The ALE-method with triangular elements: direct convection of integration point values

The arbitrary Lagrangian-Eulerian (ALE) finite element method is applied to the simulation of forming processes where material is highly deformed. Here, the split formulation is used: a Lagrangian step is done with an implicit finite element formulation, followed by an explicit (purely convective) Eulerian step. The purpose of this study is to investigate the Eulerian step for quadratic triangular elements. To solve the convection equation for integration point values, a new method inspired by Van Leer is constructed. The new method is based on direct convection of integration point values without intervention of nodal point values.\ud The Molenkamp test and a so-called block test were executed to check the performance and stability of the convection scheme. From these tests it is concluded that the new convection scheme shows accurate results. The scheme is extended to an ALE-algorithm. An extrusion process was simulated to test the applicability of the scheme to engineering problems. It is concluded that direct convection of integration point values with the presented algorithm leads to accurate results and that it can be applied to ALE-simulation

Improvements in FE-analysis of real-life sheet metal forming

An overview will be presented of recent developments concerning the application\ud and development of computer codes for numerical simulation of sheet metal forming\ud processes. In this paper attention is paid to some strategies which are followed to improve the\ud accuracy and to reduce the computation time of a finite element simulation. Special attention\ud will be paid to the mathematical modeling of the material deformation and friction, and the\ud effect of these models on the results of simulations. An equivalent drawbead model is\ud developed which avoids a drastic increase of computation time without significant loss of\ud accuracy. The real geometry of the drawbead is replaced by a line on the tool surface. When\ud an element of the sheet metal passes this drawbead line an additional drawbead restraining\ud force, lift force and a plastic strain are added to that element. A commonly used yield\ud criterion for anisotropic plastic deformation is the Hill yield criterion. This description is not\ud always sufficient to accurately describe the material behavior. This is due to the\ud determination of material parameters by uni-axial tests only. A new yield criterion is\ud proposed, which directly uses the experimental results at multi-axial stress states. The yield\ud criterion is based on the pure shear point, the uni-axial point, the plane strain point and the\ud equi-biaxial point

The construction of confidence intervals for frequency analysis using resampling techniques: a supplementary note

International audienceIn a recent contribution, Hall et al. (2004) examined the use of the Bootstrap resampling technique as a means of constructing confidence limits for the quantiles of the (two-parameter) Gumbel and the (three-parameter) Weibull distributions. Particular emphasis was placed on the behaviour of sample sizes of the order of 30, which are typical of those encountered in hydrological frequency analysis. The resampled confidence limits obtained for the Gumbel distribution were found to be comparable with those based upon a well-known theoretical approximation. However, those for samples of size 30 from the Weibull distribution were shown to be more problematical, with the results dependent upon the skewnesses of the resampled distributional parameters. For a further and more quantitative assessment of the suitability of Bootstrap resampling for constructing confidence intervals, so-called coverage rates were evaluated for the Weibull distribution in a supplementary study. The results show a satisfactory performance when using the percentile method but do not really mitigate the conclusion of the original study that resampled confidence limits should be employed with caution when sample sizes are of the order of 30. Keywords: Bootstrap, Jack-knife, frequency analysis, maximum likelihood method, maximum product of spacings method, confidence intervals, coverage rate