功能梯度球形水凝胶的化学力学耦合分析

作为一种新型智能材料,水凝胶具有特殊的化学力学耦合性能.采用功能梯度形式可使得水凝胶具有更好的适应性和可调控性.本研究中假设交联密度沿径向按幂函数规律变化,并基于水凝胶的大变形多场耦合一般理论,采用Flory-Huggins自由能函数,建立了功能梯度球形水凝胶在球对称情形的控制方程,并开展了功能梯度球形水凝胶在给定内压和化学势情行的非均匀大变形溶胀行为的理论研究.计算结果表明,不同梯度指数的球形水凝胶的内压、内孔半径曲线和内压、内表面径向伸长率曲线均呈现出一段稳定区间和另一段不稳定区间,说明内压超出某临界值会发生失稳并导致水凝胶的最终破坏.内压的临界值随梯度指数的增大而增大.研究表明,功能梯度球形水凝胶的材料参数(梯度指数、亲疏水特性、交联密度和溶剂分子的体积)和环境化学势对水凝胶溶胀行为具有重要的影响.在给定内表面压力的情况下,功能梯度球形水凝胶内表面的径向位移随梯度指数的改变接近为线性变化,而随其他参数的影响都呈现出明显的非线性.本研究有助于实现水凝胶智能结构和器件在复杂条件下的精准调控.}      

Effects of graded porous structure on local strain distribution under compression in silicone rubber

Silicone rubber samples with gradually changing pore sizes within the range of 70–610 μm are produced using an improved spacer method. The samples are scanned using an X‐ray computed tomography to evaluate their graded structure as compared to uniform rubber. A compressive test reveals that graded porous silicone rubber has characteristic stress–strain curves whose slope changes within a specific strain range depending on the porous structure. Analysis results of local strain based on a digital image correlation of the graded porous silicone rubber under compression demonstrate that the characteristic stress–strain properties are caused by shifts in the main deformation region in the graded structure. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1033–1042     

Generalized P(N)-graded Lie superalgebras

We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov. This generalization is not so restrictive but suffcient enough so that we are able to have a classification for this generalized P(N)-graded Lie superalgebras. Our result is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a super-involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov's theorem for type P(N). We also obtain a generalization of Kac's coordinatization via Tits-Kantor-Koecher construction. Actually, the motivation of this generalization comes from the Fermionic-Bosonic module construction.     

完备化Witt代数中自然出现的一些非有限阶化李代数的表示

讨论了完备化Witt代数的三类非有限阶化子代数的不可约非权模的实现,并利用它们的表示得到一些有趣的组合恒等式.     

Application of a hybrid meshless technique for natural frequencies analysis in functionally graded thick hollow cylinder subjected to suddenly thermal loading

A hybrid meshless technique based on composition of meshless local Petrov–Galerkin method (for spatial variables) and Newmark finite difference method (for time domain) is developed for natural frequencies analysis of thick cylinder made of functionally graded materials (FGMs). The FG cylinder is assumed to be under suddenly thermal loading, axisymmetric and plane strain conditions. The dynamic behaviors and time history of displacements are obtained in time domain using Green–Naghdi (GN) theory of coupled thermo-elasticity (without energy dissipation). Using fast Fourier transform (FFT) technique, the displacements are transferred to frequency domain and all natural frequencies are illustrated for various grading patterns of FGMs. The variations of mechanical properties in FG thick hollow cylinder are considered to be in nonlinear volume fraction law through radial direction. The presented hybrid meshless technique furnishes a ground to analyze the effects of various grading patterns of FGMs on natural frequencies, which are obtained employing GN coupled thermo-elasticity governing equations. Also, the frequency history and natural frequencies are illustrated for various grading patterns at several points across thickness of cylinder.     

粘弹性地基上含孔隙的石墨烯增强功能梯度板的振动

为分析粘弹性地基上含孔隙的石墨烯增强功能梯度板的自由和强迫振动特性，基于三参数粘弹性地基模型及复合材料薄板理论，建立了粘弹性地基上含孔隙石墨烯增强功能梯度板的运动方程，用伽辽金法求解其固有频率和动力响应，并通过数值算例分析了粘弹性地基参数、孔隙率、孔隙类型及石墨烯纳米片分布模式、含量等因素对自由振动和动力响应的影响．结果表明，固有频率随着孔隙率的增大非单调变化，孔隙率对固有频率的影响随着地基参数、孔隙类型的不同而不同．另外，在三种孔隙类型中，上下表面层含有最少孔隙数量的板的动挠度最小，且其动挠度随着孔隙率的增大而微弱提高．     

The rollon–rolloff waste collection vehicle routing problem with time windows

This study introduces a rollon–rolloff waste collection vehicle routing problem involving large containers that accumulate huge amounts of garbage at construction sites and shopping districts. In this problem, tractors move one container at a time between customer locations, a depot, disposal facilities, and container storage yards. The complicated constraints discussed in this study arise from having multiple disposal facilities, multiple container storage yards, seven service types of customer demands, different time windows for customer demands and facilities, various types and sizes of containers, and the lunch break of tractor drivers. In addition, real-world issues, such as changing service types, multiple demands at a customer’s location, and tractors with different work schedules, are dealt with. This study proposes a large neighborhood search based iterative heuristic approach consisting of several algorithms for the problem. The effectiveness of the proposed methods is demonstrated by computational experiments using benchmark data, some instances of which are derived from real-world problems.     

Non-Aqueous Capillary Electrophoresis for Separation and Simultaneous Determination of Magnoflorine,Taspine, and Caulophine in Caulophyllum robustum Collected in Different Seasons

A non-aqueous capillary electrophoresis (NACE) method has been developed for the simultaneous determination of magnoflorine, taspine, and caulophine in Caulophyllum robustum collected in different seasons. The relative standard deviations (RSDs) of the migration times and peak areas of the three components were 0.33 and 3.34% for magnoflorine, 0.45 and 2.67% for taspine, and 0.49 and 3.71% for caulophine, respectively. Detection limits of magnoflorine, taspine, and caulophine were 0.30 μg/mL, 0.08 μg/mL, and 0.10 μg/mL, respectively. This method has been successfully applied to simultaneous determination of the three bioactive components in the different collection seasons.     

Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch

This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail.     

具有不同功能梯度分布函数的板件的三维分析

发展了一种新颖的功能梯度结构分析的细观元法。细观元法对结构的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算。这种细观元法既能充分反映材料功能梯度变化特性;而其计算单元又和常规有限元一样,是一种针对功能梯度结构分析的有效数值方法。文中通过细观元技术进行计算、分析,给出了具有不同功能梯度分布函数板件的力学量三维分布形态。