精化直接刚度法的不协调位移模式与收敛性分析

基于精化直接刚度法的不协调位移模式及有限元收敛理论中的ＩＰＴ条件，建立了Ｃ￣０类可分离位移型精化元的收敛性充分条件——强ＩＰＴ条件。进一步推出一族平面及空间Ｃ￣０类精化元并验证了其收敛性。     

SYNTHESIS AND APPLICATION OF NANOPARTICLES BY A HIGH GRAVITY METHOD

Fast chemical reactions involved in nanomaterials synthesis, polymerization, special chemicals production, reactive absorption, etc., are often difficult to control in terms of product quality, process efficiency and production consistency.After a theoretical analysis on such processes based on chemical reaction engineering fundamentals, an idea to intensify micromixing (mixing on the molecular scale) and mass transfer and therefore to control the process ideally was proposed.By experimental investigations of mass transfer and micromixing characteristics in the Rotating Packed Bed (RPB, or “HIGEE“ device), we achieved unique intense micromixing. This led us to the invention of using RPB as a reactor for the fabrication of nanoparticles (Chen et al., 2000).RPB consists mainly of a rotating packed rotator inside a stationary casing. The high gravity environment created by the RPB, which could be orders of magnitude larger than gravity, causes aqueous reactants going through the packing to spread or split into micro or nano droplets, threads or thin films, thus markedly intensifying mass transfer and micromixing to the extent of 1 to 3 orders of magnitude larger than that in a conventional packed bed.In 1994, the first RPB reactor was designed to synthesize nanoparticles of CaCO3 through multiphase reaction between Ca(OH)2 slurry and CO2 gas, and nanoparticles of 15～30nm in mean size and with very uniform particle size distribution was obtained. In 1997, a pilot-scale RPB reactor was successfully set up for operation, and in 2000, the first commercial-scale RPB reactor for synthesis of such nanoparticles came into operation in China, establishing a milestone in the use of RPB as a reactor for the fabrication of nanomaterials (Chen et al., 2002).Since then, the high gravity method has been employed for the synthesis of inorganic and organic nanoparticles via gas-liquid, liquid-liquid, and gas-liquid-solid multiphase reactions, e.g. inorganic nanoparticles like nanosized CaCO3, TiO2,SiO2, ZnO, Al2O3, ZnS, BaTiO3, BaCO3, SrCO3, Al(OH)3 and Mg(OH)2 flame retardants, and organic nano-pharmaceuticals including benzoic acid, salbutamol sulfate and cephradine. This technology received extensive attention in the field of nanomaterials fabrication and application. Dudukovic et al. commented, “The first large-scale application of RPB as a reactor occurred in China in production of nano CaCO3 by HGRP (high gravity reactive precipitation)of carbon dioxide and lime. Uniformly small particles were made in the RPB due to achievement of a sharp supersaturation interface and very short liquid residence times in the device.“ (Dudukovic et al., 2002). Date et al. said, “HGRP represents a second generation of strategies for nanosizing of hydrophobic drugs. In our opinion, among various methodologies described eariier, supercritical anti-solvent enhanced mass transfer method and HGRP method has potential to become technologies of the future owing to their simplicity, ease of scale-up and nanosizing efficiency“ (Date et al., 2004).As-synthesized nano CaCO3 was employed as a template to synthesize silica hollow spheres (SHS) with mesostructured walls. Characterizations indicated that the obtained SHS had an average diameter of about 40 nm with a surface haviors of Brilliant Blue F (BB), which was used as a model drug. Loaded inside the inner core and on the surfaces of SHS,BB was released slowly into a bulk solution for as long as 1 140min as compared to only 10min for the normal SiO2nanoparticles, thus exhibiting a typical sustained release pattern without any burst effect. In addition, higher BET value of the carrier, lower pH value and lower temperature prolonged BB release from SHS, while stirring speed indicated little influence on the release behavior, showing the promising future of SHS in controlled drug delivery (Li et al., 2004).Nano-CaCO3 synthesized by the high gravity method was also employed as a filler to improve the performance of organic materials. By adding CaCO3 nanoparticles into polypropylene-ethylene copolymer (PPE) matrix, the toughness of the matrix was substantially increased. At a nanosized CaCO3 content of 12 phr (parts per hundred PPE resin by weight),matrix. In the nanosized CaCO3/PPE/SBS (styrene-butadiene-styrene) system, the rubbery phase and filler phase were independently dispersed in the PPE matrix. As a result of the addition of nanosized CaCO3, the viscosity of PPE matrix significantly increased. The increased shear force during compounding continuously broke down SBS particles, resulting in the reduction of the SBS particle size and improving the dispersion of SBS in the polymer matrix. Thus the toughening effect of SBS on matrix was improved. Simultaneously, the existence of SBS provided the matrix with good intrinsic toughness, satisfying the condition that nanosized inorganic particles of CaCO3 efficiently toughened the polymer matrix,thus fully exhibiting the synergistic toughening function of nanosized CaCO3 and SBS on PPE matrix (Chen et al., 2004).As-prepared nano-CaCO3 was blended with TiO2 and other additives to prepare complex master batches for use in the coloring of polypropylene. It was found that the obtained nano-CaCO3 is an excellent pigment dispersant, which can partially replace TiO2 pigments for polypropylene resin coloring. Nano-CaCO3 can prompt the dispersion of TiO2 in polymer matrix, boosting the whiteness of the materials without a negative effect on the UV absorbency of the materials (Guo et al.,2004). Studies on the mechanical properties of nano-CaCO3 toughened epoxy resin composite indicated that impact strength and flexural modulus of the composite improved remarkably when 6wt.% of nano-CaCO3 was added. Surface treatment of nano-CaCO3 by titanate coupling agents significantly improved the dispersibility of nano-CaCO3 in such a high viscous matrix (Li et al, 2005).     

