Stability of a tensegrity structure: application to cell mechanics

Stability studies of a tensegrity structure, used as a model for cell deformability, are performed. This structure is composed of 6 slender struts interconnected by 24 linearly elastic cables. The cables and the struts are governed by linear constitutive laws. The struts are allowed to buckle. Adapting experimental evidence, the struts have already buckled at the reference placement due to the prestress of the tendons. A general procedure for studying the stability behavior of the particular tensegrity model is presented. The reference placement is defined by the prestress, and the equilibrium placements are defined for any three-dimensional applied forces.     

超磁致伸缩车削加工刀架特性实验分析

利用光栅测微传感器(DG-10)和自行开发研制的优化后的超磁致伸缩车削加工刀架,对不同预压力、电流强度下刀架性能进行实验研究。实验中分别由压力传感器和改进后的控制电路调整所加预压力、电流的大小,通过数据采集系统记录光栅测微传感器所测得的磁致伸缩量。实验结果表明:在不同预压力下,刀架输出位移随着激励电流的增大而增大,直到达到饱和;同时在最大工作电流作用下,刀架的输出位移随着预压力的增大而增大,但当预压力增大到一定数值后,刀架的输出位移随着预压力的增大而减小。利用最小二乘曲线拟合、线性回归等数学方法得出了刀架在最大工作电流下,预压力与磁致伸缩量之间的拟合曲线及函数多项式,并确立了最佳工作预压力。建立了最佳工作预压力下电流与磁致伸缩量之间的函数关系式。通过误差分析看出理论分析和实验结果吻合的很好。     

Effect of prestress on the stability of electrode–electrolyte interfaces during charging in lithium batteries

We formulate a model of the growth of electrode–electrolyte interfaces in lithium batteries in the presence of an elastic prestress. The model accounts for the kinetics of Li⁺ transport through a solid electrolyte and, within the interface, for the kinetics of Li⁺ adsorption by the anode, electrostatics, and the elastic field. We specifically account for the effect of the elastic field through an asymptotic analysis of a nearly flat interface between two semi-infinite elastic bodies. We use the model as a basis for assessing the effect of prestress on the stability of planar growth and the potential of prestress as a means of suppressing the formation of deleterious dendrites. We present a linear stability analysis that results in explicit analytical expressions for the dependence of growth rates, and of the critical unstable wavelength for the interfacial roughening, on the state of prestress and on fundamental parameters such as surface diffusivities, surface energy, deposition kinetics, and elastic moduli. Finally, we examine the model in the light of experimental observations concerned with the effect of applied pressure on a lithium/dioxolane-dimethoxy ethane electrolyte systems. With reasonable choices of parameters and some calibration, the model accounts for the observation that a modest applied pressure indeed results in a substantial reduction in the roughening of the lithium surface during cycling.     

金属梁在预应力下的冲击响应

工程结构在使用过程中，大部分构件处于预应力状态。为了理清预应力对金属梁在冲击载荷作用下响应的影响机理，对不同轴向预应力条件和不同冲击强度下金属梁的塑性变形规律进行了研究。通过自主设计的预应力加载装置和落锤试验机，实现对金属梁的预应力控制和冲击加载；借助商用软件建立数值模型，对相关工况进行模拟。数值模拟结果与试验结果有较好的一致性。通过对梁的剩余挠度进行对比发现，压预应力状态下的梁受冲击载荷作用所产生的中点剩余挠度会比无预应力时更大；而拉预应力状态下的梁，挠度的变化量与预应力之间没有较一致的规律。从能量角度进行分析发现，梁的塑性变形能来自外加动能和初始内能，外加动能的能量比越高，梁的能量吸收率就越高，且在低能量比时，压预应力下的能量吸收率相对较高，拉预应力下的相对较低；高能量比时，预应力对能量吸收率几乎无影响。压预应力下，梁的极限弯矩增大，长度缩小，增大了的塑性变形能分布在长度缩小了的梁内，必然会导致更大的剩余挠度；拉预应力下，梁的极限弯矩减小，长度增大，增大了的塑性变形能分布在长度增大了的梁内，剩余挠度则没有显而易见的规律。这在一定程度上解释了预应力对冲击载荷作用下金属梁变形的影响机理。     

转子扭转-纵向耦合振动分析

针对某转子的模型,分析了扭转-纵向耦合振动.计算结果表明:设置转子预应力与旋转时的离心力相对应,其扭转振动频率将随预应力的增大而增大.转子纵向振动频率不受该预应力的影响,这是因为转子旋转时预应力的方向与轴线垂直.随着转子旋转时预应力的变化,扭转振动频率接近纵向振动频率,出现扭转-纵向耦合振动.     

