混凝土双K断裂参数计算的半解析有限元法

混凝土裂缝扩展的双$K$断裂准则，用于描述混凝土结构裂缝的起裂、稳定扩 展和失稳断裂. 其相应的双$K$断裂参数(起裂断裂韧度$K_{\rm IC}^{\rm ini} $和失 稳断裂韧度$K_{\rm IC}^{\rm un}$)一般通过简便的试验和基于虚拟裂缝扩展粘 聚力的解析方法确定. 利用平面扇形域哈 密顿体系的方程，通过分离变量法及共轭辛本征函数向量展开法，以解析的方法推导出基于混 凝土虚拟裂缝扩展线性粘聚力模型的平面裂缝解析元列式. 将该解析元与有限元相结合，构成 半解析的有限元法，可求解任意结构几何形状的混凝土平面裂缝双$K$断裂参数的计算问题. 数值计算结果表明半解析有限元法对该类问题的求解是十分有效的.     

利用维氏和玻氏压头表征半导体材料断裂韧性

压痕法是测量材料断裂韧性 ($K_{\rm IC})$ 的常用方法之一, 如何根据不同的材料、不同的压头选择适合的公式, 是当前面临的一大问题. 因此,在不同载荷下对单晶硅 (111) 和碳化硅 (4H-SiC, 0001面) 这两种半导体材料进行了维氏微米硬度和玻氏纳米压痕实验, 对实验产生的裂纹长度$c$进行了统计分析, 并采用13个压痕公式计算材料的$K_{\rm IC}$, 开展了微米划痕实验, 验证压痕法评估半导体材料$K_{\rm IC}$的适用性. 研究结果表明: 为了消除维氏压痕实验产生的$c$的固有离散性, 需要多次测量取平均值; 裂纹长度与压痕尺寸的比值随压痕载荷的增大而增大; 材料的裂纹类型与载荷相关且低载荷下表现为巴氏裂纹, 高载荷下表现为中位裂纹; 与微米划痕实验得到的单晶硅和碳化硅材料的$K_{\rm IC}$平均值 (分别为0.96 MPa,$\cdot$,$\sqrt{\rm m}$和2.89 MPa,$\cdot$,$\sqrt{\rm m}$) 相比, 在同一压头下无法从13个公式中获得同时适用于单晶硅和碳化硅材料的压痕公式,但在同一材料下可以获得同时适用于维氏和玻氏压头的$K_{\rm IC}$计算公式; 基于中位裂纹系统发展而来的压痕公式更适合用于评估半导体材料的$K_{\rm IC}$, 且维氏压头下的$K_{\rm IC}$与玻氏压头下$K_{\rm IC}$的关系不是理论上的1.073倍, 应为1.13$\pm 压痕法是测量材料断裂韧性(K_(IC))的常用方法之一,如何根据不同的材料、不同的压头选择适合的公式,是当前面临的一大问题.因此,在不同载荷下对单晶硅(111)和碳化硅(4H-Si C, 0001面)这两种半导体材料进行了维氏微米硬度和玻氏纳米压痕实验,对实验产生的裂纹长度c进行了统计分析,并采用13个压痕公式计算材料的K_(IC),开展了微米划痕实验,验证压痕法评估半导体材料K_(IC)的适用性.研究结果表明:为了消除维氏压痕实验产生的c的固有离散性,需要多次测量取平均值;裂纹长度与压痕尺寸的比值随压痕载荷的增大而增大;材料的裂纹类型与载荷相关且低载荷下表现为巴氏裂纹,高载荷下表现为中位裂纹;与微米划痕实验得到的单晶硅和碳化硅材料的K_(IC)平均值(分别为0.96 MPa·m~(1/2)和2.89 MPa·m~(1/2))相比,在同一压头下无法从13个公式中获得同时适用于单晶硅和碳化硅材料的压痕公式,但在同一材料下可以获得同时适用于维氏和玻氏压头的K_(IC)计算公式;基于中位裂纹系统发展而来的压痕公式更适合用于评估半导体材料的K_(IC),且维氏压头下的K_(IC)与玻氏压头下K_(IC)的关系不是理论上的1.073倍,应为1.13±0.01.     