A DIRECT METHOD FOR EVALUATING LINE INTEGRALS WITH ARBITRARY HIGH ORDER OF SINGULARITIES

提出了一种精确计算任意高阶奇异曲线积分的直接计算法.首先将曲线单元上的各种几何量用投影线上的几何量来表示,然后通过幂级数展开和解析的方法显式地消除了积分的奇异性.还导出了计算等参坐标对局部直角坐标偏导数的表达式.由于这种方法涉及到的是总体尺度间的坐标变换,操作起来直观明了,可以处理二维问题边界元分析中出现的任意高阶奇异边界积分.最后用具体算例验证该方法的正确性.     

A NEW METHOD FOR THE UNCERTAIN RESPONSE ANALYSIS OF STRUCTURES WITH UNCERTAIN PARAMETERS

A computing method for estimating the upper and lower bounds of the response ofstructures with uncertainties is presented.The uncertain parameters are described by the convexmodel.A numerical example of the frame structure is given to illustrate the effectiveness of thismethod.     

三维裂纹问题的高精度数值解法

提出了一种求解三维均质弹性体中任意形状平片裂纹问题超奇异积分方程组的Chebyshev多项式数值解法.数值计算结果表明:文中方法不仅收敛快,而且精度高.     

一种计算梁的挠度和转角的新方法

梁的挠曲线方程一般是分段多项式的形式,如果通过某种方法确定了多项式的系数,那么挠曲线方程完全确定。本文利用该思想提出了一种计算梁的挠度和转角的新方法。首先将梁划分为若干区间,然后将每一区间映射到标准区间,在标准区间上以若干点的挠度和转角为待定系数构造梁的挠曲线方程,用配点法得到若干代数方程,最后联合求解所有的代数方程即得到问题的解。新方法计算过程简单,可供教学参考。

     

-种确定土体固结系数C_V的新方法

计算固结系数的方法很多, 它们各有千秋, 但无论哪种都不能计算土体在任意固结时刻的固结系数。本文把几种计算方法的优点结合起来, 找到了-种计算任意固结时刻固结系数的新方法, 并用室内系列固结实验数据进行了计算。现场观测资料分析计算结果与之对比结果表明, 该方法行之有效。     

估计迹长概率分布函数的新方法及其应用

本文提出一种估计迹长概率分布函数的新方法。该方法的优点是不需要有节理在测窗上出露长度的数据, 有效的减少了野外工作量。     

陶瓷阻力曲线测定的新方法——断裂栅法

将零厚度单向试件栅刻蚀工艺应用于晶须增韧氮化硅陶瓷基复合材料表面，通过记录试件所在桥路的输出电压值，可得到随载荷不断增大裂纹逐渐向前扩展过程中每一时刻的裂尖位置和裂纹长度，从而得到该种材料的阻力曲线。     

新的圆柱曲板剪切屈曲实验的研究

提出一个用两块曲板以单向加载进行的Ｒ１０００ｍｍ的圆柱曲板剪切屈曲新实验方案。其原理清楚、装置简单紧凑、节省试材、实验进行方便和不需扭转设备等优点，而实验结果和成熟的工作符合良好．     

含摩擦与碰撞平面多刚体系统动力学线性互补算法

基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.      

构造本构方程的另一种方法——非平衡不可逆热力学方法

重点介绍了以Onsager-Casimir倒易定律为基础,从不可逆热力学观点出发,对远离平衡状态,引进新的变量(被称为动态变量),构造本构方程．并以简单剪切流场为例,求出了测黏函数．     

基于界带模型的碳纳米管声子谱的辛分析

针对碳纳米管声子谱的数值计算方法研究,基于对偶体系和辛几何算法提出了一套全新的计算方法和相应的界带结构模型,通过将碳纳米管模拟成不同的结构力学模型,利用分析结构力学中的振动理论来计算碳纳米管的色散关系.理论框架包括:周期结构的变分原理、周期结构中波的传播分析、子结构方法、界带理论和声子色散关系的基本算法.数值算例验证了理论和算法的有效性,而且也指出了针对碳纳米管的声子谱的计算,界带模型相对于其它传统模型存在着一定的优势.     

