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1.
Neuber’s type methods are dedicated to obtain fast estimation of elastic–plastic state at stress concentrations from elastic results. To deal with complex loadings, empirical rules are necessary and do not always give satisfying results. In this context, we propose a new approach based on homogenization techniques. The plastic zone is viewed as an inclusion in an infinite elastic matrix which results in relationships between the elastic solution of the problem and estimated stress–strain state at the notch tip. Three versions of the notch correction method are successively introduced, a linear one which directly uses Eshelby’s solution to compute stresses and strains at the notch, a non-linear method that takes into account plastic accommodation through a ββ-rule correction and, finally, the extended method that is based on the transformation field analysis methods. All the notch correction methods need calibration of localization tensors. The corresponding procedures are proposed and analyzed. The methods are compared on different simulation cases of notched specimens and the predictive capabilities of the extended method in situations where plasticity is not confined at the notch are demonstrated. Finally, the case of a complex multiperforated specimen is addressed.  相似文献   

2.
Measuring the turbulent kinetic energy dissipation rate in an enclosed turbulence chamber that produces zero-mean flow is an experimental challenge. Traditional single-point dissipation rate measurement techniques are not applicable to flows with zero-mean velocity. Particle image velocimetry (PIV) affords calculation of the spatial derivative as well as the use of multi-point statistics to determine the dissipation rate. However, there is no consensus in the literature as to the best method to obtain dissipation rates from PIV measurements in such flows. We apply PIV in an enclosed zero-mean turbulent flow chamber and investigate five methods for dissipation rate estimation. We examine the influence of the PIV interrogation cell size on the performance of different dissipation rate estimation methods and evaluate correction factors that account for errors related to measurement uncertainty, finite spatial resolution, and low Reynolds number effects. We find the Re λ corrected, second-order, longitudinal velocity structure function method to be the most robust method to estimate the dissipation rate in our zero-mean, gaseous flow system.  相似文献   

3.
Robust computational procedures for the solution of non‐hydrostatic, free surface, irrotational and inviscid free‐surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable prediction of free‐surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow equations. We present new detailed fundamental analysis using finite‐amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high‐order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow models. Our study is particularly relevant for fast and efficient simulation of non‐breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization parameters for different PDC strategies, we study systematically limits of accuracy, convergence rate, algorithmic and numerical efficiency and scalability of the most efficient known PDC methods. These strategies are of interest, because they enable generalization of geometric multigrid methods to high‐order accurate discretizations and enable significant improvement in numerical efficiency while incuring minimal storage requirements. We demonstrate robustness using such PDC methods for practical ranges of interest for coastal and maritime engineering, that is, from shallow to deep water, and report details of numerical experiments that can be used for benchmarking purposes. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

4.
The accuracy of turbulent kinetic energy (TKE) dissipation rate measured by PIV is studied. The critical issue for PIV-based dissipation measurements is the strong dependency on the spatial resolution, Δx, as reported by Saarenrinne and Piirto (Exp Fluids Suppl:S300–S307, 2000). When the PIV spacing is larger than the Kolmogorov scale, η, the dissipation is underestimated because the small scale fluctuations are filtered. For the case of Δx smaller than the Kolmogorov scale, the error rapidly increases due to noise. We introduce a correction method to eliminate the dominant error for the small Δx case. The correction method is validated by using a novel PIV benchmark, random Oseen vortices synthetic image test (ROST), in which quasi-turbulence is generated by randomly superposing multiple Oseen vortices. The error of the measured dissipation can be more than 1,000% of the analytical dissipation for the small Δx case, while the dissipation rate is underestimated for the large Δx case. Though the correction method does not correct the underestimate due to the low resolution, the dissipation was accurately obtained within a few percent of the true value by using the correction method for the optimal resolution of η/10 < Δx < η/2.  相似文献   

5.
We present an approach to the study of the qualitative theory of infinite dimensional dynamical systems. In finite dimensions, most of the success has been with the discussion of dynamics on sets which are invariant and compact. In the infinite dimensional case, the appropriate setting is to consider the dynamics on the maximal compact invariant set. In dissipative systems, this corresponds to the compact global attractor. Most of the time is devoted to necessary and sufficient conditons for the existence of the compact global attractor. Several important applications are given as well as important results on the qualitative properties of the flow on the attractor.  相似文献   

