Direct approach-based analysis of plates composed of functionally graded materials

The classical plate theory can be applied to thin plates made of classical materials like steel. The first theory allowing the analysis of such plates was elaborated by Kirchhoff. But this approach was connected with various limitations (e.g., constant material properties in the thickness direction). In addition, some mathematical inconsistencies like the order of the governing equation and the number of boundary conditions exist. During the last century many suggestions for improvements of the classical plate theory were made. The engineering direction of improvements was ruled by applications (e.g., the use of laminates or sandwiches as the plate material), and so new hypotheses for the derivation of the governing equations were introduced. In addition, some mathematical approaches like power series expansions or asymptotic integration techniques were applied. A conceptional different direction is connected with the direct approach in the plate theory. This paper presents the extension of Zhilin’s direct approach to plates made of functionally graded materials. The second author was supported by DFG grant 436RUS17/21/07.     

Mixed Micromechanics and Continuum Damage Mechanics Approach to Transverse Cracking in [S, 90n]s Laminates

The stiffness reduction in [S, 90 _n ] _s laminates due to transverse cracking in 90-layers is analyzed using the synergistic continuum damage mechanics (SCDM) and a micromechanics approach. The material constants involved in the SCDM model are determined using the stiffness reduction data for a reference cross-ply laminate. The constraint efficiency factor, which depends on the stiffness and geometry of neighboring layers, is assumed to be proportional to the average crack opening displacement (COD). The COD as a function of the constraint effect of adjacent layers and crack spacing is described by a simple power law. The crack closure technique and Monte Carlo simulations are used to model the damage evolution: the 90-layer is divided into a large number of elements and the critical strain energy rate G _c having the Weibull distribution is randomly assigned to each element. The crack density data for a [0₂/90₄] _s cross-ply laminate are used to determine the Weibull parameters. The simulated crack density curves are combined with the CDM stiffness reduction predictions to obtain the stiffness versus strain. The methodology developed is successfully used to predict the stiffness reduction as a function of crack density in [±/90₄] _s laminates.     

Convergence of a non-stiff boundary integral method for interfacial flows with surface tension

Boundary integral methods to simulate interfacial flows are very sensitive to numerical instabilities. In addition, surface tension introduces nonlinear terms with high order spatial derivatives into the interface dynamics. This makes the spatial discretization even more difficult and, at the same time, imposes a severe time step constraint for stable explicit time integration methods.

A proof of the convergence of a reformulated boundary integral method for two-density fluid interfaces with surface tension is presented. The method is based on a scheme introduced by Hou, Lowengrub and Shelley [ J. Comp. Phys. 114 (1994), pp. 312-338] to remove the high order stability constraint or stiffness. Some numerical filtering is applied carefully at certain places in the discretization to guarantee stability. The key of the proof is to identify the most singular terms of the method and to show, through energy estimates, that these terms balance one another.

The analysis is at a time continuous-space discrete level but a fully discrete case for a simple Hele-Shaw interface is also studied. The time discrete analysis shows that the high order stiffness is removed and also provides an estimate of how the CFL constraint depends on the curvature and regularity of the solution.

The robustness of the method is illustrated with several numerical examples. A numerical simulation of an unstably stratified two-density interfacial flow shows the roll-up of the interface; the computations proceed up to a time where the interface is about to pinch off and trapped bubbles of fluid are formed. The method remains stable even in the full nonlinear regime of motion. Another application of the method shows the process of drop formation in a falling single fluid.

     

Lateral mobility of plasma membrane proteins in dividing eggs of the loach (Misgurnus fossilis): Regional differences and changes during the cell cycle

Regional differences in lateral diffusion rates of fluorescence-labeled proteins have been studied in the plasma membrane of dividing eggs of the loach (Misgurnus fossilis) by fluorescence recovery after photobleaching (FRAP). Apparent animal-vegetal differences in fluorescence intensity, lateral diffusion coefficients, and fractions of mobile proteins have been found, with all these quantities being higher in the animal pole region than in the yolk region. Cyclic changes in protein diffusion coefficients and mobile fractions during the first few cell cycles have also been recorded. Soon after the end of a cleavage, the diffusion coefficient reaches its minimal value and increases rapidly before the next cleavage.     

