Sloshing and energy dissipation in an egg: SPH simulations and experiments

Tall structures, such as towers and bridges, can oscillate at excessive magnitudes when subjected to wind and earthquake loads. Liquid sloshing absorbers can be used to suppress these excessive oscillations by tuning the frequency of the sloshing to the critical frequency of the structure. Sloshing absorbers are simple structures consisting of a partially full container of liquid with a free surface. Tuning ensures that significant amounts of harmful energy can be extracted from the structure to the sloshing liquid. However, there needs to be a rapid means of dissipating this energy to avoid its returning back to the structure (then back to the liquid periodically).A hen׳s egg seems to have evolved to efficiently dissipate energy to protect its embryo using sloshing of its liquid content. Hence, the potential to implement the egg׳s unique properties as a sloshing absorber for structural control, is the main focus of this study. Numerical simulations, using Smoothed Particle Hydrodynamics (SPH), and experimental comparisons are presented in this paper. One objective is to demonstrate the ability of SPH to simulate complex free surface behaviour in three dimensions. Such a tool is then useful to identify different dissipation modes. Effects of fill volume and viscosity on the rate of dissipation, are also investigated.     

A hybrid model for computationally efficient fatigue fracture simulations at microelectronic assembly interfaces

Modern microelectronic assemblies are heterogeneous, layered structures joined by interconnects made of solder alloys with low homologous temperatures. The solder interconnections join devices to circuit boards and they fail by thermal fatigue fracture at their interfaces either to the device or to the circuit board. Predicting the fatigue fracture of the solder interconnections is a challenge due to the fact that they undergo large inelastic deformations during temperature cycling tests. In this paper we develop a hybrid approach inspired by cohesive zone fracture mechanics and the Disturbed State Concept to predict the crack trajectory and fatigue life of a solder interconnection subjected to both isothermal temperature cycling and anisothermal temperature cycling conditions (representing the two common accelerated test conditions for microelectronic products). A hybrid computational approach is used in which a first order approximation of the disturbance is used to estimate incremental cycles to criticality and thereby propagate the crack. The modeled crack fronts and the fatigue lives are validated through a comparison to results from the two types of accelerated tests. Overall, the model is shown to predict the fatigue life of the critical interconnection in the assembly to within 20% of the experimentally determined life. More importantly, the predicted crack trajectory is demonstrated to agree very well with the experimentally observed trajectory. Strikingly, the microscopically observed microstructural changes during crack propagation from that corresponding to creep fatigue to that of shear overload were found to be excellently correlated with the rate of change of the disturbance calculated in the model.     

An icing physics study by using lifetime-based molecular tagging thermometry technique

An experimental investigation was conducted to quantify the unsteady heat transfer and phase changing process within small icing water droplets in order to elucidate underlying physics to improve our understanding of the important micro-physical process of icing phenomena. A novel, lifetime-based molecular tagging thermometry (MTT) technique was developed and implemented to achieve temporally-and-spatially resolved temperature distribution measurements to reveal the time evolution of the unsteady heat transfer and dynamic phase changing process within micro-sized water droplets in the course of icing process. It was found that, after a water droplet impinged onto a frozen cold surface, the liquid water at the bottom of the droplet would be frozen and turned to solid ice rapidly, while the upper portion of the droplet was still in liquid state. As the time goes by, the interface between the liquid phase water and solid phase ice was found to move upward continuously with more and more liquid water within the droplet turned to solid ice. Interestingly, the averaged temperature of the remaining liquid water within the small icing droplet was found to increase, rather than decrease, continuously in the course of icing process. The temperature increase of the remaining liquid water is believed to be due to the heat release of the latent heat during solidification process. The volume expansion of the water droplet during the icing process was found to be mainly upward to cause droplet height growth rather than radial to enlarge the contact area of the droplet on the test plate. As a result, the spherical-cap-shaped water droplet was found to turn to a prolate-spheroid-shaped ice crystal with cusp-like top at the end of the icing process. The required freezing time for the water droplets to turn to ice crystals completely was found to depend on the surface temperature of the test plate strongly, which would decrease exponentially as the surface temperature of the frozen cold test plate decreases.     