Discrete bright–dark soliton solutions and parameters controlling for the coupled Ablowitz–Ladik equation

Analysis of piecewise-linear nonlinear dynamical systems is critical for a variety of civil, mechanical, and aerospace structures that contain gaps or prestress that are caused by cracks, delamination, joints or interfaces among components. Recently, a technique referred to as bilinear amplitude approximation (BAA) was developed to estimate the response of bilinear systems that have no gap or prestress. The method is based on an idea that the dynamics of a bilinear system can be treated as a combination of linear responses in two time intervals both of which the system behaves as a distinct linear system: (1) the open state and (2) the closed or sliding state. Both geometric and momentum constraints are then applied as compatibility conditions between the states to couple the linear vibrational response for each time interval. In order to estimate the response for more general cases where there are either gaps or prestress in the system, a generalized BAA method is proposed in this paper. The new method requires inclusion of contact stiffness and damping to model contact behavior in the sliding state, and new equilibrium positions for each state to establish proper coordinates. The new method also finds the bilinear frequency of the system, which cannot be computed using the bilinear frequency approximation method previously developed since that method is only accurate for the zero gap and no prestress case. The generalized BAA method is demonstrated on a single degree of freedom system, a three degree of freedom system, and a cracked cantilever beam model for various gap sizes and prestress levels.     

Stress distributions from interference fits and uniaxial tension

Machine assemblies can be prestressed (1) to eliminate stress gradients and (2) to increase fatigue life. Where prestressing is used to reduce stress gradients, the geometry is usually simple and good mathematical models are available for design purposes. The instances where fatigue life is the prime consideration are difficult to analyze because of asymmetry and variable boundary conditions. However, the interference prestress can be determined from an approximate model. The approximate solution indicates that the normal stress at the interface of a bolt-hole assembly varies almost linearly with diametral interference. When a tensile field is added to an interference prestress, even approximate techniques falter. Quantitative agreement with strain-gage data can be made at a point and for the initial loading cycle only. After several cycles, the experimental value of cycle-stress variation at the interface approximates the average applied tensile stress. The calculated value is twice as great. Stresses due to interference fits can be predicted, and prestressed bolted joints designed with greater confidence.     

Selection of prestress for optimal dynamic/control performance of tensegrity structures

This paper concerns prestress optimization of a tensegrity structure for its optimal LQR performance. A linearized dynamic model of the structure is derived in which the force-density variables that parameterize the prestress of the structure appear linearly. A feasible region for these parameters is defined in terms of the extreme directions of the prestress cone. A numerical method for computing this basis for a structure prestress cone is proposed. The problem is solved using a gradient method that provides a monotonic decrease of the objective function inside the feasible region. A numerical example of a cantilevered planar tensegrity beam is shown.     

三维光弹性中预应力结构的应力冻结研究

本文提出用三维光弹性应力冻结法模拟分析预应力钢筋混凝土结构中的应力。通过模拟体与实体结构的相似性研究,给出了模型载荷比例系数Cq参数,通过参数合理的选取,有效的解决了应力冻结水平预测这一技术关键;用光弹性应力二次冻结法,将结构预应力和负载应力冻结在同一试件中;应分析精度对模型尺寸的要求,采用了精密浇铸的方法制作模型。此外,还研制了受力清晰明确的加载系统。对这些涉及应力冻结的若干关键问题结合工程实例进行探讨。实验应力分析结果与有限元数值法一致性较好。     

有效预应力对大跨P.C.桥梁极限承载力的影响研究

采用三维实体退化虚拟层合单元理论探讨了有效预应力对大跨P.C.桥梁极限承载力的影响.针对不同的有效预应力水平,以一座典型的预应力混凝土连续刚构桥为例,采用三维精细化有限元模型,对其极限承载力进行了空间分析计算和讨论.分析表明,有效预应力对大跨P.C.桥梁极限承载力有较大影响,其中,纵向预应力筋有效预应力与竖向预应力筋有效预应力的比例是影响桥梁极限承载力的重要参数.大跨P.C.桥梁结构设计时应充分重视这一问题.     

体外预应力梁摩擦效应的非线性分析

构造了简单的体外预应力梁的摩擦单元,摩擦单元位于转向块和体外筋之间的角平分线上,能模拟转向块和体外筋之间的有摩擦或无摩擦滑移。考虑混凝土、钢筋和体外筋应力-应变的非线性关系,采用梁截面弯矩-轴力-曲率的三折线模型,探讨了体外预应力梁的性能。对简支梁和连续梁的不同因素进行计算,包括不同摩擦系数、不同体外筋和钢筋面积、不同偏心距以及对称和非对称荷载形式。计算结果表明,对于简支梁和对称荷载下的连续梁,承载力的摩擦效应可以忽略,最大预应力增量和挠度的摩擦效应不宜忽略,最小预应力增量的摩擦效应明显;对于非对称荷载下的连续梁,承载力、最大和最小预应力增量以及挠度的摩擦效应不可忽略。     

