多体系统中深沟球轴承旋转铰内接触分析

将传统方法用于铰内接触分析时,需要通过物体的相对运动细节判断接触位置. 但实际机械系统中的铰,其内部缝隙非常小以至于几乎与计算误差的数量级相同. 在这种情况下,传统方法中的数值病态非常严重,难以得到合理的结果. 结合深沟球轴承旋转铰的构造细节,分析了钢球与轨道接触时运动学描述参数之间的关系、钢球在有效承载时的受力特征以及铰内接触形式的特点. 在此基础上,提出了一种确定多体系统中深沟球轴承旋转铰内接触力和接触位置的方法. 所提方法不需要解除铰的运动学约束,也不必求解非线性互补方程,因此在数值稳定性和计算效率方面具有优势. 数值算例验证了该方法的可行性.     

Micromechanical analysis of the behavior of stiff clay

Cementations formed in geological timescale are observed in various stiff clays.A micromechanical stress strain model is developed for modeling the effect of cementation on the deformation behavior of stiff clay.The proposed approach considers explicitly cementations at intercluster contacts,which is different from conventional model.The concept of inter-cluster bonding is introduced to account for an additional cohesion in shear sliding and a higher yield stress in normal compression.A damage law for inter-cluster bonding is proposed at cluster contacts for the debonding process during mechanical loading.The model is used to simulate numerous stress-path tests on Vallericca stiff clay.The applicability of the present model is evaluated through comparisons between the predicted and the measured results.In order to explain the stress-induced anisotropy arising from externally applied load,the evolution of local stresses and local strains at inter-cluster planes are discussed.     

Evolution of mesoscopic granular clusters in comminution systems: a structural mechanics model of grain breakage and force chain buckling

A major scientific challenge in establishing a micromechanics theory for complex materials is the characterisation and modelling of emergent mesoscopic phenomena. This study demonstrates the key elements of a structural mechanics approach to the modelling of mesoscopic dissipative phenomena in comminution systems where grain breakage and force chain buckling coexist. Given the many degrees of freedom in these systems, there are multitude of possible configurations and configurational transitions accessible even for a small particle cluster (e.g. a particle and its immediate neighbours). Here, we develop a model of the evolution of a 6-particle cluster undergoing breakage and force chain buckling, in sequence. The analysis lays bare the intricate connections between the contact topology, the relative kinematics arising from the interactions of particles at the bonded versus non-bonded contacts, and the collective dynamics of these interactions as the cluster is monotonically compressed under confinement. The stress-displacement response profiles at the cluster scale exhibit qualitatively similar properties to those seen in macroscopic assemblies under confined compression. A parametric analysis is undertaken to explore the effects of grain-scale resistances to breakage and buckling with respect to the overall force-displacement behaviour of the granular cluster. The study casts light on open problems for future research into the micromechanics of emergent cluster behaviour germane to comminution systems.     

Formulation of a damage internal state variable model for amorphous glassy polymers

The following article proposes a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.     

A numerical analysis of the shear behavior of granular soil with fines

Shear behavior of granular soil with fines is investigated using the discrete element method(DEM) and particle arrangements and inter-particle contacts during shear are examined.The DEM simulation reveals that fine particles play a vital role in the overall response of granular soil to shearing.The occurrence of liquefaction and temporary reduction of strength is ascribed mainly to the loss of support from the fine particle contacts(S-S) and fine particle-to-large particle contacts(S-L) as a consequence of the removal of fine particles from the load-carrying skeleton.The dilative strain-hardening response following the strain-softening response is associated with the migration of fine particles back into the load-carrying skeleton,which is thought to enhance the stiffness of the soil skeleton.During shear,the unit normal vector of the large particle-to-large particle(L-L) contact has the strongest fabric anisotropy,and the S-S contact unit normal vector possesses the weakest anisotropy,suggesting that the large particles play a dominant role in carrying the shear load.It is also found that,during shear,fine particles are prone to rolling at contacts while the large particles are prone to sliding,mainly at the S-L and L-L contacts.     

Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures

Two recently proposed Helmholtz free energy potentials including the full dislocation density tensor as an argument within the framework of strain gradient plasticity are used to predict the cyclic elastoplastic response of periodic laminate microstructures. First, a rank-one defect energy is considered, allowing for a size-effect on the overall yield strength of micro-heterogeneous materials. As a second candidate, a logarithmic defect energy is investigated, which is motivated by the work of Groma et al. (2003). The properties of the back-stress arising from both energies are investigated in the case of a laminate microstructure for which analytical as well as numerical solutions are derived. In this context, a new regularization technique for the numerical treatment of the rank-one potential is presented based on an incremental potential involving Lagrange multipliers. The results illustrate the effect of the two energies on the macroscopic size-dependent stress–strain response in monotonic and cyclic shear loading, as well as the arising pile-up distributions. Under cyclic loading, stress–strain hysteresis loops with inflections are predicted by both models. The logarithmic potential is shown to provide a continuum formulation of Asaro's type III kinematic hardening model. Experimental evidence in the literature of such loops with inflections in two-phased FFC alloys is provided, showing that the proposed strain gradient models reflect the occurrence of reversible plasticity phenomena under reverse loading.     

