稀加筋层合板弯曲问题的半解析法

本文研讨的是复合材料稀加筋层合板的弯曲问题。取一挠度级数表达式满足内部控制方程，并由此导出相应的变形及内力显表达式。挠度试函数中的未知知量将通过边界条件和筋条与板面接触处的挠度协调，ｙ向转角协调求得。文中用此法计算了几个例题通过分析与比较，说明了这方法的合理性，并得到了一些新的结果。     

任意四边形Reissner—Mindlin板元

提出一种任意四边形Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｌｉｎ板元，挠度和转角均采用分片双线性函数。但剪切应变用它的线性扦值所代替，当板厚趋于零时这对应于Ｋｉｒｃｈｈｏｆｆ条件，因而避免了Ｌｏｃｋｉｎｇ现象。给出数值结果表明该单元的有效性。     

氢化铝锂一步还原β-烯胺酮合成1,3-胺基醇

β-烯胺酮类化合物是重要的有机合成砌块, 通过还原可用来合成具有广泛用途的1,3-胺基醇类化合物. 文献报道氢化铝锂还原β-烯胺酮为1,3-胺基醇, 只能采用两步还原的方法. 在四氢呋喃中采用过量的氢化铝锂于回流下将3-二甲胺基-1-芳基-2-丙烯酮高产率地一步还原为N,N-二甲基-3-羟基-3-芳基丙胺, 为该类化合物的合成提供了一个新方法.     

监视超声波

<正> 这种测量技术提供了超声波自由接触干涉测量法,能够测量振动的位移、运动工件的表面变形,例如快速运动的工件,在轧制或退火中的热钢等。激光束由分光镜分成两束光:一束光投射到工件的被测点,称之为测量光束;另外一束光投射到工件上的被参考点处,称之为参考光束,且参考点接近于测量点。来自测量点和参考点的反射光束再经分光镜会合后射入检测器(见图)。这种光检测器可以是光电倍增管、光电二极管,也可以是雪崩光电二极管或光电半导体     

各向异性网格下特征值问题的有限元分析

主要目的是在各向异性网格下研究二阶椭圆特征值问题的两类非协调有限元—类Wilson矩形元和Carey三角形元—的收敛性分析.通过新的技巧和方法,得到了与传统有限元网格剖分下相同的特征对的最优误差估计.推广了已有的结果.     

一类六参数非协调任意凸四边形单元

本文构造了一类六参数非协调四边形单元,证明由此产生的有限元对任意四边形网格通过Irons分片检查,其收敛效果同Wilson元相当且形状函数的选择不依赖于单元本身。类Wilson元及改进的Wilson任意四边形单元是其中的特例。     

探索:奏响数学美的乐章

这是一道在许多数学书刊可以轻易查到的习题:设a,b,c为两两不相等的有理数,求证:     

Simulation of Helium Behaviour in Titanium Crystals Using Molecular Dynamics

The behaviour of helium in Ti crystals at 300 K has been investigated by means of the molecular dynamics. The study is focused on the influences of He-Ti interaction on the aggregation of helium atoms in the substrate. When a Born-Mayer potential is used to describe the He-Ti interaction, the He atoms are unable to cluster with each other due to the weak bridge barrier that cannot trap the helium atoms, Whereas using a He-Ti potential that is constructed by fitting the ab initio pairwise He-Ti potential, the clustering of He atoms can be observed. The results indicate that suitable He-Ti potential plays an important role in the formation of He clusters in metals. Moreover, it is noted that the shape of the formed He cluster is irregular, and the produced defect prefers to congregating on one side of the He cluster rather than spreading symmetrically around it.     

Hexagonal Standing-Wave Patterns in Periodically Forced Reaction-Diffusion Systems

The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2：1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.