元件与模式相对重要度对静强度可靠度的影响分析

本文通过研究指出,在运用增量载荷法寻找每级可能破坏元件时,必须考虑每个元件变异系数的影响,以避免漏掉极限承载能力很大但可靠度很低的失效模式;同时指出,结构失效的各个模式对系统可靠性的影响不仅与其本身发生失效的概率有关,而且与这个模式的重要程度有关,并提出了采用加权系数来计及每个失效模式的重要程度对结构系统可靠性影响的方法;最后用算例说明了本文方法的合理性。     

The effect of variations in the creep exponent on the buckling of circular cylindrical shells

The senior author solved the problem of axially symmetrical creep buckling of thin circular cylindrical shells subjected to uniform axial compression. In that analysis the constitutive equation was a power law, and the exponent was taken to be equal to three. The purpose of this work was to extend the solution to a range of values of the creep exponent, n. To cope with the increasing algebraic complexity, a digital computer was employed in two ways: to generate the set of equations symbolically, and then to solve these equations. The computer programs were used to generate numerical solutions for the cases in which n was equal to 3, 5, 7 and 9. Two simple extrapolation techniques were then employed to obtain approximate solutions to the critical time problem for values of n up to 29.     

An Integral Method to Calculate Water Saturation in a Centrifuge Experiment to Determine Capillary Pressure

The centrifuge method is commonly used to determine the capillary pressure of a porous medium, and the original approximating method for data analysis developed by Hassler and Brunner is still being used. Its limitations are, however, not well understood. Application to analyze experiments where one of the assumptions was obviously violated had been given in the literature. While the result appeared to be quite reasonable, it was not clear how close was it to reality. One of the objectives of this paper is to review the assumptions that is required to develop this method, so that the experimental condition in which it is applicable can be established. The other objective is to derive a completely different solution technique to this problem. There is no need to assume that the ratio of the inlet radius to the exit radius of the core to the center of the centrifuge be close to 1. With the freedom from this limitation it is, therefore, possible to construct machines at lower cost and to improve on the data quality by allowing longer cores.     

生物力学与基因-献给周培源教授诞辰100周年

生物界包罗万象,其中有力的作用,所以有生物力学.自Galileo,Harvey, Boreli, Hooke, Euler,Young等创始以来,生物力学阐明了鸟飞鱼游,人体运动,血液循环,人工脏器等,对人世社会,有所贡献.生物力学的基础是质点力学,传统地用连续体力学的概念来简化.但近年做生物组织在应力的作用下改造的问题,引起了必须更改传统连续体力学的几个公理的问题.我们将仔细讨论这些公理,然后指出新公理存在的理由,是由于基因在细胞里的日常工作.基因不单主宰遗传,变异;并且忙着控制日常生活.不过,现在仅见其端倪.详细的情形,要等将来来阐发了.      

Systematic description of imperfect bifurcation behavior of symmetric systems

A systematic method is presented for describing experimental curves of force vs strain of a system with regular polygonal (dihedral group) symmetry subject to bifurcation behavior, with an aim toward overcoming the following problems : (1) it is difficult to judge whether the system is undergoing bifurcation or not ; (2) the perfect behavior of the system cannot be known due to the presence of initial imperfections ; (3) those curves are often qualitatively different from bifurcation diagrams predicted by mathematics. The tools employed are : the asymptotic theory for imperfect bifurcation, such as the Koiter law, and the stochastic theory of initial imperfections. The former theory is extended in this paper to the system with regular-polygonal symmetry to present asymptotic laws for recovering perfect curves with reference to the experimental ones. These laws are formulated for physically observable displacements, instead of the variables in the mathematical bifurcation diagrams, in order to make them readily applicable to the experimental curves. The stochastic theory is combined with an asymptotic law to develop a means to identify the multiplicity of the bifurcation point. The systematic method for describing the experimental curves developed in this manner is applied to the bifurcation analysis of regular-polygonal truss domes to testify its validity. Furthermore, this method is applied to the shear behavior of cylindrical sand specimens to show that they, in fact, are undergoing bifurcation, and, in turn, to demonstrate the importance of a viewpoint of bifurcation in the study of shear behavior of materials. The need of a dual viewpoint of bifurcation and plasticity in the study of constitutive relationship of materials is emphasized to conclude the paper.     

Modelling of the dyeing process of packed cotton threads using reactive dyes

The Method of Volume Averaging is used to model the process of dyeing textile threads on bobbins. This analysis allows one to upscale the relevant information at the micro-scale, composed of the textile fibres of the thread in contact with the dyeing bath fluid, to the macro-scale, consisting of the bobbins of threads inside the equipment. The final mathematical model consists of two equations, one for the fluid phase external to the thread and the other for the fluid phase internal to the thread. In order to solve the partial differential equations obtained in the mathematical model, the authors developed a computation code using the Method of Finite Volumes. This code utilized a system of generalized coordinates to facilitate application of the boundary conditions to different bobbin geometries. The numerical results for the kinetics of dyeing packed cotton threads with reactive dyes are compared to the experimental results obtained in Brazilian textile industries, leading to good agreement between theory and experiment. This demonstrates that the model developed in this paper is able to predict the operational conditions to be used in the textile industries, minimizing the consumption of dyes and other auxiliaries necessary for the dyeing process.     

