辐射(火积)耗散与空间辐射器温度场均匀化的关系

(火积)理论是针对传热优化发展起来的,并获得了越来越多的应用。本文基于辐射(?)原理,对空间辐射器散热过程中的散热量分布、发射率分布和散热面积分布问题进行了分析。对于以上三类优化分布问题,理论分析和数值计算均表明,辐射器最小的辐射(?)耗散和辐射热阻均对应于散热表面均匀的温度场。因此,辐射(?)原理可用于空间辐射器的温度场均匀化设计。     

Multiresolution Analysis of Elastic Degradation in Heterogeneous Materials

In this study we examine the stiffness properties of heterogeneous elastic materials and their degradation at different levels of observations. To this end we explore the opportunities and limitations of multiresolution wavelet analysis, where successive Haar transformations lead to a recursive separation of the stiffness properties and the response into coarse- and fine-scale features. In the limit, this recursive process results in a homogenization parameter which is an average measure of stiffness and strain energy capacity at the coarse scale. The basic concept of multiresolution analysis is illustrated with one- and two-dimensional model problems of a two-phase particulate composite representative of the morphology of concrete materials. The computational studies include the microstructural features of concrete in the form of a bi-material system of aggregate particles which are immersed in a hardened cement paste taking due account of the mismatch of the two elastic constituents. Sommario. In questo studio si esaminano le proprietà di rigidezza di materiali elastici eterogenei ed il loro degrado a diverse scale di osservazione. A questo scopo si esplorano le opportunità e le limitazioni di analisi con wavelets a risoluzione multipla, dove successive trasformazioni di Haar conducono ad una separazione ricorsiva della proprietà della rigidezza e della risposta nelle loro caratteristiche di scala fine e grossolana. Al limite, questo processo ricorsivo dà luogo ad un parametro di omogeneizzazione che rappresenta una misura media della rigidezza e della capacità di immagazzinare energia di deformazione alla grande scala. Il concetto di base dell'analisi a risoluzione multipla è illustrato per mezzo di problemi modello mono- e bi-dimensionali che si riferiscono ad un composito particolato a due fasi rappresentativo della morfologia del calcestruzzo. Le caratteristiche microstrutturali del calcestruzzo sono modellate nello studio computazionale sotto forma di un sistema a due materiali di particelle aggregate, immerse in una pasta di cemento indurita e tenendo conto della mencata congruenza tra i due constituenti elastici.     

Micro/macromechanical plastic limit analyses of composite materials and structures

The load-bearing capacities of ductile composite materials and structures are studied by means of a combined micro/macromechanics approach. Firstly, on the microscopic scale, the aim is to get the macroscopic strength domains by means of the homogenization theory of micromechanics. A representative volume element (RVE) is selected to reflect the microstructures of the composite materials. By introducing the homogenization theory into the kinematic limit theorem of plastic limit analysis, an optimization format to directly calculate the limit loads of the RVE is obtained. And the macroscopic yield criterion can be determined according to the relation between macroscopic and microscopic fields. Secondly, on the macroscopic scale, by introducing the Hill's yield criterion into the kinematic limit theorem, the limit loads of orthotropic structures such as unidirectional fiber-reinforced composite structures are worked out. The finite element modeling of the kinematic limit analysis is deduced into a nonlinear mathematical programming with equality-constraint conditions that can be solved by means of a direct iterative algorithm. Finally, some examples are illustrated to show the application of the present approach. Project supported by the National Natural Science Foundation of China (No. 19902007), the National Foundation for Excellent Doctoral Dissertation of China (No. 200025), the Fund of the Ministry of Education of China for Returned Oversea Scholars and the Basic Research Foundation of Tsinghua University.     

Homogenization process caused by competition between phase separation and ester‐interchange reactions in immiscible polyester blends: A Monte Carlo simulation

The homogenization process caused by competition between phase separation and ester‐interchange reactions in immiscible polyester blends was investigated via the Monte Carlo simulation method. Phase separation and ester‐interchange reactions were performed simultaneously with the one‐site bond fluctuation model on a homogeneous blend of immiscible polyesters. Three different values of the repulsive pair‐interaction energy (E_AB) between segments A and B and two trial ratios of phase separation to ester‐interchange reactions at a given E_AB were introduced to examine the competition between them. Phase separation was monitored by the calculation of the collective structure factor, and copolymerization was traced by the calculation of the degree of randomness (DR). In all cases, as the homogenization proceeded, the maximum intensity of the collective structure factor initially increased, reached a maximum, and finally decreased, whereas the peak position where the structure factor had a maximum shifted downward in the early stage and then remained unchanged after the intensity of the collective structure factor reached the maximum. This indicates that during the homogenization process, the domain size did not change significantly after phase‐separated structures were developed distinctly. In this simulation, phase‐separated structures were traced until the DR was above 0.8. This result indicates that homogenization can be accomplished via homogeneous ester‐interchange reactions over most of the polyester chains because copolyesters resulting from ester‐interchange reactions do not act as an efficient compatibilizer. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 590–598, 2000     