16MnR钢缺口试样解理断裂行为研究

研究了低合金热轧钢16MnR缺口试样在$-196\,{^\circ}$C和$-130\,{^\circ}$C的解理断裂机 理. 拉伸试验、单、双缺口四点弯曲实验、断口形貌观察以及有限元分析结果表明, 缺口试 样发生解理断裂时均起裂于夹杂物粒子, 一种位于缺口根部前端(IC型), 另一种位于距缺口 根部较远的条形裂纹前端(SIC型); 且随温度升高, 起裂源的类型从$-196\,{^\circ}$C下的IC 型转变为$-130\,{^\circ}$C下的SIC型. 微裂纹均形核于夹杂物, 最终的断裂由铁素体晶粒尺 寸的微裂纹扩展控制. 缺口试样IC型解理断裂遵循裂纹形核条 件$\varepsilon_{\rm p} \ge \varepsilon_{\rm pc}$和裂纹扩展条件$\sigma_{yy} \ge \sigma_{f}$, 而SIC型解理断裂条件则演化为$\varepsilon_{\rm p}+\varepsilon_{\rm ps} \ge \varepsilon_{\rm pc}$和$\sigma_{yy} +\sigma_{yy{\rm s}} \ge \sigma_{f}$.     

扩张道路收费站的元胞自动机模型

基于可变安全间距敏感驾驶模型对道路收费站系统进行了模拟研究. 与采用NS模型的收费站系统进行了比较, 发现在慢化概率较大时(p=0.5), 该模型不仅使道路的通行能力得到完全恢复, 还使其得到一定程度的提高; 当道路扩张区域长度L_{\rm B} \ge7时, 通行能力得到很好的恢复; 当L_{\rm B}<7时, 随着L_{\rm B}的减少, 通行能力也随之降低.      

磁场对多孔介质方腔内空气热磁对流的影响

数值分析了微重力下圆形载流线圈倾斜时多孔介质方腔内空气热磁对流. 磁场计算采用毕奥--萨伐定律求解; 动量方程与能量方程分别采用达西模型与局部热非平衡模型求解. 计算结果表明随着磁场力数\gamma 数和Da数的增加, 方腔内对流变得越来越强. 线圈倾斜角x_{\rm euler}从0^\circ到90^\circ变化时, 对流结果关于x_{\rm euler}=45^\circ呈现对称分布. Nu_{\rm m}数随线圈倾斜角的改变而变化且每个工况下局部最大Nu_{\rm m}数出现在x_{\rm euler}=45^\circ. 局部最小Nu_{\rm m}数出现在x_{\rm euler}=0^\circ, 90^\circ.      

分段吸气高层建筑减阻性能的数值研究

为减小高层建筑的风致阻力, 采用CFD方法研究了主动吸气控制下高层建筑模型的风载荷减阻性能, 分析了竖向开孔位置、吸气孔高度和吸气速度等参数对减阻性能的影响, 并详细展示流场,讨论吸气控制机理. 结果表明: 保持流量系数不变, 增加吸气孔高度(或减小吸气速度)使得模型各表面的风压折减效 率$\eta_{\rm{PR}}$, 阻 力折减效率$\eta_{\rm{DR}}$和基底弯矩折减效率$\eta_{\rm{MR}}$增大, 且只有$\eta_{\rm{MR}}$在较大吸气孔高度时超过1.0. 拟合了$\eta_{\rm{DR}}$ 和$\eta_{\rm{MR}}$关于吸气孔中心高度、吸气孔高度和吸气速度的经验公式, 为分段吸气控制的应用提供参考. 基于最大风压折减效率和最小吸气功率,比较了 各分段吸气模型和全高吸气模型的减阻性能, 发现全高吸气模型的减阻性能优于分段吸气模型. 可在高层建筑中上部设置吸气装置来减小基底弯矩或改善其局部风压特性.     

低雷诺数串列双方柱流致振动质量比效应的数值研究

为澄清串列双方柱流致振动的质量比效应, 采用数值模拟方法, 在雷诺数为150时, 研究了质量比($m^{\ast }=3$, 10, 20)对下游方柱振动响应特性的影响规律, 分析了下游方柱尾流模态的演变过程, 探讨了导致下游方柱振动的流固耦合机制. 结果表明: 质量比对下游方柱的流致振动有重要影响, 低质量比($m^{\ast }=3$)时下游方柱的振动响应更为复杂, 随着折减速度的增大, 下游方柱并未出现传统“锁定”现象(即振动频率比$f_{y}$/$f_{\rm n} \approx1$的锁定), 而发生了“弱锁定”现象(即$f_{y}/f_{\rm n}<1$的锁定); 随着质量比的增加($m^{\ast }=10$和20), “弱锁定”现象消失, 而出现传统“锁定”现象, 且下游方柱横流向最大振幅减小. 质量比对串列双方柱的柱心间距有明显影响, 低质量比($m^{\ast }=3$)时的柱间距在振动锁定区内会急剧减小, 而较高质量比($m^{\ast }=10$和20)下的柱间距则变化不大. 此外, 质量比对串列双方柱的尾流模态和流固耦合机制也有显著影响, 其中低质量比($m^{\ast }=3$)下的情况更为多样.      