复合固体推进剂拉伸蠕变柔量计算的新方法

复合固体推进剂的流变特性可用Wiechert体描述,其拉伸蠕变柔量只需求解一个一元n次方程就可得到.此方程的根被证实全是实根,且两两互异.算例验证表明了文中给出的蠕变柔量具有很高的精度,但计算量小,程序实现简单.此方法还可以用于求解固体推进剂的体积蠕变柔量.     

求弹性半平面问题基本解的一个新方法

本文所提到的弹性半平面问题的基本解是一个满足特殊条件的弹性半平面的应力位移解答。这些条件为:(1)半平面内一点处作用有集中力X,Y或集中力偶M;(2)半平面边界为自由或固定边。利用平面弹性的复变函数方法,文中把弹性半平面基本解的问题归结为下列问题,使一个特定解析函数和另一个解析函数的共轭值在半平面边界上相等。对上述转化后的问题,只要利用复变函数的性质,不难从基本解的第一部分推导出基本解的第二部分。其中,基本解的第一部分是弹性全平面的本基解。从而,半平面问题基本解可以方便地得到。此外,文中还首次给出了:(1)集中力偶作用于半平面内一点时的基本解;(2)当半平面边界固定情况下的基本解。     

不可压N-S方程高效算法及二维槽道湍流分析

构造了基于非等距网格的迎风紧致格式,并将其与三阶精度的Adams半隐方法相结合,构造了求解不可压N－S方程高效算法。该算法利用基于交错网格的离散形式的压力Poisson方程求解压力项,解决了边界处的残余散度问题;同时还利用快速Fourier变换将方程的隐式部分解耦,离散后的代数方程组利用追赶法求解,大大减少了计算量。通过对二维槽道流动的数值模拟,证实了所构造的数值方法具有精度高,稳定性好,能抑制混淆误差等优点,同时具有很高的计算效率,是进行壁湍流直接数值模拟的有效方法。在数值模拟的基础上对二维槽道流动进行了分析,得到了Reynolds数从6000到15000的二维流动饱和态解（所谓“二维槽道湍流”）;定性及定量结果均与他人的数值计算结果吻合十分理想。对流场进行了分析,指出了“二维湍流”与三维湍流统计特性的区别。     

复合材料旋转壳自由振动分析的新方法

提出了一种半解析区域分解法来分析任意边界条件的复合材料层合旋转壳自由振动. 沿壳体旋转轴线将壳体分解为一些自由的层合壳段, 视位移边界界面为一种特殊的分区界面;采用分区广义变分和最小二乘加权残值法将壳体所有分区界面上的位移协调方程引入到壳体的能量泛函中, 使层合壳的振动分析问题归结为无约束泛函变分问题. 层合壳段位移变量采用Fourier 级数和Chebyshev 多项式展开. 以不同边界条件的层合圆柱壳、圆锥壳及球壳为例, 采用区域分解法分析了其自由振动, 并将计算结果与其他文献值进行了对比. 算例表明, 该方法具有高效率、高精度和收敛性好等优点.     

结构拓扑变化理论中主Z值单调性定理与计算特征值的新方法

该文是文（１）～（３）的继续，主要讨论两个内容，其一是论证胸力体系的结构拓扑变化理论中的主Ｚ值具有定的定值域，这一重要性质保障着用拓扑变化法进行了分析的可靠性，称为之主Ｚ值的定值域定理，其二是引入一个新概念，质量基元，从而把动力体系也纳入拓扑变化理论，且证明动力体系中主Ｚ值对于模数变化呈单调性，称为主Ｚ值的单调性定理，作为它的应用。该方法提出了一套计算特征值的新方法，称为Ｚ变形法，新方法的主要特点     

一种新的弹塑性杂交应力元法

本文基于一个改进的弹塑性的Hellinger/Reis■ner 混合变分原理构造了一种用于解弹塑性问题的四节点等参杂交应力元.新的模型中,在单元内增加了等效应力增量、塑性等效应变增量及不协调位移变量,从而使单元内的屈服准则及流动法则平均得到满足,不协调位移改进了单元应力精度.计算表明,新的模型可以提高弹塑性杂交法的精度和计算效率.     

一种分析摆盘发动机震动力完全平衡的新方法

从机构学角度出发,抽象出摆盘发动机的RRSSC空间机构模型,通过对连杆进行震动力等效简化,将摆盘机系统分为一个复合开式链结构和一个多活塞圆形结构,分别考虑它们的震动力完全平衡问题,结果说明,只需在主轴上附加一个平衡重即可达到整个系统的震动力完全平衡．这种平衡分析方法比按照单环RRSSC机构分析的平衡方法简单、实用,符合特定环境中的使用要求．