The skin effect in vibrating systems with many concentrated masses

We address the asymptotic behaviour of the vibrations of a body occupying a domain $\Omega\subset\mathbb{R}^n, n=2,3$. The density, which depends on a small parameter $\varepsilon$\nopagenumbers\end , is of the order $O(1)$\nopagenumbers\end out of certain regions where it is $O(\varepsilon^{‐m})$\nopagenumbers\end with $m>2$\nopagenumbers\end . These regions, the concentrated masses with diameter $O(\varepsilon)$\nopagenumbers\end , are located near the boundary, at mutual distances $O(\eta)$\nopagenumbers\end , with $\eta=\eta(\varepsilon)\rightarrow 0$\nopagenumbers\end . We impose Dirichlet (resp. Neumann) conditions at the points of $\partial\Omega$\nopagenumbers\end in contact with (resp. out of) the masses. We look at the asymptotic behaviour, as $\varepsilon\rightarrow 0$\nopagenumbers\end , of the eigenvalues of order $O(1)$\nopagenumbers\end , the high frequencies, of the corresponding eigenvalue problem. We show that they accumulate on the whole positive real axis and characterize those giving rise to global vibrations of the whole system. We use the fact that the corresponding eigenfunctions, microscopically, present a skin effect in the concentrated masses. Copyright © 2001 John Wiley & Sons, Ltd.     

An integrated approach of homogenization-ultrasound-assisted extraction followed by high-speed countercurrent chromatography for rapidly preparative separation naphthoquinones and diarylheptanes from Juglands mandshurica Maxim. exocarp

This research investigated the effectiveness of an integrated method for the extraction and separation of naphthoquinones and diarylheptanes from exocarp of Juglands mandshurica Maxim. (namely, green walnut husks). The target compounds were obtained by ultra-turrax homogenization (UTH) coupled with ultrasound-assisted extraction (UAE) technology followed by high-speed countercurrent chromatography (HSCCC). The UTH-UAE extraction method achieved higher efficiency with 2.49- and 2.36-fold to those by UAE, and 1.39- and 1.34-fold to those by UTH in a short time. HSCCC was adopted for further separation and purification; six target compounds, namely, regiolone (RE), juglone (JU), myricatomento-genin (MG), galleon (GA), 2-oxatrycyclo[13.2.2.13,7]eicosa-3,5,7(20),15,17,18-hexaen-10-16-diol (OE), and juglanin A (JA), were separated with more than 95.37% purities and more than 84.71% final recovery rates, respectively. In this study, the integrated strategy of extraction and separation could get high purity compounds quickly, which would provide time and solvent saved method for the natural products separation from plants.     

Topology Optimization Design of Heat Convection Problems With Variable-Density Cells北大核心CSCD

为获得优异的散热结构设计,发展了一种基于腐蚀-扩散算子的变密度胞元层级结构设计方法.通过腐蚀-扩散算子得到了一系列拓扑相似但体积分数不同的变密度微结构,计算并拟合得到变密度微结构等效热传导系数曲线.在此基础上,采用移动渐近线法更新宏观设计变量,将变密度微结构植入相应体积分数的宏观单元中完成装配.通过数值算例对不同优化方法下温度场的热柔顺度、平均温度、方差等参数进行了比较分析,结果表明,变密度胞元层级结构比传统单尺度胞元结构和周期胞元结构具有更好的散热性能.     

Asymptotic stability of the spectrum of a parametric family of homogenization problems associated with a perforated waveguide

In this paper, we provide uniform bounds for convergence rates of the low frequencies of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane of height H. The perforations are periodically placed along the ordinate axis at a distance $O(\epsilon )$ between them, where ε is a parameter that converges toward zero. Another parameter η, the Floquet-parameter, ranges in the interval $[-\pi ,\pi ]$. The boundary conditions are quasi-periodicity conditions on the lateral sides of the rectangle and Neumann over the rest. We obtain precise bounds for convergence rates which are uniform on both parameters ε and η and strongly depend on H. As a model problem associated with a waveguide, one of the main difficulties in our analysis comes near the nodes of the limit dispersion curves.     

考虑微结构连接性的双尺度结构自然频率拓扑优化

多孔材料因具有轻量化、高孔隙率和减振/散热等优良多物理特性,在航空航天等领域具有广阔应用前景。采用拓扑优化方法对含多种多孔材料的结构进行结构与材料微结构构型一体化设计,有助于获得具有优良力学性能的结构设计。然而,传统逆均匀化微结构设计方法无法确保不同多孔材料微结构之间的连接性,设计结果不具备可制造性。本文面向含多种多孔材料的双尺度结构基频最大化设计问题,考虑不同微结构之间的连接性,协同设计多孔材料的微结构构型及其在宏观尺度下的布局。采用均匀化方法计算多孔材料的宏观等效力学性能,通过对不同多孔材料微结构单胞的边界区域采用相同的拓扑描述确保双尺度优化过程中任意空间排布下不同微结构的连接性,并通过优化算法确定微结构间的连接形式及微结构拓扑。在宏观尺度,提出结合离散材料插值模型和RAMP插值模型RAMP (Rational Approximation of Material Properties)的多孔材料各向异性宏观等效刚度及质量插值模型,获得清晰的多孔材料宏观尺度布局并减轻优化过程中伪振动模态的影响。建立以双尺度结构基频最大化为目标,以材料用量为约束的优化列式,推导灵敏度表达式,并基于梯度优化算法求解双尺度结构拓扑优化问题。数值算例表明,采用本文优化方法能够有效确保基频最大化双尺度结构设计中不同多孔材料微结构之间的连接性,增强优化设计结果的可制造性。