Thermal constriction resistance between two solids for random distribution of contacts

An infinite interface of randomly distributed contacts is modeled as a finite square region with randomly placed contacts inside it. The contacts outside the region are treated as continuum of contacts. The continuum approximation allows for an interaction between the contacts within the square and those outside it. An analytical solution is obtained for the temperature field, and the contact resistance is analyzed for randomness effects. This is the first such analytical model developed to study random distribution of contacts. The result shows an excellent agreement when tested against the the available analytical solution for the case of periodic arrangement of contacts. For the random case, the resistance is observed to be a strong function of the area fraction of contact. Received on 16 March 1998     

Stability,bifurcation, and softening in discrete systems: A conceptual approach for granular materials

Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric stiffness terms may become significant during granular failure. The geometric stiffness must be added to the mechanical stiffnesses of the contacts to produce the complete stiffness. With frictional contacts, this stiffness expression is incrementally nonlinear, having multiple loading branches. To aid the study of material behavior, a modified stiffness is derived for isolated granular clusters that are considered detached from the rest of a granular body. Criteria are presented for bifurcation, instability, and softening of such isolated and discrete granular sub-regions. Examples show that instability and softening can result entirely from the geometric terms in the matrix stiffness.     

Estimation of velocity eigenfunction and vorticity distributions from the timeline visualization technique

For the case of quasi-periodic flow, it is demonstrated that use of the hydrogen bubble timeline method leads to reasonable estimates of the eigenfunction of the streamwise velocity fluctuation. Both amplitude and phase distributions across an unstable wake flow are well-approximated. It is shown that the vorticity extrema, as well as the degree of concentration of vorticity, are in good agreement with those calculated from linear stability theory. A critical assessment is given of the possible uncertainties associated with this technique: the existence of a finite, but unknown cross-stream velocity component; bubble rise due to buoyancy effects; wake defect created downstream of the bubble wire; and resolution of the digitized image. Furthermore, the uncertainty in the streamwise velocity, arising from existence of a finite cross-stream velocity component, is actually less than that corresponding to a single-element hot film probe over certain regimes of operation.     

Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading

This paper presents the problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity, and the surface is assumed initially quiescent. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite time of rise of temperature, stress, displacement, and strain. The problem has been solved analytically using a direct approach. The derived analytical expressions have been computed for a specific situation. Numerical results for the temperature distribution, thermal stress, displacement, and strain are represented graphically. A comparison is made with the results predicted by the three theories.     

On the role of varying normal load and of randomly distributed relative velocities in the wavelength selection process of wear-pattern generation

In systems with moving contacts, as e.g. automotive vehicles on dirt-roads, friction brakes, and of course railway vehicles moving on railway tracks, spatially periodic wear patterns may appear on the contact partners’ surfaces. There is general agreement that the patterns are related to structural resonances. Using simple models with a moving point contact and an idealized wear model the present work first reviews some of the present understanding of wear-pattern generation. Then additional intuitively accessible explanations for the phenomena observed are developed and the effect of randomly specified relative velocities on the wavelength selection process is investigated. For this purpose the stability analysis of the surface evolution equation is pursued with the full, as well as with a reduced system, and a simple linear approach to deal with distributions of relative velocities is introduced. For fixed relative velocity the analysis yields an intuitively accessible picture of wear-pattern appearance or evanescence, as well as of wear-pattern motion. Based on these results it is shown, how dominant wavelengths are selected as a consequence of randomly distributed relative velocities.     

Hydrodynamic lubrication in line contacts improved by the boundary slippage

The present paper proposes three types of the boundary slippage augmentations in hydrodynamic lubricated line contacts for improving the load-carrying capacity but reducing the friction coefficient. One augmentation is at the slower moving contact surface, the second augmentation is at the faster moving contact surface, and the third is at both of the contact surfaces. They are respectively suitable for different operating conditions. The analysis was respectively carried out for the load-carrying capacity and the friction coefficient of hydrodynamic lubricated line contacts augmented with these three types of boundary slippage. The obtained results were compared with those for conventional hydrodynamic lubricated line contacts (without artificial introduction of the boundary slippage) for the same operating conditions. It was shown that in certain operating conditions these three types of the boundary slippage augmentations can respectively significantly increase the load-carrying capacity but reduce the friction coefficient of the contact. The potential application values of the proposed boundary slippage augmentations are evident for reducing the energy loss and the temperature rise as well as for improving the anti-scuffing ability of the contact.     

Iterative solution techniques for the stokes and Navier-Stokes equations

The linear system arising from a Lagrange-Galerkin mixed finite element approximation of the Navier–Stokes and continuity equations is symmetric indefinite and has the same block structure as a system arising from a mixed finite element discretization of a Stokes problem. This paper considers the iterative solution of such a system, comparing the performance of the one-level preconditioned conjugate residual method for indefinite matrices with that of a more traditional two-level pressure correction approach. Asymptotic estimates for the amount of work involved in each method are given together with the results of related numerical experiments.     

