Rate effect and coupled evolution of atomic motions and potential landscapes

Since rate effect of materials plays a key role in impact engineering, the microscopic mechanism of rate effect is investigated at molecular level in this paper. The results show that rate effect on the strength of atomic system is closely related to the coupled evolution of atomic motions and potential landscapes. Accordingly, it becomes possible to develop a new algorithm of molecular simulation, which could properly and efficiently demonstrate strain rate effect under a wide range of loading rates and unveil the mecha- nisms underlying the strain rate effects.     

-196 ℃奥氏体不锈钢母材与焊缝的动态断裂韧性

在-196 ℃对S30408奥氏体不锈钢的母材和焊缝进行了夏比摆锤冲击实验,采用改进的柔度变化率法得到了低温下不锈钢母材夏比试样的起裂点。结果表明,采用改进的柔度变化率法得到的结果比采用传统的柔度变化率法得到的结果更准确。根据实验得到的载荷-位移曲线,结合采用Schindler法和关键曲线法各自所得结果的优点,得到了不锈钢母材的动态裂纹扩展阻力曲线（动态J-R曲线）。依据不锈钢焊缝在低温动载下的载荷-位移曲线及其断裂特征,通过线弹性断裂力学计算获得其动态断裂韧性。     

A continuous–discontinuous cellular automaton method for regular frictional contact problems

In the present paper, a continuous–discontinuous cellular automaton method is developed to model the discontinuous problems caused by regular frictional contact, in which level set method, discontinuous enriched shape function, discontinuous cellular automaton method and contact friction theory are combined, by which an analysis from continuity to discontinuity can be achieved, and no assembled stiffness matrix but only cell stiffness is needed in the whole calculation, because of the use of discontinuous cellular automaton method. In the present method, level set method is used to track the discontinuous surface, and discontinuous enriched shape function is employed to describe the discontinuity of displacement and stress. Contact friction theory is applied to construct the Coulomb frictional contact model of discontinuous surfaces; besides, combined with discontinuous cellular automaton method, a new mixed iteration method is proposed to obtain the solution of the problem, and no assembled stiffness matrix is constructed. And the frictional contact iterations are done simultaneously with the updating of cellular automaton, in which the contact states and contact areas can be previously obtained in the cellular automaton updating process, and the efficiency can get much higher. Finally, some numerical examples are given to show that the present method is effective and accurate and can be further extended into some practical engineering.     

基于时域间断有限元方法的生物组织非傅立叶热行为数值分析

在热传导分析中,当热流与温度梯度存在时间延迟时,需采用非傅立叶热传导模型进行分析。生物组织具有较强的热松弛时间系数,承受激光、微波及烧烫等作用时,其呈现出较强的非傅立叶行为。本文对脉冲热源作用下生物组织的非傅立叶热传导进行研究,针对强脉冲引起的温度场在空间域的高梯度变化、波阵面的间断行为以及通用传统时域数值方法会带来虚假数值振荡的特点,提出采用所发展的时域间断Galerkin有限元法（DG-FEM ）进行求解计算。对多种脉冲热源作用下的非傅立叶热传导过程进行数值模拟,通过考量强脉冲作用下温度场分布和热致生物组织损伤行为的影响,表明了本文所发展的DGFEM 能够有效、准确地描述温度场空间分布和热传导过程以及非傅立叶行为下的生物热损伤更为明显,在生物组织热行为分析中应该受到重视。     

基于任意形状颗粒集合二值图像的体积估算模型

基于任意形状颗粒集合的二值图像,提出了估计其体积(或质量)的方法.首先利用发光背景台面获取的颗粒灰度图像变换为相应的二值图像,得到颗粒的边界轮廓.然后再基于其边界信息,定义与颗粒形状特征相关的描述量,并将其无量纲化.将由此定义的无量纲参变量作为回归变量建立一个多元线性回归(multiple linear regression)模型用以估计颗粒集合的扁平度,进而估算颗粒体积.回归变量的系数由随机采样的501个样本颗粒(尺寸范围为4.75～25 mm)用误差最小平方和求得.将模型应用于由具有相似统计分布特征的其他颗粒集合,并将得到的体积估计值与其体积真实值相比较,实验结果显示模型的相对误差在±2%以内.     

Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks

This paper considers an optimal asset-liability management problem with stochastic interest rates and inflation risks under the mean–variance framework. It is assumed that there are \(n+1\) assets available in the financial market, including a risk-free asset, a default-free zero-coupon bond, an inflation-indexed bond and \(n-2\) risky assets (stocks). Moreover, the liability of the investor is assumed to follow a geometric Brownian motion process. By using the stochastic dynamic programming principle and Hamilton–Jacobi–Bellman equation approach, we derive the efficient investment strategy and efficient frontier explicitly. Finally, we provide numerical examples to illustrate the effects of model parameters on the efficient investment strategy and efficient frontier.     

A Hopf lemma for higher order differential inequalities and its applications

We establish a sequential Hopf lemma for higher order differential inequalities in one variable and give some applications of this result.     

An application of the Kriging method in global sensitivity analysis with parameter uncertainty

For structural systems with both epistemic and aleatory uncertainties, the effect of epistemic uncertainty on failure probability is measured by the variance based sensitivity analysis, which generally needs a “triple-loop” crude sampling procedure to solve and is time consuming. Thus, the Kriging method is employed to avoid the complex sampling procedure and improve the computational efficiency. By utilizing the Kriging predictor model, the conditional expectation of failure probability on the given epistemic uncertainty can be calculated efficiently. Compared with the Sobol’s method, the proposed one can ensure reasonable accuracy of results but with lower computational cost. Three examples are employed to demonstrate the reasonability and efficiency of the proposed method.     

Polydisperse structures of composites with random elastic properties of inclusions

A generalized self-consistent method [1, 2] is developed and applied to the boundary-value problems of composites with random elastic properties of inclusions. The approach suggested makes it possible to allow for a random mutual arrangement, statistical dispersion of elastic properties and sizes of the inclusions, and their mutual correlation in terms of special homogenized indicator functions. For comparison, the analytical solutions and those obtained from a corresponding sequence of H+1 (H=0,1,…) linked homogenized problems of the self-consistent method for the strain distribution in the inclusions and for the tensor of effective elastic properties of the composite are given. A numerical calculation of the effective transversely isotropic elastic characteristics for a unidirectional polydisperse fibrous composite is also presented. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 33–58, January–February, 2000.     

非Hermitian正定线性方程组的外推的HSS迭代方法

为了高效地求解大型稀疏非Hermitian正定线性方程组，在白中治、Golub和Ng提出的Hermitian和反Hermitian分裂（HSS）迭代法的基础上，通过引入新的参数并结合迭代法的松弛技术，对HSS迭代方法进行加速，提出了一种新的外推的HSS迭代方法（EHSS），并研究了该方法的收敛性.数值例子表明：通过参数值的选择，新方法比HSS方法具有更快的收敛速度和更少的迭代次数，选择了合适的参数值后，可以提高HSS方法的收敛效率.