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1.
Stanisław Stupkiewicz 《Computational Mechanics》2009,44(5):605-619
Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite
configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of
the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem.
Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method
or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance
of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal.
It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement
results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous
Galerkin method does not help significantly. 相似文献
2.
A combined finite element evaluation of hydrodynamic pressure and boundary element calculation of film thickness is presented. The viscosity and the density of the oil are assumed to vary with pressure, however the isothermal condition is assumed to prevail. The technique is based on an iterative procedure by assuming an initial hydrodynamic pressure. The iteration cycle will then be followed by the calculation of the film thickness and hydrodynamic pressure to arrive at a converged solution. The bearings have been treated realistically as finite domain bodies and their deformations are evaluated by boundary element method. The accuracy of the technique is illustrated in elastohydrodynamic lubrication (EHL) of inclined slider and line contact problems. 相似文献
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In order to predict the macroscopic thermal response of contact interfaces between rough surface topographies, a computational contact homogenization technique is developed at the finite deformation regime. The overall homogenization framework transfers macroscopic contact variables, such as surfacial stretch, pressure and heat flux, as boundary conditions on a test sample within a micromechanical interface testing procedure. An analysis of the thermal dissipation within the test sample reveals a thermodynamically consistent identification for the macroscopic thermal contact conductance parameter that enables the solution of a homogenized thermomechanical contact boundary value problem based on standard computational approaches. The homogenized contact response effectively predicts a temperature jump across the macroscale contact interface. The strong dependence of this homogenized response on macroscale solution variables of interest is demonstrated via representative three‐dimensional numerical investigations. The proposed contact homogenization framework is suitable for the analysis of similar energy transport phenomena across heterogeneous contact interfaces where the investigation of the sources for energy dissipation is of concern. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
5.
Yongbin Zhang 《Acta Mechanica》2014,225(3):851-871
The elastohydrodynamic lubrication in a sliding line contact between a flattened rough plane surface and a smooth plane surface is analytically studied. Both surfaces are assumed as elastic and parallel to one another. The flattened rough surface is treated as equivalent to a rough plane surface with uniformly distributed cylindrical asperities evenly truncated on the top. For understanding the elastohydrodynamic lubrication performance between these two plane surfaces, an inlet zone analysis is taken for the elastohydrodynamic lubrication formed between a truncated cylindrical asperity and the smooth plane surface. It is found from the obtained results that the asperity truncation reduces the elastohydrodynamic load-carrying capacity, and this effect is significant for low sliding speeds or/and heavy loads, while it is negligible for high sliding speeds and moderate loads. The asperity truncation increases the friction coefficient of the asperity contact especially at relatively light loads, while it only slightly increases the friction coefficient of the asperity contact at heavy loads. For heavy loads, the asperity truncation can have a significant effect on the reduction in the maximum surface temperature rise. It is recommended by the present study that the surface asperity be truncated in a certain degree in an elastohydrodynamic contact with high sliding speeds and relatively heavy loads because of giving the benefits of considerably reducing the maximum surface temperature rise while maintaining the elastohydrodynamic load-carrying capacity. 相似文献
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İ. Temizer 《International journal for numerical methods in engineering》2014,100(13):953-981
A computational contact homogenization framework is established for the modeling and simulation of soft matter friction. The main challenges toward the realization of the framework are (1) the establishment of a frictional contact algorithm that displays an optimal combination of accuracy, efficiency, and robustness and plays a central role in (2) the construction of a micromechanical contact test within which samples of arbitrary size may be embedded and which is not restricted to a single deformable body. The former challenge is addressed through the extension of mixed variational formulations of contact mechanics to a mortar‐based isogeometric setting where the augmented Lagrangian approach serves as the constraint enforcement method. The latter challenge is addressed through the concept of periodic embedding, with which a periodically replicated ‐continuous interface topography is realized across which not only pending but also ensuing contact among simulation cells will be automatically captured. Two‐dimensional and three‐dimensional investigations with unilateral/bilateral periodic/random roughness on two elastic micromechanical samples demonstrate the overall framework and the nature of the macroscopic frictional response. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
8.
