基于Hellinger-Reissner变分原理的应变梯度杂交元设计

从一般的偶应力理论出发，基于Hellinger-Reissner变分原理，通过对有限元 离散体系的位移试解引入非协调位移函数，得到了偶应力理论下有限元离散系统的能量相容 条件，并由此建立了应变梯度杂交元的应力函数优化条件. 根据该优化条件，构造了一 个C0类的平面4节点梯度杂交元，数值结果表明，该单元对可压缩和不可压缩状态的 梯度材料均可给出合理的数值结果，再现材料的尺度效应.     

弹性杆与结构接触冲击的冲击力计算研究

本文提出了一种将杆与结构的接触冲击问题简化为集中力与集中阻尼的常规结构动力学问题的计算模型。对于大型结构，可采用一种特殊的人工边界，只需对人工边界域内的结构用有限元法进行计算。这种人工边界是齐次的，可根据冲击影响区的大小人为地确定     

Multi-scale and multi-order singularity approach to non-equilibrium mechanics: Coupling of atomic-micro-macro damage

Offered in this work is the development of a macro/meso/micro model that covers the lineal scale of 10⁻¹¹ to 10⁰ by application of the volume energy density function. Boundary constraints and defect geometries are shown to play a role at the smaller scale in the same way as those at the macroscopic scale. Different orders of stress (or energy density) singularities are used to describe the defect geometry and prevailing constraint via the boundary conditions in a way similar to singularity adopted in classical fracture mechanics. Two classes of singularities have been identified in addition to classical one without violating the finiteness conditions of the local displacement and energy density. Still the connection of results from the different scales is no small task and is made possible by application of a scale multiplier. It is determined by considering the interactive effects of the parameters at the different scales from the atomic to the macroscopic. Unlike the classical boundary value problem approach, application of the scale multiplier has led to closed-form asymptotic multiscale solutions that otherwise would not have been made possible. The procedure is demonstrated for the anti-plane shear of a macro-micro-atomic model that accounts for imperfection at the different scales Published in Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 3–22, January 2006.     

On the transient non-Fickian dispersion theory

The Fickian dispersion equation is the basic relationship used to describe the nonconvective mass flux of a solute in a porous medium. This equation prescribes a linear relationship between the dispersive mass flux and the concentration gradient. An important characteristic of the Fickian relationship is that it is independent of the history of dispersion (e.g. the time rate of change of the dispersion flux). Also, the dispersivities are supposed to be medium constants and invariant with temporal and spatial scales of observation. It is believed that in general these restrictions do not hold. A number of authors have proposed various alternative relationships. For example, differential equations have been employed that prescribe a relationship between the dispersion flux and its time and space derivatives. Also, stochastic theories result in integro-differential equations in which dispersion tensor grow asymptotically with time or distance. In this work, three different approaches, which lead to three different non-Fickian equations with a transient character, are discussed and their primary features and differences are highlighted. It is shown that an effective dispersion tensor defined in the framework of the transient non-Fickian theory, grows asymptotically with time and distance; a result which also follows from stochastic theories. Next, principles of continuum mechanics are employed to provide a solid theoretical basis for the non-Fickian transient dispersion theory. The equation of motion of a solute in a porous medium is used to provide a rigorous derivation of various dispersion relationships valid under different conditions. Under various simplifying assumptions, the generalized theory is found to agree with the conventional Fickian theory as well as several other non-Fickian relationships found in the literature. Moreover, it is shown that for nonconservative solutes, the traditional dispersion tensor is affected by the rate of mass exchange of the solute.Also with National Institute of Public Health and Environmental Protection (RIVM), PO Box 1; 3720BA Bilthoven, The Netherlands     

Fractals — An overview of potential applications to transport in porous media

We present an overview of the potential applicability of fractal concepts to various aspects of transport phenomena in heterogeneous porous media. Three examples of phenomena where a fractal approach should prove illuminating are presented. In the first example we consider pore level heterogeneities as typified by pore surface roughness. We suggest that roughness may be usefully modelled by fractal curves and surfaces and also cite experimental evidence for regarding pores as fractals. In the second example we consider a fractal network approach to modelling large-scale heterogeneities. The presence of features on all length scales in simple fractal models should capture the essential role played by the presence of heterogeneities on many scales in natural reservoirs. Studies of transport phenomena in such models may yield valuable insights into the problems of macroscopic dispersion. The final example concerns dispersion in multiphase flow. Here the fractal character is attributed to the distribution of the fluid phases rather than the porous medium itself. Again studies of transport phenomena in simple fractal models should help to clarify various problems associated with the corresponding phenomena in real reservoirs.     