Local and Global Transitions to Chaos and Hysteresis in a Porous Layer Heated from Below

The routes to chaos in a fluid saturated porous layer heated from below are investigated by using the weak nonlinear theory as well as Adomian's decomposition method to solve a system of ordinary differential equations which result from a truncated Galerkin representation of the governing equations. This representation is equivalent to the familiar Lorenz equations with different coefficients which correspond to the porous media convection. While the weak nonlinear method of solution provides significant insight to the problem, to its solution and corresponding bifurcations and other transitions, it is limited because of its local domain of validity, which in the present case is in the neighbourhood of any one of the two steady state convective solutions. On the other hand, the Adomian's decomposition method provides an analytical solution to the problem in terms of infinite power series. The practical need to evaluate numerical values from the infinite power series, the consequent series truncation, and the practical procedure to accomplish this task transform the otherwise analytical results into a computational solution achieved up to a finite accuracy. The transition from the steady solution to chaos is analysed by using both methods and their results are compared, showing a very good agreement in the neighbourhood of the convective steady solutions. The analysis explains previously obtained computational results for low Prandtl number convection in porous media suggesting a transition from steady convection to chaos via a Hopf bifurcation, represented by a solitary limit cycle at a sub-critical value of Rayleigh number. A simple explanation of the well known experimental phenomenon of Hysteresis in the transition from steady convection to chaos and backwards from chaos to steady state is provided in terms of the present analysis results.     

New accurate efficient modeling techniques for the vibration analysis of T-joint thin-walled box structures

We propose new accurate efficient modeling techniques for the vibration analysis of T-joint thin-walled box structures. The essence of the present techniques is to use beam elements to model thin-walled members of the joint, but the elements are based on an eight-degree-of-freedom (8-DOF) beam theory capable of handling warping and distortion. Two approaches are considered to model the interfacing joint region connected to three adjacent thin-walled box structures: the first one is to model the joint region with plate elements and the second one is to use a joint element derived to be consistent with nearby 8-DOF beam elements. The efficiency of the present techniques comes from the use of beam elements to model the box structures while the accuracy comes from the use of the higher-order beam theory accounting for warping and distortion. The procedures to match the dissimilar elements and to develop the joint element are also presented in this work. The effectiveness of the present approaches is demonstrated by numerical examples.     

基于振动监测的静载荷滑动轴承接触摩擦故障诊断实验研究

采用静载荷滑动轴承试验台模拟轴颈-轴承从液体润滑状态逐步向干摩擦状态过渡时的接触摩擦故障的发生和发展过程,进而利用振动信号诊断滑动轴承的接触摩擦故障;通过对特征参数进行归一化处理得到无量纲特征参数,进而通过无量纲特征参数的适当数学组合得到无量纲诊断准则,并探讨了无量纲诊断准则的适用性.结果表明:利用所得到的无量纲诊断准则进行轴颈-轴承接触摩擦故障诊断时无须建立用于模式识别的标准模,可实现快捷方便的故障诊断;无量纲诊断准则对工况不敏感,而对故障更敏感,适用于可变工况下滑动轴承的故障诊断,且诊断成本较低.     

Numerical solutions of Navier-Stokes equations with an integrated compartment method (ICM)

The most common numerical methods that are used by physical scientists to approximate partial differential equations employ finite differences and/or finite elements. In addition, compartment analyses have been adopted by ecological system analysts to simulate the evolution of processes governed by differential equations without spatial derivatives. An integrated compartment method (ICM) is proposed to combine the merits of these three numerical techniques. The basic procedures of the ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. These procedures are applied to the Navier-Stokes equations to yield the computational algorithm from which computer programs can be coded. The computer code is designed to solve one-, two-, or three-dimensional problems as desired. The program is applied to two simple cases: wake formation behind an obstacle in a channel and circulatory motion of a body of fluid in the square cavity. These preliminary applications have shown promising results.     

The repeated filamentation of vorticity interfaces

Arbitrarily shallow, localised disturbances to the boundary of a uniform circular vortex are found to steepen to the point of ejecting a thin filament into the surrounding irrotational fluid after a time inversely proportional to the initial wave steepness squared. Subsequent to the formation of the first filament, a second filament is produced in the much shorter time inversely proportional to the vorticity within the vortex. This process appears to repeat itself endlessly, and the vortex boundary rapidly grows in complexity.     

