原状土e-lgp曲线的S形函数表达及简化加载固结试验方法

为能够较为合理地确定土体压缩参数并简化固结试验加载过程,结合京沪高铁李窑试验段地基原状细粒土样标准固结试验数据,对比分析了多项式和三种S形曲线函数在描述原状土e-lgp曲线发展规律时的差异性,探讨了先期固结压力的合理计算原则,提出了简化加载级数的固结试验方法。结果表明,多项式函数易受数据波动而导致整体拟合偏差,S形曲线函数的待定参数可良好稳定地反映曲线最小曲率半径点和直线段斜率,为较理想的e-lgp曲线数学函数表达式;通过分析Arvidsson法、Gregory法和Casagrande法,确定先期固结压力时的不同取值原则,获得了先期固结压力值的变化区间,提出土体由超固结过渡到欠固结状态时存在正常固结状态带的概念,用于判断土体固结特性较为客观合理;利用土体初始孔隙比和两级或三级荷载下的变形值可确定S形曲线函数待定参数,据此建立了简化加载级数的固结试验方法。上述研究成果可为准确判定土体固结特性、快速获取土体压缩参数提供理论指导。     

用加权残数法计算受均布边缘径向压力变厚度圆薄板的轴对称屈曲

本文以幂函数作试函数,用加权残数法求受均布径向压力的变厚度圆薄板的最小临界压力。边界为弹性支承。轴对称圆薄板的厚度按指数函数或多项式函数变化考虑。在所有的算例中,都得到了满意收敛的结果。     

应用POD和Padé拟合的线性动力学系统辨识

提出了一种线性动力学系统辨识方法。应用Padé多项式对系统的动刚度曲线进行拟合,通过最小二乘法确定Padé多项式中的系数矩阵,利用遗传算法确定出Padé拟合式中的参数。通过比较系统动刚度矩阵的理论公式和Padé拟合式,辨识得到系统的质量阵、刚度阵和阻尼阵。当系统阶数较高时,可结合POD降阶技术对系统进行辨识,该方法适用于全阶模型和降阶模型。数值仿真算例表明,本文方法具有较高的精度和较好的鲁棒性。     

基于k_w-θ_w关系的非饱和土水力梯度模型

水力梯度计算是研究渗流问题的重要一环,对于非饱和土而言,含水率的变化使得渗透系数不再是常数,水力梯度计算更加困难.本文基于一维稳态流下连续性方程,结合具体的kw-θw关系,分别获得了基于Gardner模型、Davidson模型和Compbell模型的水力梯度模型.最后通过算例对不同的水力梯度模型进行对比分析.研究结果表明:基于Gardner模型的水力梯度模型为具有双拟合参数的幂函数,基于Davidson模型的水力梯度模型为具有单拟合参数的指数函数,基于Compbell模型的水力梯度模型为具有单拟合参数的幂函数.通过对Lakeland细砂水力梯度与含水量关系模拟计算表明,基于Gardner模型的水力梯度模型在计算细砂水力梯度上效果最佳,基于Davidson模型和Compbell模型的水力梯度模型由于均引入了饱和渗透系数和饱和体积含水率而具有更明确的物理意义.     

随机结构有限元分析的递推求解方法的改进

将随机结构有限元分析的递推求解方法和伽辽金投影方法相结合,提出了求解随机静力响应的改进的递推求解方法。利用随机收敛的非正交多项式展开表示由于材料、外部荷载或构件几何尺寸的随机性导致的结构随机响应。采用递推求解方法得到响应多项式展开的初始系数,并运用定义的数学算子显式地表达出来。然后,通过定义修正系数,应用伽辽金方法对随机力平衡方程在非正交多项式基上进行投影,得到了和响应展开阶次个数相同的确定的有限元方程,并进行求解得到了修正系数。数值算例表明,通过对递推求解方法中响应表达式系数的修正,以很小的计算代价较大地提高了随机响应的计算精度;与基于正交多项式展开的随机有限元方法相比,在精度相当的前提下新方法耗费的计算时间大大降低。     