Method of homogenization applied to dispersion in porous media

The theory of homogenization which is a rigorous method of averaging by multiple scale expansions, is applied here to the transport of a solute in a porous medium. The main assumption is that the matrix has a periodic pore structure on the local scale. Starting from the pores with the Navier-Stokes equations for the fluid motion and the usual convective-diffusion equation for the solute, we give an alternative derivation of the three-dimensional macroscale dispersion tensor for solute concentration. The original result was first found by Brenner by extending Brownian motion theory. The method of homogenization is an expedient approach based on conventional continuum equations and the technique of multiple-scale expansions, and can be extended to more complex media involving three or more contrasting scales with periodicity in every but the largest scale.     

Evolutive and nonlinear vibrations of rotor on aerodynamic bearings

The use of air as a lubricant in aerodynamic bearings is advantageous, particularly in the food industry. Aerodynamic bearings with tilting pads have complicated stiffness and damping properties and need a very detailed theoretical and experimental research. Response curves of rigid rotor supported on aerodynamic bearings are presented for a linear but evolutive mathematical model. Due to non-monotone properties of stiffness and damping matrices at variable revolutions, a new resonance appears. The mathematical model of rotor vibrations in the whole area of bearing clearance is also developed in the consideration of strongly nonlinear properties of aerodynamic bearing.     

粘塑性损伤模型模拟准超塑性单轴拉伸行为

发展了Chaboche粘塑性本构模型的大变形隐式算法，用损伤(DM)和无损伤(NDM)模型模拟准超塑性单轴拉伸。发现变形过程可分为三个阶段：均匀变形、颈缩发展、断裂破坏阶段。DM可准确模拟前两个阶段变形，NDM只能较好地模拟均匀变形阶段，表明DM可以较精确地描述稳定发展的动态过程。由于有限元方法只能描述连续介质，因此对于断裂破坏阶段，NDM模拟载荷大于试验结果，DM的载荷小于试验结果，这是由高应变速率敏感性造成。DM能够描述试验中出现地多处颈缩现象，局部应变速率分布随时间演化反映了颈缩发展程度。严重颈缩部位的距离代表着超塑性变形能力，距离越大，抗颈缩能力越好。     

微梁与基底间的毛细粘附作用

在表面微型机械结构的制造过程中,强的毛细相互作用常常使得组成这些结构的微桥、微梁与基底粘附而导致失效。而在微尺度实验中,微桥与微梁又是微尺度材料常数和性能检测的常用的试件样式,如果实验中加载端与被检测的微尺度试件发生毛细粘附,将直接影响检测数据的准确性。本文应用微悬臂梁试件,讨论微梁与基底间的毛细粘附作用,并通过能量原理计算其粘附力的大小和试件几何尺寸、粘附面距离、粘附液体特性之间的关系。最后应用微散斑干涉,检测粘附平衡态时微桥和微梁的粘附力以及由毛细粘附所导致的弯曲变形,并与理论计算结果进行比较。     

A phenomenological and extended continuum approach for modelling non-equilibrium flows

This paper presents a new technique that combines Grad’s 13-moment equations (G13) with a phenomenological approach to rarefied gas flows. This combination and the proposed solution technique capture some important non-equilibrium phenomena that appear in the early continuum-transition flow regime. In contrast to the fully coupled 13-moment equation set, a significant advantage of the present solution technique is that it does not require extra boundary conditions explicitly; Grad’s equations for viscous stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations of transport. The relative computational cost of this novel technique is low in comparison to other methods, such as fully coupled solutions involving many moments or discrete methods. In this study, the proposed numerical procedure is tested on a planar Couette flow case, and the results are compared to predictions obtained from the direct simulation Monte Carlo method. This test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from non-equilibrium phenomena, which cannot be captured by the Navier–Stokes–Fourier constitutive equations or phenomenological modifications.