Closed-loop control of a free shear flow: a framework using the parabolized stability equations

In this study the parabolized stability equations (PSE) are used to build reduced-order-models (ROMs) given in terms of frequency and time-domain transfer functions (TFs) for application in closed-loop control. The control law is defined in two steps; first it is necessary to estimate the open-loop behaviour of the system from measurements, and subsequently the response of the flow to an actuation signal is determined. The theoretically derived PSE TFs are used to account for both of these effects. Besides its capability to derive simplified models of the flow dynamics, we explore the use of the TFs to provide an a priori determination of adequate positions for efficiently forcing along the direction transverse to the mean flow. The PSE TFs are also used to account for the relative position between sensors and actuators which defines two schemes, feedback and feedforward, the former presenting a lower effectiveness. Differences are understood in terms of the evaluation of the causality of the resulting gain, which is made without the need to perform computationally demanding simulations for each configuration. The ROMs are applied to a direct numerical simulation of a convectively unstable 2D mixing layer. The derived feedforward control law is shown to lead to a reduction in the mean square values of the objective fluctuation of more than one order of magnitude, at the output position, in the nonlinear simulation, which is accompanied by a significant delay in the vortex pairing and roll-up. A study of the robustness of the control law demonstrates that it is fairly insensitive to the amplitude of inflow perturbations and model uncertainties given in terms of Reynolds number variations.     

结构频率误差修正参数的最优选取问题

利用摄动理论和广义逆理论，研究了结构固有频率随机误差的修正及修改参数的选取问题，提出了理想修改参数、最优修改参数和最优修改参数组的概念，讨论了如何选取修改参数才能使结构修改后频率误差均方值的数学期望最小，并得到了该最小值的表达式，数值例子说明了方法的实用性和有效性。     

A Theoretical Model for the Simulation of Microdamage Accumulation and Repair in Compact Bone*

This paper describes a new theoretical approach to bone microdamage, in which a population of cracks is explicitly modelled. A given sample of bone is assumed to contain a certain number of cracks, whose growth characteristics are described with an equation containing stochastic variables to create statistical differences from one crack to another. This type of model allows us to predict a wide variety of data. The present paper illustrates the different types of prediction which can be made, including: (i) standard damage parameters such as the number and length of cracks and the reduction in stiffness; (ii) fatigue test data such as the number of cycles to failure as a function of stress level, including scatter; (iii) effects due to the living system, including repair, remodelling and adaptation. A useful feature of the model is our ability to examine the statistics of the crack population in detail to find, for example, the number of cracks which are potentially dangerous as opposed to those which are dormant, and to investigate the reasons for increased crack numbers in the bones of older people. The potential also exists to use the model to investigate different theories of bone remodelling and adaptation.     

THE ANALYTIC RESOLUTIONS AND APPLICATIONS OF THE NON－LINEAR SEEPAGE FLOW EQUATIONS OF COAL INFUSION

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Electro-osmotic pore pressures in soil due to an alternating electrical field

Pore pressure development in a soil specimen due to electro-osmosis under alternating current conditions is examined theoretically. Solutions to the governing equation are derived for one-dimensional flow with boundary conditions corresponding to an impervious (conventional no-flow boundary), a partially drained boundary, and a partially drained boundary with an intervening permeable zone between the boundary and the soil. These latter two boundary conditions can arise from details of pore pressure measuring systems at the specimen boundaries during laboratory experiments. An analysis of the solutions indicates that for a perfect no-flow boundary, excess pore pressures measured at an electrode consist of a steady state and rapidly-decaying transient response. The pore pressures exhibit a 45 degree phase shift relative to the applied electric current. The effect of the partially drained boundary is to reduce the peak to peak amplitude of the pore pressure and to increase the phase shift to as much as 90 degrees depending on the compressibility of the pore pressure measuring system. The effect of the impeded and partially drained boundary is to further reduce the amplitude of the pore pressures and to increase the phase shift to as much as 180 degrees depending on the relative permeability of the impeded boundary.     

Resonant Capture and Separatrix Crossing in Dual-Spin Spacecraft

We consider the rotational motion of a spacecraft composed of two bodies which are free to rotate relative to one another about a common shaft S. A motor on one of the bodies provides a small constant internal torque which influences the relative motion of the two bodies, and which may influence the orientation of their common shaft S. Resonant capture refers to the phenomenon that the spacecraft may end up in one of several possible orientations, including a nearly flat spin (transverse to S), in addition to the expected simple rotation about S.The method of averaging is used to treat the original equations of motion, and it is shown that the essential mathematical problem involves separatrix crossing in a problem with slowly moving separatrices. Energy changes represented by Melnikov integrals are used to supplement the averaged equations in the neighborhood of the heteroclinic motions. The method is used to predict which initial conditions lead to capture into each of three distinct capture regions. The asymptotic results are compared to those obtained by direct numerical integration of the equations of motion.