压电材料迟滞非线性特性的幂函数多项式模型

针对现有迟滞模型多应用于迟滞电学响应分析和控制方面的研究,且较少运用于动力学分析的问题,本文综合考虑压电材料的特性和迟滞曲线特点提出了建立动力学分析的迟滞模型。分别建立幂函数多项式介电迟滞模型和压电迟滞模型,并且通过与实验结果或已有模型对比,表明幂函数多项式介电迟滞模型和压电迟滞模型能准确描述压电材料的迟滞特性。同时分析了迟滞参数η和ζ对饱和极化强度和剩余应变的影响,结果表明：η的变化会影响压电迟滞曲线的形状和剩余应变的大小,当ζ不变、η增大时,饱和极化强度未改变,但剩余应变变小;ζ的变化主要影响最大变形量,当η不变、ζ增大时,产生的最大变形增大,而剩余应变变化很小。该迟滞模型比较简单,为动力学分析提供了便利。     

估计三种常用疲劳应力—寿命模型P—S—N曲线的统一经典极大似然法

拓展经典极大似然法到Langer模型,提出了估计三参数、Langer和Basquin三种常用疲劳应力-寿命模型P-S-N曲线及其置信限的统一方法。方法用于处理极大似然法疲劳试验得到的S-N数据,该试验在特别关注的参考载荷试验一组试样,其余试样在不同载荷下试验,以参考载荷试验数据的统计参量为基础,按照每个模型中材料常数协同处于相同概率水平原则,将曲线表示为对数疲劳寿命均值和均方差线的广义形式,至多4个材料常数,曲线中的材料常数按极大似然原理采用数学规划法求出。45#碳钢缺口试样（kt=20)对称循环加载试验数据的分析说明了方法的有效性,分析还揭示合理模型有必要通过比较拟合效果、预计误差和应用安全性来确定,三参数模型的拟合效果最好,Langer模型稍差,Basquin模型较差,从拟合效果、预计误差和应用安全性角度,Basquin模型不适于描述该套数据。此外,经典极大似然法估计结果可能因受局部统计参量影响而给出非安全估计,有必要发展改进的可以最大限度着小这种影响的方法。     

岩土力学参数概率分布的切比雪夫多项式推断

提出了较大样本岩土力学参数概率分布的切比雪夫多项式逼近法。基于数值逼近原理，直接根据试验样本矩，运用切比雪夫多项式推断岩土力学参数的概率密度函数，并用精度较高的K—S检验法，从理论上证明所求密度函数的正确性和实用性。该方法直接根据试验样本信息和统计方法推断，而不是事先假定成经典的理论概率分布，因此数学和物理意义更加充分。通过对各种经典分布曲线（正态分布、指数分布、对数正态分布等）数值检验，结果表明所得到的逼近表达式有很好的拟合性能。根据样本数据得出的某岩石抗压强度概率密度函数，与实际统计所得分布频率非常接近，可以满足岩土工程可靠性分析的要求。     

四参数全范围da/dN曲线测定方法研究

机械结构设计的损伤容限分析,需要使用材料疲劳裂纹扩展速率曲线性能。在总结传统疲劳裂纹扩展曲线的基础上,本文讨论了四参数全范围da/dN曲线公式;基于断裂力学原理,分别给出了此公式中材料裂纹扩展门槛值ΔKth,断裂韧性K1C和张开函数f的测定方法;利用多元线性回归法对试验数据进行了曲线拟合,得到了四参数全范围da/dN曲线公式的参数估计式;将此公式运用于不同应力比下的裂纹扩展速率试验数据拟合,通过试验数据的拟合结果可以看出:四参数全范围da/dN曲线公式,能够充分有效合理地表征全范围裂纹扩展速率的物理特性和宏观数据规律,且参数估计简便,拟合精度高;从而验证了四参数全范围da/dN曲线公式的有效性和合理性,并将得到广泛应用。     

飞艇外型设计中曲线参数化方法的比较

采用合适的参数化方法快速准确地描述优化前后的几何结构是形状和气动性能优化问题的前提.目前常用的曲线参数化基本方法有三种:Bezier,B-spline和NURBS曲线.参数化曲线拟合的关键是从已知形状反求控制点的信息,本文综合对比了三种不同参数化方法关于飞艇外形拟合性能的差异.结果表明,与其它两种曲线参数化方法相比,N...     