Wing Kam Liu Shangwu Xiong Yong Guo Q. Jane Wang Yansong Wang Qingmin Yang Kumar Vaidyanathan 《International journal for numerical methods in engineering》2004,60(10):1759-1790
A finite element model is presented for mixed lubrication of journal‐bearing systems operating in adverse conditions. The asperity effects on contact and lubrication at large eccentricity ratios are modelled. The elastic deformation due to both hydrodynamic and contact pressure, and the cavitation of the lubricant film are considered in the model system. Two verification problems with both theoretical and experimental comparisons are given to show the effectiveness of this model. Finally, a new example is presented which discusses the influence of waviness depth, secondary roughness, external force and shaft speed on the mixed lubrication. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
Lloyd BA Szczerba D Rudin M Székely G 《Philosophical transactions. Series A, Mathematical, physical, and engineering sciences》2008,366(1879):3301-3318
The biology of cancer is a complex interplay of many underlying processes, taking place at different scales both in space and time. A variety of theoretical models have been developed, which enable one to study certain components of the cancerous growth process. However, most previous approaches only focus on specific aspects of tumour development, largely ignoring the influence of the evolving tumour environment. In this paper, we present an integrative framework to simulate tumour growth, including those model components that are considered to be of major importance. We start by addressing issues at the tissue level, where the phenomena are modelled as continuum partial differential equations. We extend this model with relevant components at the cellular or even sub-cellular level in a vertical fashion. We present an implementation of this framework, covering the major processes and treat the mechanical deformation due to growth, the biochemical response to hypoxia, blood flow, oxygenation and the explicit development of a vascular system in a coupled way. The results demonstrate the feasibility of the approach and its applicability to in silico studies of the influence of different treatment strategies (like the usage of novel anti-cancer drugs) for more effective therapy design. 相似文献
10.
《Engineering Analysis with Boundary Elements》2003,27(5):439-454
A wavelet BEM is applied to the evaluation of the effective elastic moduli of unidirectional composites, based on the homogenization theory. This attempt is devoted to the reduction of computational cost for the BE-based homogenization analysis. Truncation for matrix compression is carried out by the Beylkin-type algorithm. A thresholding value for the truncation is set such that the discretization error of BE solution is comparable to its truncation error. Besides, rearrangement of the BE equations is proposed to attain rapid convergence of iterative solutions. Through investigation of asymptotical convergence of the effective moduli, it is found that the BE-based homogenization analysis ensures the same rate of convergence for effective moduli as for characteristic functions. By applying the wavelet BEM to heterogeneous media which have microstructures with many voids, the effective moduli with agreement of 2–4 digits can be evaluated using 20–50% memory requirements of conventional BE approaches. 相似文献
11.
Qingbing Dong 《先进材料力学与结构力学》2017,24(15):1300-1308
A semi-analytic solution is developed for heterogeneous elasto-plastic materials with inhomogeneous inclusions under elastohydrodynamic lubrication in point contact or line contact. The inhomogeneous inclusions within a material are homogenized as homogeneous inclusions with properly determined eigenstrains based on the equivalent inclusion method, and the surface displacements induced by these eigenstrains are then introduced into the gap between the contact bodies to update surface geometry. The accumulative plastic deformation is iteratively obtained by a procedure involving a plasticity loop and an incremental loading process. The model takes into account the interactions among the contact bodies, the embedded inclusions, and the plastic zones, thus leading to a solution of the surface pressure distributions, film thickness profiles, plastic zones, and subsurface stress fields. This solution is of great importance for the analysis of elasto-plasto damage of heterogeneous materials subject to lubricated contact. 相似文献
12.
Marcin Wierszycki Krzysztof Szajek Tomasz Łodygowski Michał Nowak 《Computational Mechanics》2014,54(2):287-298
In this paper the numerical implementation of two-scale modelling of bone microstructure is presented. The study is a part of long-term project on bone remodelling which drives bone microstructure change based directly on trabeculae surface energy. The proposed approach is based on a first-order computational homogenization technique. The coincidence of macro- and micro-model kinematics is done with the use of uniform displacement and traction boundary conditions. The computational homogenization procedure is driven by a self-prepared manager which is coded in Python. The computation on real bone structure (a piece of female Wistar rat bone) is performed as well. 相似文献
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依据齿轮啮合动态激励基本原理和弹性流体动力润滑理论,建立同时追求齿轮啮合时变刚度激励最小、齿间最小油膜厚度最大(倒数最小)及齿轮传动总体积最小的约束多目标优化设计数学模型.对现有的用于两目标优化设计的粒子群优化方法加以改进,给出了约束3目标优化设计方法.利用Matlab编制优化程序,并对范例进行分析计算.优化过程及结果表明,采用较多的齿数,在小于1的范围内采用较大的正变位系数,适度采用较大的压力角可以增大轮齿啮合综合刚度谱图中基频谐波的幅值,有效地提高齿轮传动系统抵抗内部激励振动的能力及性价比. 相似文献
14.
