Explicit elasticity-conductivity connections for composites with anisotropic inhomogeneities

Explicit elasticity-conductivity connections for anisotropic heterogeneous materials were recently derived and verified experimentally by the present authors. The constituents were assumed isotropic, so that the overall anisotropy was due solely due to nonrandom orientations of inhomogeneities. Motivated by the materials science applications that deal with strongly anisotropic inclusions, we derive alternative elasticity-conductivity connections that cover these cases. They hold for a broad class of orientation distributions—up to three families of parallel inhomogeneities forming arbitrary angles with each other, with moderate orientation scatter allowed in each of the families. In the case of the isotropic inhomogeneities, this form has substantially better accuracy than the approximate connections derived earlier. The results are compared with experimental data on fiber-reinforced plastics. The agreement is quite good for the entire set of the effective anisotropic constants, and it is achieved without any fitting parameters.     

On non-linear vibration analyses of continuous systems with quadratic and cubic non-linearities

This paper examines the validity of non-linear vibration analyses of continuous systems with quadratic and cubic non-linearities. As an example, we treat a hinged-hinged Euler-Bernoulli beam resting on a non-linear elastic foundation with distributed quadratic and cubic non-linearities, and investigate the primary (Ω≈ω_n) and subharmonic (Ω≈2ω_n) resonances, in which Ω and ω_n are the driving and natural frequencies, respectively. The steady-state responses are found by using two different approaches. In the first approach, the method of multiple scales is applied directly to the governing equation that is a non-linear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure, and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained numerically by the finite difference method.     

Asymptotic determination of effective elastic properties of composite materials with fibrous square-shaped inclusions

We propose an asymptotic approach for evaluating effective elastic properties of two-components periodic composite materials with fibrous inclusions. We start with a nontrivial expansion of the input elastic boundary value problem by ratios of elastic constants. This allows to simplify the governing equations to forms analogous to the transport problem. Then we apply an asymptotic homogenization method, coming from the original problem on a multi-connected domain to a so called cell problem, defined on a characterizing unit cell of the composite. If the inclusions' volume fraction tends to zero, the cell problem is solved by means of a boundary perturbation approach. When on the contrary the inclusions tend to touch each other we use an asymptotic expansion by non-dimensional distance between two neighbouring inclusions. Finally, the obtained “limiting” solutions are matched via two-point Padé approximants. As the results, we derive uniform analytical representations for effective elastic properties. Also local distributions of physical fields may be calculated. In some partial cases the proposed approach gives a possibility to establish a direct analogy between evaluations of effective elastic moduli and transport coefficients. As illustrative examples we consider transversally-orthotropic composite materials with fibres of square cross section and with square checkerboard structure. The obtained results are in good agreement with data of other authors.     

含微裂纹的95%Al2O3陶瓷的力学性能

本文采用三种不同加载方式(单轴拉伸,三点弯曲以及圆盘压缩)研究含微裂纹Al_2O_3的陶瓷的弹性性能及其抗拉强度.微裂纹是通过对材料瞬时突变加热和冷却(简称热冲击)形成的.试验结果表明:1)三点弯曲试验得到的力学性能参数较其它两种加载方式所得到的结果要稳定和集中.单轴拉伸试验结果分散性最大.2)热冲击温度越高,材料的等效弹性模量?和等效泊松比?以及各种加载方式下试件的抗拉强度??都有不同程度的下降.电镜观察证实了力学性能参数下降主要与材料内部微裂纹密度增加有关.3)Budiansky-O'Connell方法被用来估计不同热冲击处理后的圆盘试件在断裂过程中的微裂纹密度变化,结果表明实际材料的微裂纹密度较理想材料的微裂纹密度都有一定的偏差.     

Direct Numerical Algorithm for Constrained Variational Problems

We propose a direct treatment for the numerical simulation of optimal solutions for vector, one-dimensional variational problems under pointwise constraints in the form of several inequalities. It is an iterative procedure to approximate the optimal solutions of such variational problems that rely on our ability to e?ciently approximate the optimal solutions of variational problems without restrictions, except possibly for end point constraints. One main advantage is that there is no need to control the free boundary, or the contact set, during the iterative process where constraints are active. In addition to proving some convergence results, the scheme is illustrated through several typical situations.     