Local detrended fluctuation analysis for spectral red-edge parameters extraction

Nowadays, spectrum technology makes it possible to nondestructively monitor crop and provide real-time diagnostic advice. Spectral red-edge parameters are important detection target for the growth of rapeseed. In this work, we propose a new method to acquire the rapeseed’s spectral red-edge parameters based on local detrended fluctuation analysis (L-DFA). In practice, by using the L-DFA, local Hurst exponent of the spectrum is calculated firstly. And then, six traditional red-edge parameter extraction methods, namely maximum first derivative method, adjusted linear extrapolation method, linear four-point interpolation method, inverted Gaussian method, Lagrangian interpolation method, and polynomial fitting interpolation, are employed to act on the estimated local Hurst exponent, and thus four red-edge parameters, i.e., red-edge position, red-edge amplitude, and left and right red-edge area, are obtained. In our experiments, by using the above four local Hurst exponent-based red-edge parameters as argument, a prediction model is developed to forecast the SPAD values (soil and plant analyzer development, often used as a parameter to indicate the chlorophyll content) for the five rapeseed’s growth periods based on random decision forest method. The results show that the local Hurst exponent-based red-edge feature can produce better model effect than the original spectrum-based one for the all phenological periods. Significance test for the four kinds of plant patterns shows that there is huge difference of the proposed four-dimensional red-edge features between the transplant and direct plant in the whole process of rapeseed’s growth. The differences between the other three groups of plant factors (two planting densities, two fertilizer types, and two weed controls) are not significant in certain specific growth periods of rapeseed. These findings provide a basis for studying difference of rapeseed yield and oil differences between different planting patterns.     

高压捕获翼前缘型线优化和分析

为分析翼前缘形状变化对高压捕获翼构型气动性能的影响,基于一种锥体组合捕获翼概念构型,采用幂次函数和余弦函数组合形式对翼前缘型线进行了参数化设计,在比较了多项式和径向基函数两种代理模型的拟合精度基础上,以飞行马赫数7,飞行攻角0° 为计算条件,结合使用均匀实验设计方法、计算流体力学、径向基函数代理模型方法和遗传算法,选择升阻比最大化为目标开展了数值优化,最后基于优化结果进行了单参数的灵敏度分析. 优化结果表明,相对于基准外形而言,优化后构型升力系数增大了约8.1%,阻力系数减小了约12.2%,升阻比提高了约23.4%. 此外,灵敏度分析结果表明升阻比与5 个设计参数均呈非线性关系,其中展向角度对升阻比影响最大,其次为幂次曲线的比例参数,其余3 个参数对升阻比的影响相对较弱.      

Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial

In this paper, a memristor with a fourth degree polynomial memristance function is used in the simplest chaotic circuit which has only three circuit elements: a linear passive inductor, a linear passive capacitor, and a nonlinear active memristor. We use second order exponent internal state memristor function and fourth degree polynomial memristance function to increase complexity of the chaos. So, the system can generate double-scroll attractor and four-scroll attractor. Systematic studies of chaotic behavior in the integer-order and fractional-order systems are performed using phase portraits, bifurcation diagrams, Lyapunov exponents, and stability analysis. Simulation results show that both integer-order and fractional-order systems exhibit chaotic behavior over a range of control parameters.     

Determination of the mechanical constants of ZnS nanobelt by combining nanoindentation test and finite element method

