动力学系统精细算法的逼近机理与误差上界

发现以下三者的协同作用是实现精细算法高精度,高效率的内在机理和根本原因：１）指数矩阵ｅ＾Ｈｚ的Ｍａｃｌａｕｒｉｎ级数展开式绝对收敛;２）初始Ｍａｃｌａｕｒｉｎ级数展开式中有效展开项总数能够通过递推算法以指数方式扩展;３）新增有效展开项的系数能够通过递推算法以指数或拟指数方式逼近其真值。此外,本文还给出了精细算法的截项误差递推公式和相关的误差上界,发现随着保留项数Ｍ或递推阶数Ｎ的增大,精细算法的逼近     

含等档的输电线面内自由振动理论

连续档导线运动方程包含平方和立方非线性项,倍频时会产生多模态耦合的复杂响应,因此研究连续档导线模态及共振的频率分布规律尤为重要．基于模态综合法获得了具有相等档距的连续档导线模态函数,基于动刚度理论得到了不同模态对应的频率理论公式,并应用有限元方法验证了模态及频率理论公式的准确性．研究了不同模态对应频率随几何参数的变化趋势,结果表明有相等档距的连续档导线的共振条件和单档导线有明显区别,连续档导线面内对称模态之间容易产生1:1共振,面内对称与反对称模态之间易产生1:2共振．本文研究内容可用来分析连续档导线内共振及其分岔行为．     

应变率及温度对FGH95粉末高温合金塑性变形性能影响的实验研究

在420℃～650℃的温度范围内,实验研究了FGH95粉末高温合金在应变率0．0001s^-1～0．01S^-1范围内的拉伸一断裂性能,分析了温度和应变率对该合金流动应力的影响,结果表明,应变率对杨氏模量、拉伸屈服强度和塑性模量的影响不是很大,随着应变速率的增大和温度的升高,合金的塑性流动应力有所提高,断裂强度和断裂韧性增强。并通过流动应力与应变、应变率和温度之间的函数关系,分别讨论了硬化指数咒、应变速率敏感系数m及应力相关系数K与温度ε和应变率;的函数关系。SEM断口分析表明FGH95合金是微缺陷敏感材料,在高温（420℃-650℃）应变率范围为10^-4s^-1～10^-1s^-1时的拉伸断裂都是韧性断裂。     

316L不锈钢不同取向压痕应变率敏感性研究

本研究探讨了不同取向对激光选区熔化(SLM)成形316L不锈钢力学性能的影响．使用纳米压痕测试系统对SLM成形316L不锈钢扫描平面方向和叠加成形方向两个取向的试样进行测试,并通过相关计算得出了材料在这两个方向的弹性模量、硬度、应变率敏感性指数等力学参数．实验结果表明,扫描平面方向的弹性模量和叠加成形方向的弹性模量基本相同;在相同的压入应变率下,扫描平面方向的硬度大于叠加成形方向的硬度;而对于不同的压入应变率,在高应变率下的压痕硬度相对较大;随着压入深度的增加,硬度逐渐减小并趋于稳定值．此外,本研究分析了不同压入应变率下硬度和应变率敏感性指数m的压痕尺寸效应,并得到与尺寸无关的硬度和应变率敏感性指数m．最后,通过引入扫描平面方向准静态宏观压缩工况下的应变率敏感性指数m加以验证本研究的合理性,揭示了SLM成形316L不锈钢在不同取向上应变率敏感性的差异,进而为研究准静态宏观压缩下叠加成形方向的应变率敏感性提供了支撑．     

Whitham公式在球形内爆实验中的适用性研究

球形内爆实验是实现超高压状态方程测量的方法之一,Whitham公式可对球面聚心冲击波的传播特性进行描述。文中给出了确定Whitham公式系数的方法,针对使用两种不同厚度样品球形内爆实验,通过Whitham系数不确定度分析及其求解方程组的性态分析,探讨了Whitham公式在球形内爆实验中的适用范围。结果表明,样品厚度过薄时,Whitham公式不能应用;当0．8〈A1=R1／R0〈0．857且A2=R2／R0〈0．657时,在内爆实验的结果分析和处理中应用Whitham公式可能会取得较好的结果。     

