面转移,在一定程度上阻止了复合材料与440C不锈钢对摩材料的直接接触,显著降低了材料摩擦系数和磨损率,实现了高温自润滑性能.本文进一步探索了单一润滑组元润滑膜和两种润滑组元润滑膜的承载能力,发现两种固体润滑组元产生的协同润滑效应显著改善了润滑膜的润滑性能.     

高压下受限齿轮油成膜特性研究

本文揭示了在实际应用中极端工况下齿轮油的润滑特性.为了测量在高接触压力和不同温度条件下齿轮油的成膜能力,制作了高精度的膜厚测量仪,采用相对光强法实现纳米级膜厚测量.试验中共采用了5种性质不同的齿轮油,在纯滚动条件下测量接触区的油膜厚度,结果表明：随着接触压力的升高油膜厚度明显降低,但压力对润滑状态影响不大;温度的改变不但能影响油膜厚度,对润滑状态的影响也很明显;GL-5 85W/190和GL-5 85W/90齿轮油在接触压力达3 GPa温度提高到120℃时仍能形成很厚的油膜,但其余3种润滑剂在极端工况下成膜能力不足.本文最后根据试验结果还提出了含有丰富添加剂的齿轮油润滑模型.     

Decaying Turbulence in the Generalised Burgers Equation

This work is concerned with the derivation of optimal scaling laws, in the sense of matching lower and upper bounds on the energy, for a solid undergoing ductile fracture. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. The solid is assumed to obey deformation-theory of plasticity and, in order to further simplify the analysis, we assume isotropic rigid-plastic deformations with zero plastic spin. When hardening exponents are given values consistent with observation, the energy is found to exhibit sublinear growth. We regularize the energy through the addition of nonlocal energy terms of the strain-gradient plasticity type. This nonlocal regularization has the effect of introducing an intrinsic length scale into the energy. Under these assumptions, ductile fracture emerges as the net result of two competing effects: whereas the sublinear growth of the local energy promotes localization of deformation to failure planes, the nonlocal regularization stabilizes this process, thus resulting in an orderly progression towards failure and a well-defined specific fracture energy. The optimal scaling laws derived here show that ductile fracture results from localization of deformations to void sheets, and that it requires a well-defined energy per unit fracture area. In particular, fractal modes of fracture are ruled out under the assumptions of the analysis. The optimal scaling laws additionally show that ductile fracture is cohesive in nature, that is, it obeys a well-defined relation between tractions and opening displacements. Finally, the scaling laws supply a link between micromechanical properties and macroscopic fracture properties. In particular, they reveal the relative roles that surface energy and microplasticity play as contributors to the specific fracture energy of the material.     

Vortex dipolar structures in a rigid model of the larynx at flow onset

Starting jet airflow is investigated in a channel with a pair of consecutive slitted constrictions approximating the true and false vocal folds in the human larynx. The flow is visualized using the Schlieren optical technique and simulated by solving the Navier-Stokes equations for an incompressible two-dimensional viscous flow. Laboratory and numerical experiments show the spontaneous formation of three different classes of vortex dipolar structures in several regions of the laryngeal profile under conditions that may be assimilated to those of voice onset.     

Time-Periodic Solutions of the Burgers Equation

We investigate the time periodic solutions to the viscous Burgers equation u_t − μu_xx + uu_x = f for irregular forcing terms. We prove that the corresponding Burgers operator is a diffeomorphism between appropriate function spaces.      