开裂孔隙材料渗透率的细观力学模型研究

采用细观力学方法对含随机裂纹网络的孔隙材料渗透性进行研究.开裂孔隙材料渗透性的影响因素包括裂纹网络的密度、连通度、裂纹的开度以及孔隙材料基体渗透性.对于不连通的裂纹网络,该文采用已有的相互作用直推法(interaction direct derivative,IDD)的理论框架,引入裂纹的密度$\rho$和裂纹开度比$b$,提出了裂纹夹杂$\!$-$\!$-$\!$基体两相复合材料渗透率的IDD理论解.对于部分连通裂纹网络,考虑局部裂纹团内部各个裂纹对有效渗透率的相互放大作用,引入裂纹网络的连通度$f$,定义与连通度相关的水平裂纹密度$\rho^{h}$,按照增量法将表征连通特征的水平裂纹嵌入有效基体中,以此方式来考虑裂纹夹杂间的相互搭接,提出了考虑裂纹连通特征的扩展IDD理论解,分别考虑了基体材料渗透率$K_{m}$、裂纹密度$\rho $、裂纹开度比$b$以及与连通度$f$相关的$\rho ^{\rm h}$.最后通过对有限区域内含随机裂纹网络孔隙材料渗透过程的有限元模拟分别验证了不连通和部分连通裂纹网络扩展IDD模型的适用性:(1)当裂纹不连通时,由于基体对流体渗透的阻隔作用,裂纹的开度对有效渗透率影响不大;(2)当裂纹部分连通时,裂纹密度分别小于1.1(无关联裂纹网络,分形维数为2.0)、1.2(关联裂纹网络,分形维数为1.75)时,扩展IDD模型能够很好地估计开裂孔隙材料的有效渗透率,但是随着裂纹进一步扩展,最大裂纹团主导作用凸显,扩展IDD模型不再适用.      

超声弯曲疲劳试验方法及其应用

在三点弯曲超声疲劳试验方法的基础上开发了对称弯曲超声疲劳试验系 统. 介绍了对称弯曲超声疲劳试样的设计及其加工误差的影响,并利用对称弯曲超声疲劳系 统(20\,KHz)测定了50$^{\#}$车轴钢的$S$-$N$曲线. 结果表明,50$^{\#}$车轴 钢的$S$-$N$曲线是一条连续下降型曲线. 与对称拉压加载下50$^{\# }$车轴钢的$S$-$N$曲线对比结果表明,在高周阶段,加载方式对疲劳性能有明显 影响,而在超高周阶段,加载方式无明显影响.     

动力学平衡方程的Euler中点辛差分求解格式

给出了动力学方程${\pmb M}\ddot {\pmb x} + {\pmb C}\dot {\pmb x} + {\pmb K \pmb x} = {\pmb R}$的二阶Euler中点隐式差分求解格式，分保守系统、无 阻尼受迫振动系统和阻尼系统3种情况, 讨论了算法中Jacobi矩阵${\pmb A}$的性质，譬 如${\pmb A}$是否为辛矩阵以及谱半径等. 对于无阻尼系统，证明了无论是否存在外 载荷，Jacobi 矩阵都是辛矩阵. 证明了辛矩阵的所有本征值的模为1，其谱半径永远 为1, 以及$\delta = 0.5$和$\alpha = 0.25$的Newmark算法就是Euler中点隐式差 分格式，对保守系统它们都是辛算法. 严格证 明了Euler中点辛格式是严格保持系统能量的. 通过算例详细讨论了保辛算法用于求解非保 守系统动态特性的优越性，如广义保结构特性等；分析了保辛算法的相位误差以及由其引起 的系统的附加能量特性；分析了保辛算法和$\delta \ne 0.5$的Newmark算法的精度随着激励频率与系统固有频率比的变化情况等     

外包钢-砼组合梁纯扭作用下抗扭刚度的实验及数值模拟

为了研究新型外包钢-砼T形截面组合梁在纯扭作用下的变形性能,设计了5根不同配箍率的的足尺悬臂组合梁。通过对5根悬臂梁的抗扭性能的实验研究,得到了组合梁的扭矩-扭率关系曲线。利用有限元分析软件ANSYS,对组合梁的抗扭性能进行了非线性有限元分析,得到了混凝土与外包钢在极限阶段的应力云图。根据实验以及有限元结果分析了组合梁在整个加载过程中扭转刚度的变化。基于现行砼结构设计规范,提出了组合梁从开裂到极限阶段抗扭刚度的计算公式,可供组合梁受扭设计参考。把有限元模型和公式的计算结果与实验结果进行比较,三者吻合较好。     