关于悬链冲击效应的两个通项公式

本文对悬挂在重力场中的链条或珠串，其端部受冲击时，导出了求各链环所受冲击与角速度问题的两个通项公式．     

用高阶剪切变形理论研究双模量梁的弯曲

利用高阶剪切变形理论研究了双模量梁的弯曲变形问题，推导出了双模量梁的挠曲线方程及弯曲正应力公式．讨论分析了翘曲函数的指数n对挠度、正应力的影响．研究结果表明：拉压弹性模量的差异对梁的弯曲应力有较大影响．把高阶剪切变形理论的计算结果与弹性理论计算结果进行比较，可知该方法计算精度非常高．     

不同模量壳体理论广义弹性定律的普遍表达式

本文研究了拉伸和压缩不同模量材料制成的壳体弱矩理论的本构关系,导出了广义弹性定律的普遍表达式,即中曲面法向坐标的各任意幂次项系数的公式,并指出文献[1]中最终公式保留的线性项,仅为本文普遍表达式的一个较简单的特殊情形,因此,可以不顾文献[1]中关于应力沿壳厚按线性规律变化的基本假设。     

凹边坡参数对边坡稳定性的影响

抽象出凹边坡的几何模型,采用量纲分析的方法,给出凹边坡几何参数和物理力学参数对边坡稳定系数的影响通式．在FLAC定义的边坡稳定系数意义下,经过数万次计算,采用二次回归的方法,确定了通式中的影响指数,形成经验公式．结果表明,受Mohr-Coulomb和拉应力两个强度准则控制的材料,形成的凹边坡的稳定性受无量纲粘聚力、边坡角、内摩擦角的控制．凹形边坡有利于边坡的稳定,边坡稳定性与岩土的抗拉强度关系不大．这一稳定系数公式对于形状规则均匀性好且符合Mohr-Coulomb破坏准则的凹边坡可以给出精度高的估计．对于其它边坡的稳定性评价还需要做有针对性的工作．     

膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显．     

Decoupling of Autogenous Shrinkage and Tensile Creep Strain in High Strength Concrete at Early Ages

Appropriately interpreting the measured creep strain is critical for obtaining the actual creep strain, especially for high-strength concretes characterized by a low water/cement ratio (w/c) because autogenous shrinkage is significant in such concrete at early ages. To investigate the interaction between the autogenous shrinkage and tensile creep of concrete at early ages, various tests were conducted on concretes with water/cement (w/c) ratios =0.3 and 0.4, including basic tensile creep, strength, autogenous shrinkage, and the internal relative humidity (RH) measurements. The load was applied at the ages of 1 and 7 days at the stress/strength levels of 40% and 70%, respectively. It was found that the measured early-age tensile creep strain becomes negative due to the large autogenous shrinkage involved. The principle of superposition can be used for creep-autogenous shrinkage decoupling to obtain the actual basic tensile creep, as there is virtually no additional RH reduction or stress-induced shrinkage in concrete due to the sustained tensile load at early ages. An average tensile strength gain of 8.2% was found in specimens after sustained tensile loading compared to the unloaded specimens. An exponential function is proposed to quantify the autogenous shrinkage effect on the basic tensile creep in terms of specific creep/autogenous shrinkage ratio.     

脆性材料中应力波衰减规律与层裂实验设计的数值模拟

对混凝土、岩石类脆性材料的层裂实验进行了有限元模拟,研究了应力波在此类材料中传播的衰减规律,包括两类机制:弹性波因大尺寸试样的几何弥散产生的小幅度线性衰减、与应变率相关的黏塑性波因本构关系导致的指数衰减。在此基础上,提出了包含常数项的指数型应力波峰值拟合公式。建议采用可以忽略应力波衰减影响的细长形试样进行层裂实验。混凝土类脆性材料层裂破坏模拟结果显示,有限元模拟得到的层裂片厚度与一维应力波理论得到的结果非常吻合,验证了按一维应力波理论确定层裂强度的实验方法的有效性。通过对比3种不同入射波形下层裂片的形状和净拉应力波形,发现不对称的入射波形状更有利于实验获得平直的层裂断面和较准确的层裂强度。     

