快速多极边界元法用于扩散光学断层成像研究

在求解扩散光学断层成像中的正向问题时, 目前普遍采用有限元法, 但是随着实际模型规模的增大, 有限元法的计算量问题日益显著, 而边界元法则由于可以降低计算维度使计算量减少而备受关注. 本文以均匀的高散射介质为模型, 研究了将快速多极边界元法用于扩散光学断层成像的正向问题. 快速多极边界元法利用核函数的多极展开, 将常规边界元法中系数矩阵和迭代矢量的乘积项等价为相应四叉树结构的一次递归, 再结合广义最小残量法进行迭代求解. 将计算结果和蒙特卡罗法的模拟结果进行了比较, 表明利用快速多极边界元法的模拟结果和蒙特卡罗法的结果有很好的一致性. 研究结果验证了快速多极边界元法可以用于扩散光学断层成像, 为其大规模和实时成像带来可观的前景. 关键词： 扩散光学断层成像 边界元法 快速多极边界元法     

新的对角形式快速多极边界元法求解声学Helmholtz方程

传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势,     

新的对角形式快速多极边界元法求解声学Helmholtz方程

传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势, 具有良好的工程应用前景.     

声辐射计算的改进体积源边界点法

对体积源边界点法做了较大的改进,提出了在加权余量意义下,通过在边界结点法线方向(背离分析域)构作的四面体上对Ｈｅｌｍｈｏｌｔｚ方程的基本解进行积分,来对偶地表达系统方程中的系数矩阵,从而求解结构振动声辐射问题。对大量算例和模拟车床主轴箱辐射声场的改进体积源边界点法分析表明:改进的方法在计算速度较原体积源边界点法提高了１０余倍的情况下,在计算精度、计算稳定性、对振动体任意表面几何形状的适应性以及克服解的非唯一性等方面,表现出了良好的性态。     

三维声学多层快速多极子边界元及其应用

快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log²N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.     

二维声场预测的快速多极基本解法

传统基本解法在二维大规模模型的声场求解过程中,系统方程形成和求解的计算量正比于自由度N的二次方O(N2)和三次方O(N3),求解效率低;为此,引入快速多极子算法并采用广义极小残差法迭代求解,提出一种用于二维声场预测的快速多极基本解法。对无限长圆柱体及二维类车体辐射模型的仿真结果表明,当N为3000时,分别采用快速多极基本解法与传统基本解法求解所需的时间比值约为百分之四,且N越大比值越小;最终实现系统方程的形成和求解的计算量降低到正比于自由度O(N),提高了对二维大规模模型声场预测计算效率。      

二维声学多层快速多极子边界元及其应用

与模型自由度的平方成正比的存储量和计算量,使传统边界元无法应用到大型模型的计算。为此,发展了一种二维声学多层快速多极子边界元算法。通过二维Helmholtz核函数展开理论的简要介绍,推导了源点矩计算、源点矩转移、源点矩至本地展开转移、本地展开转移公式,并详细描述了二维声学快速多极子边界元算法的具体实现步骤。使用快速傅里叶插值进行源点矩和本地展开系数的多层传递。采用对角左预处理方法,改善边界方程的条件数,减少迭代求解次数。最后通过数值算例,验证了所发展的二维声学快速多极子算法的正确性和高效性。      

消声器声学性能预测的子结构快速多极子边界元法

鉴于快速多极子边界元法的应用主要局限于单区域声学问题计算,发展基于子结构技术的快速多极子边界元法以计算多区域声场问题,介绍基本原理、具体实施过程以及优缺点.以带有插进口管的膨胀腔消声器为例,应用子结构快速多极子边界元法和传统边界元法计算其传递损失,通过与实验测量结果的比较,验证方法的有效性和计算精度.研究表明,快速多极子边界元法与传统边界元法相比,节点数越多,其在节省计算时间,减少计算量等方面的优势越明显.     

基于蒙特卡洛法的关节臂坐标测量机工作空间分析

传统的求解关节臂式坐标测量机工作空间的方法需要借助繁琐的数学公式、计算量大,针对这一问题选用蒙特卡洛法对工作空间进行分析。首先运用D-H方法建立关节臂式坐标测量机的数学模型得出运动学方程。然后采用蒙特卡洛法分析该测量机的工作空间,得出工作空间点云图。最后,采用局部象限分布的方法对关节臂式坐标测量机工作空间点云图的边界点进行提取。仿真实验结果表明用蒙特卡洛法对工作空间分析更简单易于实现,采用基于局部象限分布法提取到的边界点轮廓也更准确避免了虚假边界点的提取。     

