含分层复合材料层合梁弯曲问题的一般解法

基于一阶剪切梁理论,考虑分层边缘区域的变形特点,提出了含穿透分层复合材料梁模型．与传统分层模型不同,该文将未分层部分看作上下子梁,放弃了传统模型中分层前缘横截面始终保持平面的假设．通过分层前缘的位移连续条件和内力连续条件,建立了粘合段和分层段的控制方程．并且,应用该模型对不同边界条件下含不同分层尺寸对称和非对称分层的复合材料层合梁弯曲问题进行了求解,结果与三维有限元计算的结果一致,从而证明了模型的有效性和适用性．     

复合材料层合板低速冲击后压缩的损伤累积模型

为了分析复合材料层合板低速冲击后的压缩性能,首先用三维动态有限元素法对两种层合板进行了低速冲击损伤模拟计算,以此作为冲击后压缩（CAI）层合板的初始损伤,然后用三维静态有限元对含损伤的层合板进行压缩破坏模拟和剩余强度计算,从而实现了层合板从冲击损伤到压缩破坏损伤全过程的模拟．结果表明,损伤投影面积和CAI强度的计算值与试验结果有较好的一致性．     

带裂纹层合板能量释放率分析

为了进一步了解裂纹尖端应力场的特性,本文对复合材料层合板的界面裂纹作了分析.文中强调了能量释放率分量存在的条件,并给出能量释放率分量和应力强度因子间的关系式.结合经典板理论的分析结果,根据外荷作用及某些几何参数和材料多数,导出了一般复合材料层合板的应力强度因子的封闭形式解.为了得到在一般荷载条件下能量释放率的分量,必须分别确定模型混合参数Ω,文中讨论了确定参数Ω的方法,最后,应用本文方法于几种不同种类的复合材料层合板,证明其结果可应用于工程实践.     

不同铺层厚度复合材料的低速冲击特性与损伤模式研究

复合材料凭借其轻质、高强的特性逐渐在工程材料界占据重要地位,对于复合材料的冲击损伤的研究也一直吸引着诸多研究学者的关注．为表征不同铺层厚度复合材料层合板的抗冲击性能,利用自由落体冲击设备,进行了复合材料层合板的冲击实验研究．给出了不同冲击能量下的损伤模式,并利用位移、速度、接触力以及能量的时间变化曲线,深入分析了侵入和穿透两种损伤模式的特点．研究发现,随着铺层厚度的增加,复合材料在冲击过程中吸收的能量也随之增加．引入能量平衡法,基于体系的能量守恒定律,利用Newton-Raphson数值方法求解了侵入损伤模式下的接触力大小,通过实验结果给定挠度求解了对应的速率变化情况,并将理论结果与实验结果进行比较．     

具损伤压电智能层合板的非线性主动控制和损伤监测

基于Hamilton原理、高阶剪切变形板理论、von Krmn型几何非线性应变-位移关系以及应变能等效原理,考虑压电层的质量和刚度及复合材料层内的损伤效应,建立了具损伤压电智能层合板的非线性运动方程．采用耦合正、逆压电效应的负速度反馈控制原理,形成闭环控制回路,实现了对压电智能层合板的主动控制和损伤监测．数值计算中,以四边简支面内不可动的层合矩形板为例,讨论了压电层位置对振动控制的影响,以及损伤程度和损伤位置对传感层输出电压的影响,提出一种损伤监测的方法．     

考虑阻尼的状态向量方程和层合板的振动分析

基于考虑弹性体粘滞阻尼的修正后的Hellinger-Reissner (H-R)变分原理,推导了相应的状态向量方程．结合精细积分法和Muller法为四边简支矩形层合板的简谐振动分析提出了新的方法．依据线性阻尼振动理论,简要地给出了复合材料层合板欠阻尼、临界阻尼和过阻尼3种自由运动的通解公式．通过数值实例研究了粘滞阻尼对复合材料层合板振动的影响．丰富了状态向量方程的理论体系和应用领域．     

外部压力作用下复合材料层合圆柱壳的脱层扩展分析

含脱层的层合圆柱壳在承受外部压力作用时,容易发生脱层扩展,进而引起结构失效．基于可动边界变分原理并考虑脱层间的接触效应对圆柱壳在外部压力作用下的脱层扩展进行了分析,同时应用Griffith准则,导出了脱层前缘各点处的能量释放率表达式,且以轴对称脱层层合圆柱壳为例进行了数值计算,讨论了脱层大小、脱层深度、几何尺寸、材料性质及纤维铺层方式等因素对脱层扩展的影响．     

带裂纹层合板复应力强度分析

本文用经典板理论求得了复合材料层合板的界面应力强度因子.利用裂纹尖端能量释放率和复应力强度因子间的关系,给出最一般的复合材料层合板,在相应外荷载和模型混合参数下的复应力强度因子的一个封闭形式的解.然后提出确定这一模型混合参数的步骤,给出某些层合板的数值结果.并给出在相应外荷载下的小范围接触条件.特别证明了界面韧度曲线的对称性质.最后讨论振荡指数消失后,预计的断裂荷载的精确性.还通过一个实例表明β=0法的有效性和局限性.     

不同铺层厚度复合材料的低速冲击特性与损伤模式研究

复合材料凭借其轻质、高强的特性逐渐在工程材料界占据重要地位,对于复合材料的冲击损伤的研究也一直吸引着诸多研究学者的关注.为表征不同铺层厚度复合材料层合板的抗冲击性能,利用自由落体冲击设备,进行了复合材料层合板的冲击实验研究.给出了不同冲击能量下的损伤模式,并利用位移、速度、接触力以及能量的时间变化曲线,深入分析了侵入和穿透两种损伤模式的特点.研究发现,随着铺层厚度的增加,复合材料在冲击过程中吸收的能量也随之增加.引入能量平衡法,基于体系的能量守恒定律,利用Newton-Raphson数值方法求解了侵入损伤模式下的接触力大小,通过实验结果给定挠度求解了对应的速率变化情况,并将理论结果与实验结果进行比较.     

对称复合材料层合板弯曲的三维数值分析

本文采用三维各向异性有限单元模拟纯弯曲载荷下的复合材料层合板，给出了应力、应变沿厚度方向的变化规律。分析结果表明，在斜交对称铺层层合板的中心区域（远离加载端和自由边的区域），板的层间粘接界面附近，有根强的应力集中现象，可称之为层间效应。层间界面处力学性质的突变导致了层间应力的产生，并使层合板处于三向应力状态。三维数值模型给出的应变分布不同于基于Ｋｉｒｃｈｈｏｆｆ－Ｌｏｖｅ直法线假设的经典层合板理论给出的应变分布。     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].