The single nanobelt simplified as transversely isotropic is modeled by three dimension element during the modeling of finite element method (FEM), and the mechanical constants of ZnS nanobelt are obtained by combining nanoindentation test and FEM. In the forward analysis, the numerical loading curves at the appropriate penetration depth are simulated by using the purely mechanical indentation (PMI) and piezoelectric indentation (PI) modes to extract the numerical maximum indentation load and numerical loading curve exponent, and they are used to establish the dimensionless equations related with the mechanical constants of nanobelt by fitting the mechanical constants vs numerical maximum indentation load and numerical loading curve exponent curves. In the reverse analysis, the experimental indentation curve performed on ZnS nanobelt is fitted as the power function to obtain the maximum indentation load and the loading curve exponent and they are substituted into the dimensionless equations to solve the mechanical constants of the nanobelt. In order to verify the validity, the mechanical constants are inputted into ABAQUS software to obtain the computational loading curves under PMI and PI modes, and they are in good agreement with the experimental indentation curve of ZnS nanobelt. The combination solutions of mechanical constants under PMI mode is of larger total error than those under PI mode, and it indicates that the piezoelectric effect should be reasonably considered into the developed method, which is effective to determine the mechanical property of single nanobelt.     

非牛顿流体两相渗流问题的摄动解

本文用奇异摄动法结合正则摄动法求解了考虑毛管力因素时多孔介质中弱非牛顿流体的两相驱替问题,得到了分流函数和湿相饱和度的渐近解析解。所得结果同数值解和经典的牛顿流体两相渗流结果进行了比较,并着重讨论了非牛顿因素的影响。     

Convective-Region Top Front Propagation in a Uniform Medium under the Action of Point, Linear, and Plane Heat and Momentum Sources

A relation between the height of a convective front rising in an unstratified medium and the momentum and heat fluxes released on the substrate surface is proposed for point, linear, and uniform plane sources arbitrarily dependent on time. This relation makes it possible to determine the integral power of a plume on the basis of optical observations of the height of the propagating convective front. As particular solutions, three classes of self-similar regimes related with the heat and momentum sources, whose rate is a step-shaped, power-law, or exponential function of time, are obtained. A one-dimensional integral model of a rising convective jet is constructed. The classes of self-similar jets corresponding to power or exponential heat and momentum sources are described. It is shown that all self-similar jets corresponding to heat and momentum sources governed by a power law with a fairly large exponent are characterized by the same temperature and velocity profiles.     

The asymptotic stability analysis in stochastic logistic model with Poisson growth coefficient

The asymptotic stability of a discrete logistic model with random growth coefficient is studied in this paper. Firstly, the discrete logistic model with random growth coefficient is built and reduced into its deterministic equivalent system by orthogonal polynomial approximation. Then, the linear stability theory and the Jury criterion of nonlinear deterministic discrete systems are applied to the equivalent one. At last, by mathematical analysis, we find that the parameter interval for asymptotic stability of nontrivial equilibrium in stochastic logistic system gets smaller as the random intensity or statistical parameters of random variable is increased and the random parameter's influence on asymptotic stability in stochastic logistic system becomes prominent.     

岩石三轴蠕变试验黏弹性解析及参数识别

基于岩石三轴蠕变试验,推导了相应的黏弹性解析解,并对三参量H-K流变模型给出 了黏弹性解析解的显式以及流变参数的识别方法. 在此基础上,针对花岗岩及片岩两种岩石 的室内蠕变分级加载试验曲线进行了流变参数的识别与反演. 分析表明,同一岩样在不同加 载级别下的弹性及黏弹性参数在量值上均有所不同,其中黏弹性模量和黏滞系数的量值随 载荷的增加出现损伤衰减,基于试验反演所获参数的解析蠕变曲线与试验蠕变曲线吻合较好.     

岩石蠕变模型的比较和修正

对三种岩石在不同的应力下进行了蠕变实验,对蠕变实验曲线用粘弹模型进行了模型参数的反演,结果认为标准线性体、伯格斯和对数模型都是实验曲线的很好近似.为了进一步了解蠕变实验时间对模型参数的影响,研究了蠕变模型的预测功能.将实验蠕变曲线分成二部分,第一部分用于模型参数的反演,第二部分用于模型预测数据的检验.时间外延所得的模型的预测曲线都明显偏离了实测曲线,伯格斯和对数模型的预测曲线比实测曲线偏高,而标准线性体模型则偏低.根据不同时间的蠕变实验数据的比较和分析,认为实验时间对蠕变模型参数的反演有较为明显的影响,但只要对标准线性体模型作适当修正,引入与时间尺度有关的函数C(t),则该模型的预测能力就有较大的提高.