一种新型的多包层光子晶体光纤的分析方法

传统有效折射率方法只能模拟具有相同空气孔大小的单包层光子晶体光纤.针对这一问题,提出了一种改进的有效折射率法,能够计算具有不同孔径的多包层光子晶体光纤的传输特性.并用此方法对三包层光子晶体光纤的基模有效折射率和色散等特性进行了数值模拟,结果与多极法模拟出的结果符合得很好.这种改进的有效折射率法拓展了传统有效折射率法的适用范围,对快速准确地分析和设计具有不同传输特性的多包层光子晶体光纤提供了理论依据. 关键词： 光子晶体光纤 多包层 有效折射率方法 色散     

混杂复合材料等效热传导性能预测的小波-机器学习混合方法

混杂复合材料是一种新型复合材料,其复杂的细观结构导致预测其等效热传导性能极富挑战性.本文结合渐近均匀化方法、小波变换方法和机器学习方法发展了一种新的可以有效预测混杂复合材料等效热传导性能的小波-机器学习混合方法.该方法主要包括离线多尺度建模和在线机器学习两部分.首先借助渐近均匀化方法通过离线多尺度建模建立了混杂复合材料的热传导性能材料数据库,然后利用小波变换方法对离线的材料数据库进行预处理,接下来分别运用人工神经网络和支持向量回归方法建立混杂复合材料等效热传导性能预测的在线机器学习模型.最后通过对周期和随机混杂复合材料进行数值实验,验证了小波-机器学习混合方法的有效性,数值实验结果表明小波-神经网络混合方法具有最优的预测效果和抗噪能力.此外,需要强调的是对于具有高维大规模数据特征的随机混杂复合材料,小波-机器学习混合方法不仅可以提取离线材料数据库的重要特征,还可以显著减少在线监督学习的输入数据规模并提高机器学习模型的训练效率及抗噪性能.本文建立的小波-机器学习混合方法不仅适用于混杂复合材料等效热传导性能的预测,还可进一步推广应用于复合材料等效物理、力学性能的预测.     

Dynamic thermo-mechanical coupled response of random particulate composites:A statistical two-scale method

This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials.Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of the problem by a statistical second-order two-scale(SSOTS) analysis method and the algorithm procedure based on the finite-element difference method are presented. Numerical results of coupled cases are compared with those of uncoupled cases. It shows that the coupling effects on temperature, thermal flux, displacement, and stresses are very distinct, and the microcharacteristics of particles affect the coupling effect of the random composites. Furthermore, the coupling effect causes a lag in the variations of temperature, thermal flux, displacement, and stresses.     

A new method for the determination of damping in cocured composite laminates with embedded viscoelastic layer

A new method for the determination of damping in cocured composite laminates with embedded viscoelastic layer is developed based on mode superposition and modal strain energy method. The calculated damping value is not modal loss factor but a combination of damping from the contributing modes. The dynamic mechanical properties of the viscoelastic material cocured with composites were investigated and were substituted in the present method for calculating the damping in cocured composites. The analytical results were compared with the experimental results by dynamic mechanical thermal analysis (DMTA). The results demonstrate a good agreement between analytical and experimental results. This work provides a means for the study of damping in this structure with different environment temperature and excited frequency.     

Synergistic Effect of Polyhedral Oligomeric Silsesquioxane and Multiwalled Carbon Nanotubes on the Flame Retardancy and the Mechanical and Thermal Properties of Epoxy Resin

A novel polyhedral oligomeric silsesquioxane containing phosphorus and boron (PB-POSS) was synthesized. The resulting PB-POSS and multiwalled carbon nanotubes (MWCNTs) were incorporated into an epoxy resin (EP) to prepare PB-POSS/MWCNTs/EP composites through a solution mixing method. The synergistic effect of MWCNTs and PB-POSS on the thermal and mechanical properties and the flame retardancy of these flame retardant composites were studied. The experimental results showed that the introduction of PB-POSS or MWCNTs further improved the LOI values of the epoxy resin, and the highest LOI value (32.8%) was obtained for the formulation containing 14.6 wt% PB-POSS and 0.4 wt% MWCNTs. In addition, the incorporation of both PB-POSS and MWCNTs significantly improved the thermal and mechanical properties of the composites. The mechanical properties of composites containing 14.7 wt% PB-POSS and 0.3 wt% MWCNTs reached the maximum. The impact strength and flexural strength increased by 42% and 7%, respectively, compared to the neat epoxy resin. Thus, a combination of PB-POSS and MWCNTs in the appropriate ratio could effectively enhance the thermal and mechanical properties and the flame retardancy of the epoxy resin matrix.     

