Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage

In this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body Ω is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non‐uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage. Copyright © 2014 John Wiley & Sons, Ltd.     

Convergence of FFT‐based homogenization for strongly heterogeneous media

The FFT‐based homogenization method of Moulinec–Suquet has recently attracted attention because of its wide range of applicability and short computational time. In this article, we deduce an optimal a priori error estimate for the homogenization method of Moulinec–Suquet, which can be interpreted as a spectral collocation method. Such methods are well‐known to converge for sufficiently smooth coefficients. We extend this result to rough coefficients. More precisely, we prove convergence of the fields involved for Riemann‐integrable coercive coefficients without the need for an a priori regularization. We show that our L² estimates are optimal and extend to mildly nonlinear situations and L^p estimates for p in the vicinity of 2. The results carry over to the case of scalar elliptic and curl ? curl‐type equations, encountered, for instance, in stationary electromagnetism. Copyright © 2014 John Wiley & Sons, Ltd.     

Structural and anisotropic elastic properties of hexagonal MP (M = Ti,Zr, Hf) monophosphides determined by first-principles calculations

First-principles calculations were performed to investigate the structural properties, phase stabilities, elastic properties and thermal conductivities of MP (M = Ti, Zr, Hf) monophosphides. These monophosphides are thermodynamically and mechanically stable. Values for the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by Voigt–Reuss–Hill approximation. The mechanical anisotropy was discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The order of elastic anisotropy is ZrP > HfP > TiP. The minimum thermal conductivities of these monophosphides were investigated using Clarke’s model and Cahill’s model. The results revealed that these monophosphides are suitable for use as thermal insulating materials and that their minimum thermal conductivities are anisotropic.     

Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations

In the present work, a three-dimensional (3D) elastic plate model capturing the small scale effects is developed for the free vibration of functionally graded (FG) nanoplates resting on elastic foundations. The theoretical model is formulated employing the nonlocal differential constitutive relations of Eringen in conjunction with the 3D equations of motion of elasticity.The material properties are assumed to vary continuously along the thickness of the nanoplate in accordance with the power law formulation. Through extending the generalized differential quadrature (GDQ) method to the three-dimensional case, the governing equations are simultaneously discretized in every three coordinate directions and are then recast to the standard form of an eigen value problem. Solving the acquired problem, the natural frequencies of the nanoplates with different boundary conditions are calculated. The convergence behavior of the numerical results is checked out and comparison studies are conducted to make sure of the accuracy and reliability of the present model. Finally, the dependence of the vibration behavior of the nanoplate on edge conditions, elastic coefficients of the foundation, scale coefficient, mode number, material and geometric parameters are discussed.     

Free vibration of non-uniform nanobeams using Rayleigh–Ritz method

In this article, boundary characteristic orthogonal polynomials have been implemented in the Rayleigh–Ritz method to investigate free vibration of non-uniform Euler–Bernoulli nanobeams based on nonlocal elasticity theory. Non-uniform cross section of nanobeams has been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinate. Detailed analysis has been reported for all the possible cases of such variations. The objective of the present study is to analyze the effects of nonlocal parameter, boundary condition, length-to-diameter ratio and non-uniform parameter on the frequency parameters. It is found that clamped nanobeams are having highest frequency parameters than other types of boundary conditions for a particular set of parameters. It is also observed that frequency parameters decrease with increase in scaling effect parameter. First four deflection shapes of non-uniform nanobeams have also been incorporated. In this analysis, some of the new results in terms of boundary conditions have also been included.     

Nonlinear phase field theory for fracture and twinning with analysis of simple shear

A phase field theory for coupled twinning and fracture in single crystal domains is developed. Distinct order parameters denote twinned and fractured domains, finite strains are addressed and elastic nonlinearity is included via a neo-Hookean strain energy potential. The governing equations and boundary conditions are derived; an incremental energy minimization approach is advocated for prediction of equilibrium microstructural morphologies under quasi-static loading protocols. Aspects of the theory are analysed in detail for a material element undergoing simple shear deformation. Exact analytical and/or one-dimensional numerical solutions are obtained in dimensionless form for stress states, stability criteria and order parameter profiles at localized fractures or twinning zones. For sufficient applied strain, the relative likelihood of localized twinning vs. localized fracture is found to depend only on the ratio of twin boundary surface energy to fracture surface energy. Predicted criteria for shear stress-driven fracture or twinning are often found to be in closer agreement with test data for several types of real crystals than those based on the concept of theoretical strength.     

锂离子电池多孔电极理论的回顾与新思考

本文总结了Newman多孔电极理论的基本内容,提出若干改进思路. 提出基于离子-空穴耦合传输机制描述浓电解质中的离子输运过程,在此基础上引入离子-电子耦合转移反应的思想处理电极材料中的离子传输问题,并通过计算嵌锂材料的离子扩散系数验证其合理性. 总结了描述多孔电极多尺度结构的相关理论和技术,表明均质化方法和基于结构重建的介观模拟方法均能给出比较合理的有效输运参数,从而提高多孔电极理论模拟结果的准确性.     

Retinex彩色图像增强理论的物理思考及其截断区间对图像质量的影响

指出了Retinex彩色图像增强理论的物理意义,在对数空间中,将原图像减去高斯函数与原图像的卷积,其物理本质是除去了原图像中的平滑的部分,突出了原图像中的快速变化的部分,而且高斯函数越尖锐,越是突出图像中的细节,高斯函数越平坦,图像色调保持得越好,多尺度Retinex综合了不同高斯函数与原图像进行卷积的优点。研究了多尺度Retinex标准差截断法,结果是,以多尺度Retinex处理后的图像强度在其平均值附近1倍标准差截断后再拉伸得到的图像,普遍好于以2倍、3倍标准差截断后再拉伸得到的图像。     

需求弹性在价格决策中的应用

将着眼点由总收益改变为总利润,对于需求弹性用于价格决策,利用微积分方法,分5种情况进行推导,得到的结论修正和补充了现行"经济数学"、"市场营销学"和"管理经济学"等教科书里讲的内容,并在此基础上进一步研究了最佳调价量问题.     

汇率变动对进出口影响的实证分析

本文研究了汇率变动对中国进出口的影响,在间接标价法下对论文中所用到的汇率贬值改善国际收支的三个必要条件给出了结论和证明(弹性法);在经济理论及经验研究的基础上,建立了论文中所需要的所有模型并且根据模型对相关经济问题利用现代计量经济学方法进行了实证研究.通过实证研究我们得到的结论是:我国满足汇率贬值改善国际收支的必要条件;出口增加有助于GDP的增长,进口增加对GDP的影响是反向的且随着进口增加这种影响逐渐减弱最终趋于零.