6.
We study Boltzmann's collision operator for long-range interactions, i.e., without Grad's angular cut-off assumption. We establish a functional inequality showing that the entropy dissipation controls smoothness of the distribution function, in a precise sense. Our estimate is optimal, and gives a unified treatment of both the linear and the nonlinear cases. We also give simple and self-contained proofs of several useful results that were scattered in previous works. As an application, we obtain several helpful estimates for the Cauchy problem, and for the Landau approximation in plasma physics. Accepted: November 23, 1999  相似文献   

7.
An approach is proposed to determine the dissipation function in viscoelasticity theory. The first and second laws of thermodynamics and naive and integrated viscoelastic models are considered by the example of linear viscoelasticity __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 87–93, September 2005.  相似文献   

8.
Scalar dissipation is of great importance in the theory and modelling of combustion and other reacting turbulent flows. Measurements of scalar dissipation are found to lack the quality assurance of checks available from the conservation equations. Conditional averages of the scalar dissipation, so important in turbulent reacting flow theory and modelling, have qualitative and quantitative dependences that are very dependent on the details of the flow and mixing conditions. Accordingly, effort needs to focus on viable means of modelling it. Fluctuations of the scalar dissipation about the conditional mean are also important. Research results in this area need to be made more accessible to the combustion scientist. Heat release effects, so important in turbulent premixed combustion, are found to be much less important in non-premixed combustion.  相似文献   

9.
Magyari  E.  Keller  B. 《Transport in Porous Media》2003,53(1):105-115
The quasi-parallel regime of a Darcy–Boussinesq boundary-layer flow over a permeable vertical flat plate adjacent to a fluid saturated porous medium is considered. Quasi-parallel means here a plane flow with a constant transversal velocity v=–v 0 directed perpendicularly towards the vertical surface, where a lateral suction with the same velocity –v 0 is applied. The plate is held at a constant temperature T w which coincides with the ambient temperature T of the fluid. The heat released by viscous dissipation induces a density gradient in the fluid. Thus, although T w=T , a thermal convection occurs. The steady regime of this self-sustaining buoyant flow has been examined in detail. Wall jet-like profiles with a continuous but finite spectrum of the momentum flow have been found. These self-sustaining buoyant jets show a universal behavior, that is, there exist certain length, velocity and temperature scales such that the flow characteristics become independent of the (constant) material properties of the fluid and the porous medium as well.  相似文献   

10.
A nonlinear dynamical perspective addresses an area of behavior that tends to be ignored: trial-to-trial variability under seemingly identical conditions. Data exhibiting sequence effects are excellent candidates for a nonlinear dynamical analysis, because of their dependence on previous trial events. When applying nonlinear dynamical tools to behavioral data, the assumptions underlying the tools may require changes in experimental methodology. In this paper, the assumptions of trial timing and their potential impact on nonlinear dynamical analysis are explored. This is done with the intent of initiating a discussion on the appropriate control of trial timing. To examine these issues, each participant's response times on simple two-choice tasks were treated as a time series and submitted along with two comparisons to two nonlinear dynamical measures. Two experimental variables, stimulus rate and stimulus-response mapping, were manipulated in order to examine the issue of controlling trial timing via stimulus rate. Significant differences between the observed and comparison time series were found for estimated dimensionalities(m). Differences in dimensionality(m) estimates were also found between the experimental variables. Of the two methods for controlling stimulus rate, response-stimulus-interval and inter-stimulus-interval, the latter is recommended when applying nonlinear dynamical measures.  相似文献   

11.
Pressure correction concept is widely used to solve incompressible Navier–Stokes problems numerically. Based on Krylov subspace methods, we introduce several new pressure correction algorithms. Compared with the traditional pressure correction methods, they do not need to solve the pressure Poisson equation, which appears to reduce the computational cost. The preconditioning technique links the pressure correction methods based on Krylov iterations and with the pressure Poisson equation. In order to investigate the convergence performance of the new methods, we carried out various numerical experiments. Moreover we also discuss some ways on computational cost. Finally, these pressure correction methods are applied to solve the three‐dimensional lid‐driven cavity flows. © Crown Copyright 2004. Reproduced with permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd.  相似文献   