Three-phase plane composites of minimal elastic stress energy: High-porosity structures

The paper establishes exact lower bound on the effective elastic energy of two-dimensional, three-material composite subjected to the homogeneous, anisotropic stress. It is assumed that the materials are mixed with given volume fractions and that one of the phases is degenerated to void, i.e., the effective composite is porous. Explicit formula for the energy bound is obtained using the translation method enhanced with additional inequality expressing certain property of stresses. Sufficient optimality conditions of the energy bound are used to set the requirements which have to be met by the stress fields in each phase of optimal effective material regardless of the complexity of its microstructural geometry. We show that these requirements are fulfilled in a special class of microgeometries, so-called laminates of a rank. Their optimality is elaborated in detail for structures with significant amount of void, also referred to as high-porosity structures. It is shown that geometrical parameters of optimal multi-rank, high-porosity laminates are different in various ranges of volume fractions and anisotropy level of external stress. Non-laminate, three-phase microstructures introduced by other authors and their optimality in high-porosity regions is also discussed by means of the sufficient conditions technique. Conjectures regarding low-porosity regions are presented, but full treatment of this issue is postponed to a separate publication. The corresponding “G-closure problem” of a three-phase isotropic composite is also addressed and exact bounds on effective isotropic properties are explicitly determined in these regions where the stress energy bound is optimal.     

小冲杆试验确定材料拉伸断后伸长率的研究

小冲杆试验技术可以近似无损地测试材料的力学性能.本文对几十种材料进行了小冲杆试验研究,对小冲杆试样的抽向挠度δ与拉伸断后伸长率A进行了经验关联.研究表明,对于试验中涉及的几十种材料,二者之间没有统一的线性相关公式,但可以按材料的杭拉强度和屈强比将材料分类,然后分别对δ和A进行线性关联.对于抗拉强度小于600MPa的材料...     

基于巴西盘试验的海冰拉伸强度研究

海冰拉伸强度是其基本力学性能之一, 同时也是冰区船舶与海洋工程结构设计所需的重要参数. 对于脆性材料的拉伸强度测试, 巴西盘劈裂试验相比单轴拉伸试验在试样制备与加载上具有明显的优势. 为研究海冰的拉伸强度特征, 对渤海辽东湾沿岸的粒状冰开展了系统的巴西盘劈裂试验研究. 在加载过程中与试样破坏后, 分别对加载横梁的位移与加载力以及试样最终破坏模式进行了记录. 同时, 对试样的冰晶结构、盐度、温度以及密度进行了测量. 通过改变加载速率、试样厚度与试样温度以研究不同参数对试验结果的影响. 针对传统试验中试样的刚体假设, 考虑了试样变形对应力状态的影响并将其引入了理论模型. 试验过程中所有海冰试样均以劈裂模式破坏. 试验结果表明, 加载速率与试样厚度对拉伸强度的影响并不显著, 但孔隙率的影响较为明显. 当孔隙率由75‰降低至10‰时,拉伸强度由1.0 MPa升高至2.8 MPa. 与单轴拉伸试验所测得数据对比, 巴西盘劈裂试验所得到的拉伸强度随孔隙率的变化趋势相一致. 但该方法所得到的粒状冰拉伸强度要高于预期结果. 试验表明巴西盘劈裂试验中海冰试样的破坏模式与试验结果均较为合理, 可成为海冰拉伸强度的有效测试方法.      

Estimation of Dynamic Relative Permeability and Capillary Pressure from Countercurrent Imbibition Experiments

Direct laboratory measurements of in situ water-phase saturation history are used to estimate relative permeability and capillary pressure functions. The magnitude of so-called nonequilibrium effects during spontaneous imbibition is quantified and, if significant, these effects are incorporated within the estimation technique. The primary constraint employed is that curves must increase or decrease monotonically; otherwise, no predetermined functionality is assumed. The technique is demonstrated using water saturation profile histories obtained for diatomite (a low-permeability and high-porosity rock). Results indicate that nonequilibrium effects detected at laboratory scale in low-permeability rocks influence the estimation of unsteady-state relative permeability and capillary pressure.     