基于非线性吸能机理的涡激振动减振理论与实验研究

流致振动现象广泛存在于机械、航空、土木和石油等重要工程领域, 为防止工程结构因流致振动行为而造成疲劳破坏, 有必要对稳定性、动力学响应及其振动控制做深入研究. 本文提出了一种由弹簧和质量块构成的非线性吸能器(nonlinear targeted energy transfer, NTET), 研究了该非线性吸能器对弹性支承圆柱体涡激振动的被动控制影响机制. 基于能量法推导了圆柱体涡激振动非线性被动控制的耦合动力学方程, 通过设计非线性弹簧?质量块构型的NTET, 进一步开展了涡激振动控制的实验研究, 并与理论预测结果进行了较好的对比, 获得提升涡激振动控制效果的最佳参数值. 研究发现, NTET的质量、弹簧刚度以及弹簧预应力等参数会对涡激振动控制效果产生显著的影响. 本文研究结果表明, 该耦合系统中圆柱体和NTET均表现出周期性的稳态振动响应, NTET质量的改变会显著影响系统的耦合频率. 在无预应力状态下, NTET质量越大、刚度越小时, 有更好的减振效果. 当弹簧预应力逐渐增大时, NTET的非线性刚度逐渐变弱, 会降低涡激振动控制性能. 参数分析表明: 随着涡激振动控制性能的提升, 圆柱体的振幅逐渐较小, NTET的振幅逐渐增大, 能量传递效率逐渐提高. 研究结果可为工程中涡激振动控制策略的高效设计提供有用的理论支撑和实验数据.      

Anisotropic hardening model and its application to cyclic loading

The experimental study of evolution rules of two state variables: back street _ij and yield stress R are first discussed. It is shown that back stress evolution is affected by the maximal prestress, and asymptotic value of yield stress depends on strain amplitude. The constitutive model is presented next, and its prediction for cyclic loading program is compared with experimental data.     

Analytical models for the mechanical behavior of closed and open-cell Al foams

Two 3D analytical models are proposed for the determination of mechanical properties of Al closed and open-cell foams under compression load. The first model, referring to closed cell foams, is symmetrical, considering ellipsoid cells equally arranged in a rectangular plate, whereas the second one, related to open-cell foams, consists of a simple unit parallelepiped cell.The closed cell model produces much higher values of the plateau stress than comparable experimental results, mainly due to the associated conditions of symmetry, contrary to the open-cell model which yields values close to experimental and theoretical results of other investigators. Additionally, in the latter case, a unit cubic cell is also considered for comparison reasons. Both models are solved by the finite element method using a commercial program. The open-cell model is simple, time sparing and easy to use. Finally, a fracture analysis of the model is conducted based on the energy density concept and results are given for distortion and dilatational effects.     

Dynamics of a prestressed stiff layer on an elastic half space: filtering and band gap characteristics of periodic structural models derived from long-wave asymptotics

Anti-plane and plane-strain, time-harmonic, small-amplitude vibrations of an elastic layer on an elastic half space are considered, superimposed upon a state of finite, uniform stress and strain. A (compressible) elastic material is considered, orthotropic with orthotropy axes aligned parallel and orthogonal both to the layer and the prestress principal directions. A non-uniform mass density is assumed in the layer. A formal long-wave asymptotic solution is derived under the assumptions of high contrast between the stiffnesses of the layer and the half space and between certain prestress components and the current elastic shear modulus.It is shown that (i) the layer asymptotically behaves as a beam subject to transversal and axial vibrations; (ii) the response of the half space can be found in a closed-form, under the assumption of plane wave motion (which becomes consistent when the density of the layer is uniform), otherwise it is represented by a hypersingular integral equation; (iii) if the nonlocality introduced by the hypersingular integral equation is restricted to an influence area of finite extent, the integral can be analytically approximated, so that a Winkler-type spring model representing the half space is rigorously derived. For uniform density of the layer, the constants defining the spring model are given as functions of the prestress and anisotropy parameters of the half space; and, finally, (iv) the asymptotic solution provides new analytical expressions for incremental displacement of the layer, which, compared to the exact numerical solution (also included), are shown to perform quite well, even for values of parameters much beyond the limits imposed by the asymptotic analysis.The asymptotic analysis allows us to explore, for the first time, dynamic properties of a periodic layer bonded to an elastic half space and subject to a uniform prestress state. We find that the system exhibits band gaps (ranges of forbidden frequencies) and that the prestress can be used as a parameter tuning the filtering properties of the structure, an effect which may have important consequences in the design of resonant devices.     