In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method. 相似文献
15.
In this article, we prove theorems establishing the existence of solutions to a highly nonlinear variational inequality arising in the study of the flow of an incompressible Newtonian lubricant between elastically-deforming bearings. The problem is formally equivalent to Reynolds' equation in elastohydrodynamic lubrication theory. The key to the analyses of this class of problems is that they are characterized by pseudomonotone operators, which means that established results on pseudomonotone variational inequalities are applicable. 相似文献
16.
Erik Svenning Martin Fagerström Fredrik Larsson 《International journal for numerical methods in engineering》2016,108(1):76-90
The effective response of microstructures undergoing crack propagation is studied by homogenizing the response of statistical volume elements (SVEs). Because conventional boundary conditions (Dirichlet, Neumann and strong periodic) all are inaccurate when cracks intersect the SVE boundary, we herein use first order homogenization to compare the performance of these boundary conditions during the initial stage of crack propagation in the microstructure, prior to macroscopic localization. Using weakly periodic boundary conditions that lead to a mixed formulation with displacements and boundary tractions as unknowns, we can adapt the traction approximation to the problem at hand to obtain better convergence with increasing SVE size. In particular, we show that a piecewise constant traction approximation, which has previously been shown to be efficient for stationary cracks, is more efficient than the conventional boundary conditions in terms of convergence also when crack propagation occurs on the microscale. The performance of the method is demonstrated by examples involving grain boundary crack propagation modelled by conventional cohesive interface elements as well as crack propagation modelled by means of the extended finite element method in combination with the concept of material forces. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd. 相似文献
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Paolo Bocchini Dan M. Frangopol 《Reliability Engineering & System Safety》2011,96(2):332-349
This paper presents a probabilistic computational framework for the Pareto optimization of the preventive maintenance applications to bridges of a highway transportation network. The bridge characteristics are represented by their uncertain reliability index profiles. The in/out of service states of the bridges are simulated taking into account their correlation structure. Multi-objective Genetic Algorithms have been chosen as numerical tool for the solution of the optimization problem. The design variables of the optimization are the preventive maintenance schedules of all the bridges of the network. The two conflicting objectives are the minimization of the total present maintenance cost and the maximization of the network performance indicator. The final result is the Pareto front of optimal solutions among which the managers should chose, depending on engineering and economical factors. A numerical example illustrates the application of the proposed approach. 相似文献
19.
In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the \(C^*\)-integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantity \(\hat{C}_k\) needs to be determined from the Finite Element analysis in terms of a dimensionless quantity \(\phi _0\), which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack growth response in the limits of small and large \(\phi _0\), for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments. 相似文献
20.
Andreas Almqvist Dag Lukkassen Peter Wall 《International Journal of Engineering Science》2007,45(1):139-154
This work introduces a new concept of homogenization that enables efficient analysis of the effects of surface roughness representations obtained by measurements in applications modeled by the Reynolds equation. Examples of such applications are trust- and journal-bearings. The numerical analysis of these types of applications requires an extremely dense computational mesh in order to resolve the surface roughness, suggesting some type of averaging. One such method is homogenization, which has been applied to Reynolds type equations with success recently. This approach is similar to the technique proposed by Patir and Cheng, who introduced flow factors determining the hydrodynamic action due to surface roughness. The difference is, however, that the present technique has a rigorous mathematical support. Moreover, the recipe to compute the averaged coefficients is simple without any ambiguities. Using either the technique proposed by Patir and Cheng or homogenization, the coefficients determining the averaged Reynolds equation are obtained by solving differential equations on a local scale. Unfortunately, this is detrimental when investigating the effects induced by real, measured, surface roughness, even though these local problems may be solved in parallel.The present work presents a solution by applying the technique based on bounds. This technique transforms the stationary Reynolds equation into two computationally feasible forms, one for the upper bound and one for the lower bound, where the flow factors are obtained by straightforward integration. Together with the preciseness of these bounds, the bounds approach becomes an eminent tool suitable for investigating the effect of real, measured, surface roughness on hydrodynamic performance. 相似文献