激光辐照下复合材料热响应的轴对称数值分析

为了模拟激光辐照下碳纤维增强复合材料的瞬态热响应,建立了轴对称计算模型。模型考虑了激光辐照过程中基体热分解、质量迁移、比热容和热导率等物理量的变化情况。采用有限元方法求解控制方程,边界条件包含了激光辐照、对流换热以及辐射换热。在此基础上编写了计算程序,预测了激光辐照下碳纤维增强复合材料的瞬态温度场和基体热分解状况。为了校核模型,开展了激光辐照碳纤维复合材料试验。计算结果与试验数据比较表明,模型预测的复合材料温度-时间曲线与试验结果较好吻合,在较低功率密度激光辐照下复合材料热响应以基体热分解为主,与试验烧蚀形貌观察结果一致。     

Energy potential of solid composite propellants based on 1,1-diamino-2,2-dinitroethylene

To obtain new formulations for solid composite propellants for creating composites with low sensitivity to mechanical stress and improved thermal stability, the energy potential of composites based on 1,1-diamino-2,2-dinitroethylene (FOX-7) and additionally containing a hydrocarbon or active binder, aluminum, and inorganic oxidant was studied. A formulation with 60% FOX-7 and 19 vol % active binder can be created which is characterized by a specific impulse I _sp ~ 251 s, density ~1.91 g/cm³, and T _c below 3600 K. The composites containing FOX-7 have smaller specific impulse values than the same formulations with HMX: by 10 s at 60% FOX-7 and by 4 s at 30% HMX.     

非一致随机分布复合材料力学参数预测的统计二阶双尺度方法

通过建立统计的二阶双尺度计算方法,预测了非一致随机分布复合材料结构的力学参数,包括刚度参数和弹性极限强度参数.所谓非一致随机分布复合材料结构,是指在整个结构中夹杂随机分布,但分布特征并不是处处相同,而是逐渐变化的,从而导致材料在宏观上具有随着位置连续变化的力学性能.描述了一致和非一致随机分布复合材料结构的特征及其细观表征方法,并建立了统计的二阶双尺度计算公式,讨论了材料的弹性极限强度准则.最后,针对不同的非一致随机分布复合材料,预测了材料的力学参数并与实验数据进行了对比.结果表明,统计的二阶双尺度方法对于预测非一致随机分布复合材料的力学参数是有效的. 关键词： 统计二阶双尺度方法 非一致随机分布 复合材料结构     

A four-phase confocal elliptical cylinder model for predicting the effective thermal conductivity of coated fibre composites

A four-phase confocal elliptical cylinder model is proposed from which a generalised self-consistent method is developed for predicting the thermal conductivity of coated fibre reinforced composites. The method can account for the influence of the fibre section shape ratio on conductivity, and the physical reasonableness of the model is demonstrated by using the fibre distribution function. An exact solution is obtained for thermal conductivity by applying conformal mapping and Laurent series expansion techniques of the analytic function. The solution to the three-phase confocal elliptical model, which simulates composites with idealised fibre–matrix interfaces, is arrived at as the degenerated case. A comparison with other available micromechanics methods, Hashin and Shtrikman's bounds and experimental data shows that the present method provides convergent and reasonable results for a full range of variations in fibre section shapes and for a complete spectrum of the fibre volume fraction. Numerical results show the dependence of the effective conductivities of composites on the aspect ratio of coated fibres and demonstrate that a coating is effective in enhancing the thermal transport property of a composite. The present solutions are helpful to analysis and design of composites.     

一类各项异性半线性椭圆方程自然边界元与有限元耦合法

将冯康和余德浩提出的自然边界归化方法用于研究一类半线性椭圆方程外区域问题，提出一种自然边界元与有限元的耦合算法、针对某一类半线性椭圆方程，应用变分原理，研究其弱解性及Galerkin逼近，得到有限元解的误差估计及收敛阶O(h^n)，最后给出相应数值例子。     

Thermal transport enhancement of multi-walled carbon nanotubes/ high-density polyethylene composites

Multi-walled carbon nanotubes (MWCNTs) enhanced high-density polyethylene (HDPE) composites were prepared and their thermophysical properties were measured. The thermal diffusivity of the composites increases with the increase in the amount of MWCNTs. A thermal diffusivity of more than three times that of pure HDPE was obtained for 38 vol. % MWCNTs/HDPE composites. An equation based on an effective medium approach model was used to discuss the thermal diffusivity enhancement of MWCNTs/HDPE composites as a function of the volume fraction of MWCNTs. The results from this analysis can be a predictive guideline for further improvements in the thermal transport properties of MWCNTs/HDPE composites. Moreover, the intrinsic longitudinal thermal conductivity k_z of an individual MWCNT was deduced from the measured results on the MWCNTs/HDPE composites. PACS 67.55.Hc; 61.46.Fg; 66.30.Xj