多自应力模态索穹顶结构的几何构造分析

索穹顶结构是发展和推广Fuller张拉整体结构思想后唯一实现的一种新型大跨空间结构,它的几何构造分析是一项非常重要的工作。本文在对一般空间杆件体系的分类、自应力模态和机构位移模态研究的基础上,从索穹顶结构特有的杆件拓扑关系入手,提出了单位整体可行预应力这一新概念,并最终解决了多自应力模态下该体系稳定性判定问题;通过对若干类型索穹顶结构的几何构造分析,得出了一些对结构设计有用的结论。     

Fast numerical evaluation of flow fields with vortex cells

A vortex cell (in this paper) is an aerodynamically shaped cavity in the surface of a body, for example a wing, designed specially to trap the separated vortex within it, thus preventing large-scale unsteady vortex shedding from the wing. Vortex stabilisation can be achieved either by the special geometry, as has already been done experimentally, or by a system of active control. In realistic conditions the boundary and mixing layers in the vortex cell are always turbulent. In the present study a model for calculating the flow in a vortex cell was obtained by replacing the laminar viscosity with the turbulent viscosity in the known high-Reynolds-number asymptotic theory of steady laminar flows in vortex cells. The model was implemented numerically and was shown to be faster than solving the Reynolds-averaged Navier–Stokes equations. An experimental facility with a vortex cell was built and experiments performed. Comparisons of the experimental results with the predictions of the model are reasonably satisfactory. The results also indicate that at least for flows in near-circular vortex cells it is sufficient to have accurate turbulence models only in thin viscous layers, while outside the viscosity should only be small enough to make the flow effectively inviscid.     

心肌细胞大变形黏弹性模型及在实验中的应用

在衡量单个细胞力学行为的研究中,越来越多地采用结合实验的数值模拟方法. 在连续介质力学框架下,发展了一种新的心肌细胞本构模型,并与微管吮吸实验结合,探讨了心肌细胞的力学特性. 本构模型是对普遍使用的仅能用于小变形分析的标准线性固体模型的一种扩展,它将超弹性性能引入到黏弹性模型中,用以描述细胞的大变形黏弹性效应. 基于改进的本构模型,对心肌细胞微管吮吸实验过程进行了有限元模拟,并将计算结果与实验结果以及经典理论解进行了对比. 结果显示发展的本构模型适合细胞大变形问题的有限元数值模拟.      

Theoretical and experimental analysis of the accuracy and reproducibility of cell tracking velocimetry

A theoretical and experimental analysis has been conducted to determine the accuracy of cell tracking velocimetry (CTV). CTV is an analytical technique for quantifying magnetically induced velocity of immunomagnetically labeled cells (or particles), in which the computer algorithm, particle tracking velocimetry (PTV), has been modified and combined with a well-defined magnetic energy gradient. In addition, this technique can calculate the size of a cell (or particle) through the use of experimentally measured settling velocities. A model was developed which determines the minimum and maximum cell velocities that can be determined based on a number of intrinsic constants and variables associated with this technique. This model was experimentally tested using a number of calibration particles and very good agreement between model and experimental data was obtained. The combination of model and experimental validation establishes the proper operating parameters for CTV. Received: 14 January 2000/Accepted: 10 July 2000     

一种力-电协同驱动的细胞微流控培养腔理论模型

细胞培养液在微流控生物反应器中受到外界物理场（如压力梯度或者电场）作用流动而产生流体剪应力,并进一步刺激种子细胞调控其内部基因的表达,从而促进细胞的分化和生长,这个过程在自然生命组织内的微管中亦是如此。考虑到细胞培养微腔隙中液体流动行为很难实验量化测定,理论建模分析是目前可行的研究手段。因此建立了矩形截面的细胞微流控培养腔理论模型,将外部的物理驱动场（压力梯度与电场）与培养腔内液体的流速、切应力和流率联系起来,分别得到了压力梯度驱动（Pressure gradient driven,PGD）、电场驱动（Electric field driven,EFD）及力-电协同驱动（Pressure-electricity synergic driven,P-ESD）三种驱动方式下的液体流动理论模型。结果表明该理论模型与现有的实验结果基本一致,具体地:力-电协同作用下的解答为压力梯度驱动和电场驱动结果的叠加。细胞培养腔内的流体流速、剪应力及流率幅值均正比于外部物理场强幅值,但随着压力梯度驱动载荷频率的增大而减小,随着电场驱动频率的变化不明显。在压力梯度驱动作用下,细胞贴壁处的切应力随着腔高的增大而线性增大,流率则随着腔高的增大而非线性增大,而电场驱动下的结果不受腔高的影响。生理范围内的温度场变化对压力和电场驱动的结果影响不大。另外,在引起细胞响应的流体切应力水平,电场驱动能提供较大的切应力幅值而压力梯度驱动则能提供较大的流率幅值。该理论模型的建立为细胞微流控生物反应器实验系统的设计及参数优化提供理论参考,同时也为力-电刺激细胞生长、分化机理的研究的提供基础。