韧性金属大变形拟流动角点理论及应用

本文提出韧性金属弹塑性大变形拟流动角点理论（ｑｕａｓｉ－ｆｌｏｗｃｏｒｎｅｒｔｈｅｏｒｙ）．该理论从塑性变形正交法则出发，将”模量衰减函数”及屈服面的尖点效应引入本构模型，从而实现了由正交法则本构模型向非正交法则本构模型以及从塑性加载向物理弹性却载的光滑过渡，使一般无角点各向异性硬化屈服函数与有角点硬化情形相结合成为可能．用于数值模拟各向异性金属薄板单向拉伸失稳与剪切带分析并与实验结果作比较，表明本文理论的有效性．     

准各向同性复合材料弹性和强度的各向异性效应(Ⅰ)──模型*

实验观测表明,准各向同性材料,如N轴纤维增强复合材料层合板和编织材料,其面内刚度和强度具有不同程度的方向性,且强度的各向异性程度往往明显高于弹性性质的各向异性程度。本文根据张量函数表示理论所提出的本构方程和强度准则的一般模型,结合有关实验数据,分析了材料弹性性能和强度的非各向同性效应。具体给出了几类本构模型和强度准则的特殊形式并讨论了本文所得到结果的若干力学性质。本文第Ⅱ部分具体讨论了含单个椭圆孔或裂纹的无限大板的有关强度的各向异性效应,并用细观力学方法检验了本文的模型。     

混凝土轴拉加卸载随机损伤模型的建立与试验验证

为了分析及深入探讨混凝土在受拉加载及卸载情况下的力学特性,基于随机损伤本构关系提出了一种混凝土轴拉加卸载模型,推导出了混凝土加卸载的应力 应变关系表达式.为了印证理论表达式,进行了混凝土轴向拉伸及加卸载的试验研究,测得了混凝土的材料参数及其相应的轴拉加卸载应力-应变曲线.结合模型的计算结果,对混凝土的轴拉加卸载试验结果进行了对比分析,结果表明:混凝土轴拉加卸载模型能够预测混凝土的极限强度,同时能描述混凝土的强度软化、加载过程中的弹模折减及卸载后的塑性变形.     

准各向同性复合材料弹性和强度的各向异性效应(Ⅱ)──应用与细观力学分析*

文献中尚未见到针对准各向同性复合材料的各向异性效应对复合材料结构影响的分析。本文在第(Ⅰ)部分[1]所提出的强度准则模型的基础上,给出了复合材料各向异性特性在含椭圆孔和单个裂纹问题中的具体应用。在椭圆孔问题中分析了远场载荷随材料几何参数变化的规律;在含裂纹问题中分析了裂纹扩展方向随裂纹方向的变化规律。最后,用细观力学方法分析了一类三轴编织复合材料的弹性本构方程和强度准则,以及各向异性效应,得到了与实验和第(Ⅰ)部分理论模型相一致的结果。     

考虑纤维弯曲刚度的橡胶-帘线复合材料各向异性超弹性本构模型

针对纤维增强复合材料的有限变形,基于Spencer的连续介质力学不变量理论,提出了一种考虑纤维弯曲刚度的非线性超弹性本构模型.通过引入变形后纤维方向向量的梯度项,把单位体积的自由应变能分解为便于参数识别的体积变形、等容变形、各向异性变形和弯曲刚度4部分.理论和实验分析均表明传统的基于连续介质力学的纤维增强复合材料有限变形理论不适用于弯曲变形,必须考虑纤维弯曲刚度的影响.数值仿真结果也验证了在应变能函数中增加弯曲刚度项是必要的.     

热弹性马氏体相变材料单晶体的细观力学统一本构模型

基于马氏体相变的晶体学理论和Hill Rice内变量本构理论 ,建立了热弹性马氏体相变材料单晶体的细观力学统一本构模型并对它进行了详细的讨论 .该本构模型能描述在复杂热力学加载条件下 ,热弹性马氏体相变材料微结构正向相变、反向相变以及重取向过程在单晶体中所表现出来的宏观本构特性 .理论预测与实验结果符合很好 .     

计及相变与塑性的NiTi形状记忆合金循环伪弹性特性描述

结合NiTi形状记忆合金单轴循环变形试验研究结果,采用基于混合物理论的计及相变、重取向与塑性变形的形状记忆合金本构模型发展了相应的算法和程序.对NiTi形状记忆合金单轴循环变形行为进行了描述.通过试验结果与模拟结果的比较,验证了本构模型与算法的有效性.     

有限变形下的混凝土动态本构关系研究

讨论有限变形和小变形假设下本构关系的区别,并将其运用于混凝土的弹-粘塑性本构关系研究,提出了一个应变率相关的动态力学模型．模型基于Ottosen的4参数屈服准则,分别考虑混凝土在硬化阶段和软化阶段加载面的不同变化规律,建立冲击荷载下的混凝土本构关系．该模型可以应用于冲击载荷下混凝土材料响应的模拟．引进Green-Naghdi客观率建立有限变形的混凝土模型．根据大量实验结果对应变率和材料强度的关系提出合理假设,使模型可以反映混凝土大变形的动态力学行为,为相关工程问题的研究提供有益的思路和有效的工具．     

用于应变局部化行为分析的弹塑性损伤耦合本构研究

在已有的损伤塑性耦合本构模型基础上,进行了本构意义上的参数辨识,对不同参数取值时的材料行为进行了数值模拟,并对损伤演化律提出了改进措施．应用改进了的模型,在结构意义上进行了数值检验,模拟了简单试件拉伸时的变形局部化．数值结果表明这一理论模型有更好的数值稳定性,能较为准确地模拟金属韧性断裂的变形局部化现象．     

非正交模的广义耦合模理论

本文对无耗波导结构提出了非正交模的广义耦合模理论.如果该多波导结构沿波导轴是均匀的,则非正交模的适当组合将形成该多波导系统的正交本征模系;如果该系统沿波导轴是缓变参数的,则上述组合形成一组正交的本地耦合模方程组。最后对两个模耦合情况作了应用举例。     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.