12.
13.
A system of coupled symmetric solids (Lagrange gyroscopes) moving under the simultaneous action of dissipative and nonconservative positional forces is analyzed for stability. The equations of perturbed motion are transformed so that nonconservative terms are eliminated and the Thomson-Tait-Chetaev theorems can be applied.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 127–135, November 2004.This revised version was published online in April 2005 with a corrected cover date.  相似文献   

14.
We study families of convex Sobolev inequalities, which arise as entropy–dissipation relations for certain linear Fokker–Planck equations. Extending the ideas recently developed by the first two authors, a refinement of the Bakry–émery method is established, which allows us to prove non-trivial inequalities even in situations where the classical Bakry–émery criterion fails. The main application of our theory concerns the linearized fast diffusion equation in dimensions d ≧ 1, which admits a Poincaré, but no logarithmic Sobolev inequality. We calculate bounds on the constants in the interpolating convex Sobolev inequalities, and prove that these bounds are sharp on a specified range. In dimension d = 1, our estimates improve the corresponding results that can be obtained by the measure-theoretic techniques of Barthe and Roberto. As a by-product, we give a short and elementary alternative proof of the sharp spectral gap inequality first obtained by Denzler and McCann. In further applications of our method, we prove convex Sobolev inequalities for a mean field model for the redistribution of wealth in a simple market economy, and the Lasota model for blood cell production.  相似文献   

15.
16.
Quantitative Impact Testing of Energy Dissipation at Surfaces   总被引:1,自引:0,他引:1  
Impact testing with nanoscale spatial, force, and temporal resolution has been developed to address quantitatively the response of surfaces to impingement of local contact at elevated velocities. Here, an impact is generated by imparting energy to a pendulum carrying an indenter, which then swings towards a specimen surface. The pendulum displacement as a function of time x(t) is recorded, from which one can extract the maximum material penetration x max , residual deformation x r , and indentation durations t in and t out. In an inverse application one can use the x(t) response to extract material constants characterizing the impact deformation and extent of energy absorption, including material specific resistance coefficient Cin, coefficient of restitution e, and dynamic hardness H imp . This approach also enables direct access to the ratio H/E, or resilience of the deformed material volume, at impact velocities of interest. The impact response of aluminum was studied for different contact velocities, and the mechanical response was found to correlate well with our one-dimensional contact model. Further experiments on annealed and work hardened gold showed that dynamic hardness H imp scales with contact velocity and highlighted the importance of rate-dependent energy absorption mechanisms that can be captured by the proposed experimental approach.
K. J. Van Vliet (SEM member)Email:
  相似文献   

17.
18.
PIV error correction   总被引:15,自引:9,他引:6  
 A non-post-interrogation method of reducing subpixel errors and eliminating spurious vectors from particle image velocimetry (PIV) results is presented. Unlike methods that rely on the accuracy or similarity of neighboring vectors, errors are eliminated before correlation information is discarded using available spatial and/or temporal data. Anomalies are removed from the data set through direct element-by-element comparison of the correlation tables calculated from adjacent regions. The result is a processing technique that yields a symmetric correlation profile representing the velocity at the boundary of the combined regions. This correlation based correction (CBC) technique greatly improves subpixel accuracy, and is highly robust to out-of-boundary particle motion, particle overlap, unmatched particle correlations, and electronic and optical imaging noise. Received: 22 June 1999/Accepted: 21 September 1999  相似文献   

19.
Azad and Kassab (1989) presented a new technique for estimating dissipation in turbulent flows and they referred to the method as the zero-wire-length technique. The validity of the approach has been here checked experimentally for the flow in the far wake of a circular cylinder for which Browne et al. (1987) had obtained reasonable estimates of the dissipation. It has been found that the zero-wire-length technique provides no more than an estimate of the isotropic dissipation: the actual dissipation values cannot be estimated by this technique.  相似文献   

20.
This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated; the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered; one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined; one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows, pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

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