An Effective Method to Construct Cluster‐based Frameworks with Multifarious Structures,Luminescence, and Sorption Properties

An effective method was developed for the synthesis of three cluster‐based frameworks with multifarious secondary building units (SBUs) and various structures, which were formulated as [Me₂NH₂]₂[Zn₁₀(BTC)₆(μ₃‐O)(μ₄‐O)(H₂O)₅] · 3DMA · 9H₂O ( FJI ‐ 3 ), [Me₂NH₂]₂[Zn₉(μ₃‐OH)₂(BTC)₆(H₂O)₃] · 5DMA · 6H₂O ( FJI ‐ 4 ) and [Me₂NH₂][Zn₃(μ₃‐OH)(BTC)₂DMF] · H₂O ( FJI ‐ 5 ) (H₃BTC = 1,3,5‐benzenetricarboxylic acid, DMA = N,N′‐dimethyl acetamide and DMF = N,N′‐dimethyl formamide), respectively. X‐ray structural analysis reveals that FJI ‐ 3 displays 3D highly porous metal‐organic framework with four kinds of microporous cages constructed by two paddle‐wheel Zn₂(CO₂)₄, trimeric Zn₃O(CO₂)₆, and tetrameric Zn₄O(CO₂)₆ SBUs. FJI ‐ 4 exhibits 3D microporous MOFs with a dodecahedral cavities built by paddle‐wheel Zn₂(CO₂)₄ and trimeric Zn₃O(CO₂)₆. FJI ‐ 5 shows 3D microporous MOFs with an 1D channel assembled by the Zn₃O(CO₂)₆ SBUs. In addition, the fluorescence and sorption properties in these cluster‐based frameworks were also investigated. Furthermore, the method employed in this work may provide an useful approach to the design and synthesis of novel cluster‐based frameworks.     

驱蚊植物提取物活性成分的提取分析及驱蚊效果研究

为配制出驱蚊效果好、持续效果长的天然蚊虫驱避剂,通过文献查询和问卷调查,详细分析了最为人所知的驱蚊植物,以及可以接受的驱蚊产品价格范围。对提及率最高的植物使用超声波加旋转蒸干法进行提取和浓缩,得到了粗提物浸膏,并测试了成分。将粗提物浸膏用不同溶剂配制成不同浓度的天然提取物溶液,通过小白鼠测试了其效力和有效保护时间。基于实验数据得出了一些结论。     

The effective Hamiltonian for the coupling between inversion-torsion states of hydrazine

In the present paper, a procedure to calculate matrix elements of the group-theoretical Hamiltonian for hydrazine is described and explained in detail, and a complete set of rovibrational matrix elements responsible for interstate interactions is presented. The transformation properties of the framework functions under the symmetry operators of the double group are explained in a simple way using the MS Excel spreadsheet.     

On permittivity and density of the systems (tetraglyme + dimethyl or diethyl carbonate) and the formulation of Δε in terms of volume or mole fraction

Relative permittivity and density on mixing from T = 288.15 K to 328.15 K and atmospheric pressure have been measured over the whole composition range for CH₃O(CH₂CH₂O)_mCH₃ polyoxyethyleneglycol dimethyl ether with m = 4 (also called 2,5,8,11,14-pentaoxapentadecane or tetraglyme) + (dimethyl or diethyl carbonate). For these systems the deviation of permittivity, Δε, changes sign depending on whether it is defined on the basis of mole fractions of volume fractions. Arguments are put forward that support the choice of the definition in terms of mole fraction. The Redlich-Kister equation has been used to estimate the binary fitting parameters and standard deviations from the regression lines were calculated. The density and excess molar volumes were fitted as a function of temperature and mole fraction to a polynomial equation. The temperature dependence of derived magnitudes, such as the isobaric thermal expansion coefficient, α, , and were computed, due to its importance in the study of specific molecular interactions. Different traditional mixing rules have been applied to predict the permittivity of these mixtures.     

Regioselective synthesis of fused benzopyrazolo[3,4-b]quinolines under solvent-free conditions

New 6,8-dihydro-5H-benzo[f]pyrazolo[3,4-b]quinolines 6 have been obtained in a novel solvent-free three-component reaction involving β-tetralone along with 5-aminopyrazoles 1 and benzaldehydes 2. The isomeric 6,10-dihydro-5H-benzo[h]pyrazolo[3,4-b]quinolines 9 could not be prepared in a similar fashion directly from α-tetralone, but were obtained by the reaction of amines 1 with benzylidene-derivative 10 of α-tetralone in similar conditions. The yields of quinolines obtained via this novel protocol were good and the reaction times varied from few minutes to just few seconds.