Deformation and long-term damage of layered materials with stress-rupture microstrength described by an exponential power function

The theory of long-term damage of homogeneous materials is generalized to layered materials. The damage of the components is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the exponential power dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the components at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of exponential power microdurability function     

Analysis and modelling of the cohesion strength of concrete at high strain-rates

With the exponential increase of computational power, numerical simulations are more and more used to model the response of concrete structures subjected to dynamic loadings such as detonation near a concrete structural element or projectile-impact. Such loadings lead to intense damage modes resulting from high strain-rate tensile loadings in the concrete structure. However, the modelling of the post-peak tensile response of concrete still remains difficult due to the lack of experimental data at high strain-rates. This work aims at improving the modelling of the softening behaviour of concrete based on the following statement: despite the propagation of unstable cracks in the tested specimen cohesion strength exists in the vicinity of triggered cracks and is driving the whole softening behaviour of concrete. This statement is justified in the present work by means of experiments and Monte-Carlo calculations: firstly, concrete samples have been subjected to a dynamic tensile loading by means of spalling experiments. Several specimens have been recovered in a damaged but unbroken state and have been subsequently loaded in quasi-static tensile experiments to characterise the residual strength and damage level in the sample. In addition, Monte-Carlo simulations have been conducted to clarify the possible influence of cohesion strength in the vicinity of cracks. Finally, the DFH (Denoual–Forquin–Hild) anisotropic damage model has been adapted to take into account the cohesion strength in the damaged zone and to describe the softening behaviour of concrete. Numerical simulations of experiments conducted on dry and saturated samples at different levels of loading-rate illustrate the new capability of the model.     

CO2腐蚀环境下P110套管材料性能的实验研究

针对CO2腐蚀环境下P110套管材料性能动态变化的难题,基于腐蚀实验与拉伸实验,对含腐蚀损伤的P110套管进行了力学性能分析。根据现场资料对钻井液注入CO2配置腐蚀液,将腐蚀后试件与现场失效套管的腐蚀产物进行EDS能谱分析对比,确定了腐蚀液的适用性。设置固定井深,在100℃高温时不同的腐蚀实验周期内,将所得的含腐蚀损伤试件进行质量损失测试及拉伸实验,分析了材料力学性能的变化。由MTS液压式万能试验机得出应力-应变曲线,并拟合得到了等效屈服强度变化公式及等效抗拉强度变化公式。结果表明:套管试样腐蚀后的屈服强度和抗拉强度随着失重率增大而减小,当套管试样经腐蚀后失重率低于15%时,材料的力学性能,如等效屈服强度和等效抗拉强度随失重率的增加会以较大幅度降低;而当试样失重率大于15%时,随着失重率的增加,等效屈服强度急剧减小,等效抗拉强度则以较为平缓的趋势降低。     

Tensile fracture behavior of heterogeneous materials based on fractal geometry

Many of heterogeneous structural materials, like concrete, have different behavior under tensile stresses in comparison to their behavior under compressive stresses. The aim of this paper is to interpret behavior of such materials subjected to tensile stresses, by using newly introduced concept of fractal geometry. In the first part of this paper, tensile behavior of granular composites has been studied by using fractal geometry. It is shown that the fractality of the cross section in this kind of composites can be used to interpret the size effect on tensile strength. In fact, this work is a modification with innovations on the previous studies on fractal based size effect.This hypothesis that the fracture surfaces of quasi-brittle materials are fractals has been verified by several investigations. Accordingly, in the other part of this paper, softening process in heterogeneous materials is studied. Resulting from presented approach, a new softening curve for quasi-brittle materials is proposed. This new softening curve is denominated “Quasi-fractal softening curve” and is consisted of two parts, a linear portion in beginning part and an exponential portion in rest of the curve. This makes it very compatible to the pre-existing softening curves.