Hybrid Parallel Linear System Solvers

This paper presents a new approach to the solution of nonsymmetric linear systems that uses hybrid techniques based on both direct and iterative methods. An implicitly preconditioned modified system is obtained by applying projections onto block rows of the original system. Our technique provides the flexibility of using either direct or iterative methods for the solution of the preconditioned system. The resulting algorithms are robust, and can be implemented with high efficiency on a variety of parallel architectures. The algorithms are used to solve linear systems arising from the discretization of convection-diffusion equations as well as those systems that arise from the simulation of particulate flows. Experiments are presented to illustrate the robustness and parallel efficiency of these methods.     

Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures

This paper reviews the basis and applications of the finite-difference time -domain (FD-TD) numerical modeling approach for Maxwell's equations. FD-TD is very simple in concept and execution. However, it is remarkably robust, providing highly accurate modeling predictions for a wide variety of electromagnetic wave interaction problems. The accuracy and breadth of FD-TD applications will be illustrated by a number of two- and three-dimensional examples. The objects modeled range in nature from simple geometric shapes to extremely complex aerospace and biological systems. In all cases where rigorous analytical, code-to-code, or experimental validations are possible, FD-TD predictive data for penetrating and scattered near fields as well as radar cross sections are in excellent agreement with the benchmarks. It will also be shown that opportunities are arising in applying FD-TD to model rapidly time-varying systems, microwave circuits, and inverse scattering. With continuing advances in FD-TD modeling theory as well as continuing advances in supercomputer technology, there is a strong possibility that FD-TD numerical modeling will occupy an important place in high-frequency engineering electromagnetics as we move into the 1990s.     

On transient creep bounds and approximate solutions for the torsion of thin strips

Integral equations are derived which govern transient primary and secondary creep in thin rectangular strips subject to torsion. Formal similarity between these equations and others arising in previous work are exploited to obtain bounds, monotonicity and convexity of the stress profile as well as uniform approximations.     

Implications for Fisheries Policy of Complex Ecologic–Economic Dynamics

Fishery dynamics are considered within the context of an integrated ecologic–economic, or bioeconomic, approach. The possibility of complex dynamics is examined, both of the chaotic as well as the catastrophic variety. Issues involving learning and convergence by fishers are considered as are complications arising from the hierarchical nature of fisheries. Policy responses to these problems are seen to involve the precautionary principle to mitigate the threat of catastrophic discontinuities and the scale-matching principle to ensure that management and property rights system are properly implemented.     

Unsteady Flow to Wells Partially Penetrating in Two-Layered Aquifers

The unsteady flow of water to well in a layered aquifer with an interlayer flow is examined in this paper. The system studied comprises an aquifer consisting of two productive layers of finite thickness that are in a perfect hydraulic contact and a well which partially penetrates in one of the layers. Each layer is assumed to be homogeneous and isotropic and the water contained in the aquifer is of identical physical properties and small compressibility.The analytical solutions are derived for the case when the system is characterised by equality of hydraulic diffusivity of layers. These solutions give the results accurate enough for practical applications and allow to estimate the effects of partial penetration and contrast in parameters of formation on distribution of the flow potential both at large distances from wells and at the wells.The obtained solutions also provide a basis for predicting the interlayer flow arising from the performance of a pumping well as well as between a pair of wells which have an open interval located in different layers of the aquifer. Two cases have been analysed: (1) a pumping pair of wells which is used to prevent water inflow to the productive well, and (2) a pumping-injection pair of wells providing the demanded mixing of water from adjacent layers. Some examples of flow patterns and specially computed diagrams are given to illustrate the operation of such systems.     

Fundamental Concepts of Collective Intelligence

A collective intelligence consists of a large number of quasi-independent, stochastic agents, interacting locally both among themselves as well as with an active environment, in the absence of hierarchical organization, and yet which is capable of adaptive behavior. The major concepts arising from our current understanding of collective intelligence are reviewed. These include stochastic determinism, interactive determinism, nondirected communication, nonrepresentational contextual dependency, stigmergy. These are illustrated using examples drawn from the literature on ant behavior. Several speculations into the dynamics of collective intelligence are presented, including nondispersive temporal evolution, broken ergodicity and broken symmetry. Several questions for future study are posed.     

A design of residual error estimates for a high order BDF‐DGFE method applied to compressible flows

We deal with the numerical solution of the non‐stationary compressible Navier–Stokes equations with the aid of the backward difference formula – discontinuous Galerkin finite element method. This scheme is sufficiently stable, efficient and accurate with respect to the space as well as time coordinates. The nonlinear algebraic systems arising from the backward difference formula – discontinuous Galerkin finite element discretization are solved by an iterative Newton‐like method. The main benefit of this paper are residual error estimates that are able to identify the computational errors following from the space and time discretizations and from the inexact solution of the nonlinear algebraic systems. Thus, we propose an efficient algorithm where the algebraic, spatial and temporal errors are balanced. The computational performance of the proposed method is demonstrated by a list of numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.