Determining Critical Stresses for Axially Compressed Cylindrical Shells from an Analysis of Response Characteristics

The stability of metallic and glass-reinforced plastic cylindrical shells is analyzed experimentally. It is established that if the equivalent stiffness is taken as an argument of the formula used to evaluate critical stresses in designing a shell, then the critical stresses depend linearly on its stiffness     

核工程钢板混凝土墙防撞击贯穿实用计算方法

针对带对拉钢筋的双钢板混凝土墙，研究了双钢板混凝土墙防贯穿计算方法，建立了基于能量法的防贯穿计算公式。在已知弹体和钢板混凝土墙体材料与几何相关参数时，利用防贯穿实用计算公式可对带对拉钢筋的核工程双钢板混凝土墙体贯穿速度以及弹体剩余速度进行计算，避免了复杂的结构抗撞击反应动力时程数值分析。为验证公式的可靠性，将公式计算结果与已有刚性弹体撞击双钢板混凝土墙实验结果及其动力有限元计算结果进行对比，结果表明:防贯穿实用计算公式可以正确判断双钢板混凝土墙的贯穿状态，实用计算公式给出的弹体剩余速度与实验结果符合良好。为进一步验证公式的适用范围，将公式计算结果与共10个工况的飞机发动机撞击双钢板混凝土墙的有限元计算结果进行了对比分析，结果表明:除1个工况计算结果偏差略超10%外，其余工况的偏差均在10%以内，说明该计算方法合理可行。     

Residual stiffness assessment of structurally failed reinforced concrete structure by dynamic testing and finite element model updating

When an under-reinforced concrete beam structure has been loaded to the point where reinforcing steel on the tension side has yielded, it is deemed to have structurally failed and the full load capacity and stiffness can no longer be developed. When unloaded from the point of failure, the residual stiffness of the structure is difficult to estimate. There is a need to establish the serviceability of the structure and ultimately establish the levels of further loading that can be sustained before total collapse. In this paper we present a method for assessing residual stiffness of such a “failed” reinforced concrete structure, through the application of dynamic testing and finite element (FE) model updating. In an experimental study, failed zones in a beam structure were simulated in a FE model. Through a procedure of sensitivity-based updating using the measured modal properties, the stiffness distribution along the failed beam structure was identified.     

On prestress stiffness analysis of bolt-plate contact assemblies

Bolt connections are among the most important connections used in structures. The stiffnesses of the bolt and of the connected members are the primary qualities that control the lifetime of the connection. The stiffness of the bolt can be estimated rather easily, in contrast to the member stiffness, but with finite element (FE) and contact analysis, it is possible to find the stiffness of the member. In the case of many connections and for practical applications, it is not suitable to make a full FE analysis. The purpose of the present paper is to find simplified expressions for the stiffness of the member, including the case when the width of the member is limited. The calculation of the stiffness is based on the FE, including the solution to the contact problem, and we express the stiffness as a function of the elastic energy in the structure, whereby the definition of the displacements related to the stiffness is circumvented. The contact analysis is performed using a method where iterations are not necessary, and the results are compared to alternative available results. New practical formulas for the stiffnesses are suggested.     

An Experimental–Numerical Methodology for a Rapid Prototyped Application Combined with Finite Element Models in Vertebral Trabecular Bone

In the present study, a novel evaluation method involving rapid prototyped (RP) technology and finite element (FE) analysis was used to study the elastic mechanical characteristics of human vertebral trabecular bone. Three-dimensional (3D) geometries of the RP and FE models were obtained from the central area of vertebral bones of female cadavers, age 70 and 85. RP and FE models were generated from the same high-resolution micro-computed tomography (μCT) scan data. We utilized RP technology along with FE analysis based on μCT for high-resolution vertebral trabecular bone specimens. RP models were used to fabricate complex 3D objects of vertebral trabecular bone that were created in a fused deposition modeling machine. RP models of vertebral trabecular bone are advantageous, particularly considering the repetition, risks, and ethical issues involved in using real bone from cadaveric specimens. A cubic specimen with a side length of 6.5 mm or a cylindrical specimen with a 7 mm diameter and 5 mm length proved better than a universal cubic specimen with a side length of 4 mm for the evaluation of elastic mechanical characteristics of vertebral trabecular bones through experimental and simulated compression tests. The results from the experimental compression tests of RP models closely matched those predicted by the FE models, and thus provided substantive corroboration of all three approaches (experimental tests using RP models and simulated tests using FE models with ABS and trabecular bone material properties). The RP technique combined with FE analysis has potential for widespread biomechanical use, such as the fabrication of dummy human skeleton systems for the investigation of elastic mechanical characteristics of various bones.     