Steady Vortex Ring with Isochronous Flow in the Vortex Core

Steady-state solutions to the problem of a thin vortex ring in an inviscid incompressible fluid in infinite space are investigated. The Fraenkel procedure is used to construct the steady-state solutions. In this procedure a given vorticity distribution in plane flow with circular streamlines is transformed into a steady vortex ring using an expansion in the ring thinness parameter. For example, a two-dimensional vortex of constant vorticity is transformed into a steady vortex ring with the uniform distribution in which the absolute value of vorticity is proportional to the distance from the axis of symmetry. The principal aim of our study is to construct the algorithm of finding the flow for an isochronous vortex ring in which the periods of revolution are the same for all the liquid particles in the vortex core. The problem is that the two-dimensional distribution which goes over in the isochronous ring in accordance with the Fraenkel procedure is unknown in advance. In particular, the ring with the uniform distribution is not isochronous despite the isochronism of the initial two-dimensional flow. In this connection the Fraenkel procedure is significantly modified so that the initial two-dimensional vorticity distribution is determined in each of the steps of the iteration procedure. The solution for the vortex ring with the uniform distribution obtained in the present study is significantly used to construct the isochronous solution. The necessary corrections to the former solution are calculated in each step. Obtaining of the isochronous flow is the key step for the investigation of stability of three-dimensional oscillations of the vortex ring since the oscillation spectrum of this flow is discrete.     

Si掺杂对NbTaWMo难熔高熵合金的高温摩擦学性能的影响

采用放电等离子烧结技术在NbTaWMo难熔高熵合金中掺杂Si元素成功制备了NbTaWMoSi_0.25难熔高熵合金,研究了物相组成、显微结构和力学性能的变化,并重点对比了25 ~800 ℃的摩擦学性能. 结果表明:NbTaWMo高熵合金由单一的BCC相组成,而NbTaWMoSi_0.25合金由BCC相和硅化物两相组成. 在NbTaWMo难熔高熵合金中掺杂Si元素后,高熵合金室温下的屈服强度、抗压强度和断裂应变均有显著的提高. NbTaWMo难熔高熵合金掺杂Si元素后从25 ℃到800 ℃摩擦系数变化较小,但其耐磨性显著改善,其耐磨性的提高主要由于硅化物增强了合金的强度. NbTaWMoSi_0.25难熔高熵合金从室温到中温阶段的磨损机制主要为磨粒磨损,而高温阶段的磨损机制主要表现为磨粒磨损和氧化磨损的综合作用. NbTaWMoSi_0.25高熵合金在宽温域内具有良好的耐磨性,在高温摩擦学领域具有较大的应用潜力.      

混凝土高温动态力学特性与本构方程

混凝土材料是多相复合材料,高温动荷载作用下其力学行为非常复杂。为此,对混凝土在爆炸、火灾等高温环境中力学特性的研究,有利于减小混凝土结构在爆炸及火灾事故中的损失。文中首先利用分离式霍普金森压杆试验装置(SHPB)设计出一套混凝土高温试验方案,然后基于15组试验工况对混凝土在温度为16℃至650℃范围内,加载撞击速度分别为5m/s、7m/s和12m/s时进行了SHPB试验,获得了与之对应的应力应变曲线。试验结果表明,混凝土应变率增强效应与高温弱化效应相互耦合,致使混凝土受温度的影响显著大于其应变率。最后,由试验结果以经典损伤理论模型为基础,根据混凝土高温动态力学特性,构建了一个统一的方程来描述混凝土高温动态应力应变关系的全过程,并且该本构方程计算结果与试验数据吻合良好。     

基于纳米压入法Sn-Ag-Cu无铅焊料高温力学性能的研究

无铅化和微型化已经成为电子封装的发展趋势,温度对无铅焊点的可靠性产生了不可忽视的影响。本文对Sn96.5Ag3Cu0.5无铅焊料进行回流处理,采用纳米压入法研究其在实际工况下的高温力学性能。结果表明,温度对焊料试样的力学性能影响显著。随着温度的升高,弹性模量和硬度逐渐降低,焊料发生软化;较高温度下的蠕变应力指数较小,焊料的蠕变抗力降低,其相应的蠕变激活能为76kJ/mol。由此可知,随温度的升高,焊料的蠕变机制由位错攀移逐渐转变为晶界滑移。