An effective computer modelling approach to the study of aeroelastic characteristics of an aircraft composite wing with high aspect ratio

Static aeroelastic and flutter characteristics of an aircraft composite wing with high aspect ratio were analysed by an effective Computational Fluid Dynamics and Computational Structure Dynamics coupled method. Effects of stiffness distribution on aeroelastic characteristics were considered. Honeycomb core sandwich composite was considered to be equivalent to an orthotropic material by stiffness and inertance equivalent method to allow highly efficient numerical simulation, which was used for analysis of bending and torsional stiffness distribution. The results showed that the redistributed aerodynamic load leads to a decrease of pressure difference between the upper and lower airfoils. The flutter speed of the composite wing is near 0.64 Ma. Both bending and torsional stiffness increases with a small increase of beam size. Stiffness of the wing root has a major influence generally on the static aeroelastic characteristics. Both the lift coefficient and the loss percent decrease with a small increase of beam size. Effects of stiffness distribution on frequency are not obvious. Flutter speed remains close to the initial value when the beam size is changed.     

Electronic Currents Induced by Optical Fields and Rotatory Power Density in Chiral Molecules

The electric dipole–magnetic dipole polarizability tensor κ′, introduced to interpret the optical activity of chiral molecules, has been expressed in terms of a series of density functions kαβ′, which can be integrated all over the three-dimensional space to evaluate components καβ′ and trace καα′. A computational approach to kαβ′, based on frequency-dependent electronic current densities induced by monochromatic light shining on a probe molecule, has been developed. The dependence of kαβ′ on the origin of the coordinate system has been investigated in connection with the corresponding change of καβ′. It is shown that only the trace kαα′ of the density function defined via dynamic current density evaluated using the continuous translation of the origin of the coordinate system is invariant of the origin. Accordingly, this function is recommended as a tool that is quite useful for determining the molecular domains that determine optical activity to a major extent. A series of computations on the hydrogen peroxide molecule, for a number of different HO–OH dihedral angles, is shown to provide a pictorial documentation of the proposed method.     

弹性支座分析方法及其应用

针对结构杆件之间真实的联系和约束, 在结构力学常用支座的基础上, 提出 弹性支座概念. 建立弹性支座两种基本体系, 解两种反馈基本力法方程, 导出杆端两个方向 的约束刚度递推计算公式. 提出弹性支座基本分析方法. 给出弹性支座分析方法的有限元形 式. 应用弹性支座分析方法, 导出一次弯距分配法, 将高层结构内力计算方 法------分层法、$D$值法提升到一个更高的水平. 该法对弹性结构内力分析计算 工程实践应用和教学有参考价值.     

预制预应力综合管廊接头设计计算方法研究

以2010年上海世博会园区预制预应力综合管廊工程为背景, 基于内力平衡和变形协调条件, 并考虑接头拼缝变形形态、预应力筋伸长和遇水膨胀橡胶条弹性模量的影响, 提出了包含抗 弯刚度计算模型和抗弯承载力计算模型的采用预应力筋连接的预制预应力综合管廊接头设计 计算方法. 与现有试验结果的对比分析表明, 该方法的计算结果与试验结果吻合良 好. 该文的主要研究成果已成功应用于2010年上海世博会园区预制预应力综合管廊工程.     

分数阶黏弹性土层中分数阶三维轴对称桩的竖向振动

将桩基和土体视为三维连续介质,桩基和土体的应力一应变关系采用分数阶黏弹性模型描述。在三维轴对称情况下,利用三维弹性理论和连续介质力学理论,运用分离变量法和分数阶导数的性质,得到了分数阶黏弹性土层中分数阶黏弹性桩基的三维轴对称解;并分析了相关参数对桩顸动态刚度和等效阻尼的影响。研究结果表明：与土体相比,桩基的相关参量对桩顶复刚度的影响较大;桩基和土体的密度比、模量比对桩顶复刚度都有较大的影响。