Development and experimental validation of a continuum micromechanics model for the elasticity of wood

This contribution covers the development and validation of a microelastic model for wood, based on a four-step homogenization scheme. At a length scale of several tens of nanometers, hemicellulose, lignin, and water are intimately mixed, and build up a polymer (polycrystal-type) network. At a length scale of around one micron, fiberlike aggregates of crystalline and amorphous cellulose are embedded in an contiguous polymer matrix, constituting the so-called cell wall material. At a length scale of about one hundred microns, the material softwood is defined, comprising cylindrical pores (lumen) in the cell wall material of the preceding homogenization step. Finally, at a length scale of several millimeters, hardwood comprises larger cylindrical pores (vessels) embedded in the softwood-type material homogenized before. Model validation rests on statistically and physically independent experiments: The macroscopic stiffness values (of hardwood or softwood) predicted by the micromechanical model on the basis of tissue-independent (‘universal’) phase stiffness properties of hemicellulose, amorphous cellulose, crystalline cellulose, lignin, and water (experimental set I) for tissue-specific composition data (experimental set IIb) are compared to corresponding experimentally determined tissue-specific stiffness values (experimental set IIa).     

考虑Steigmann-Ogden表面的微纳米圆柱解析模型

基于Steigmann-Ogden（S-O）表面理论,研究了圆柱形微纳米材料在轴向对压荷载作用下的力学性能。利用级数展开求解材料内部的弹性控制方程,获得了考虑表面效应时的域内解析表达式。当所得结果忽略表面弯曲参数时可退化为Gurtin-Murdoch（G-M）表面模型。用文献中有限元数值结果对本理论进行退化验证,结果得到良好一致性。在此基础上,讨论了表面弯曲参数和圆柱尺寸大小对材料特性的影响。结果显示：考虑了表面弯曲效应的S-O模型和G-M模型在应力分布中有很大的不同。另外,随着圆柱尺寸的减小,其表面效应对材料的力学特性的影响逐渐增大。     

The effects of the interphase and strain gradients on the elasticity of layer by layer (LBL) polymer/clay nanocomposites

A synergistic stiffening effect observed in the elastic mechanical properties of LBL assembled polymer/clay nanocomposites is studied via two continuum mechanics approaches. The nanostructure of the representative volume element (RVE) includes an effective interphase layer that is assumed to be perfectly bonded to the particle and matrix phases. An inverse method to determine the effective thickness and stiffness of the interphase layer using finite element (FE) simulations and experimental data previously published in Kaushik et al. (2009), is first illustrated. Next, a size-dependent strain gradient Mori–Tanaka (M–T) model (SGMT) is developed by applying strain gradient elasticity to the classical M–T method. Both approaches are applied to LBL-assembled polyurethane–montmorillonite (PU–MTM) clay nanocomposites. Both two-dimensional (2D) and three-dimensional (3D) FE models used in the first approach are shown to be able to accurately predict the stiffness of the PU–MTM specimens with various volume fractions. The SGMT model also accurately predicts the experimentally observed increase in stiffness of the PU–MTM nanocomposite with increasing volume fraction of clay. An analogy between the strain gradient effect and the role of an interphase in accounting for the synergistic elastic stiffening in nanocomposites is provided.     

Equivalence conditions between linear Lagrangian finite element and node‐centred finite volume schemes for conservation laws in cylindrical coordinates

A complete set of equivalence conditions, relating the mass‐lumped Bubnov–Galerkin finite element (FE) scheme for Lagrangian linear elements to node‐centred finite volume (FV) schemes, is derived for the first time for conservation laws in a three‐dimensional cylindrical reference. Equivalence conditions are used to devise a class of FV schemes, in which all grid‐dependent quantities are defined in terms of FE integrals. Moreover, all relevant differential operators in the FV framework are consistent with their FE counterparts, thus opening the way to the development of consistent hybrid FV/FE schemes for conservation laws in a three‐dimensional cylindrical coordinate system. The two‐dimensional schemes for the polar and the axisymmetrical cases are also explicitly derived. Numerical experiments for compressible unsteady flows, including expanding and converging shock problems and the interaction of a converging shock waves with obstacles, are carried out using the new approach. The results agree fairly well with one‐dimensional simulations and simplified models. Copyright © 2013 John Wiley & Sons, Ltd.