Modelling, screening, and solving of optimisation problems: Application to industrial metal forming processes

Coupling Finite Element (FEM) simulations to mathematical optimisation techniques provides a high potential to improve industrial metal forming processes. In order to optimise these processes, all kind of optimisation problems need to be mathematically modelled and subsequently solved using an appropriate optimisation algorithm. Although the modelling part greatly determines the final outcome of optimisation, the main focus in most publications until now was on the solving part of mathematical optimisation, i.e. algorithm development. Modelling is generally performed in an arbitrary way. In this paper, we propose an optimisation strategy for metal forming processes using FEM. It consists of three stages: a structured methodology for modelling optimisation problems, screening for design variable reduction, and a generally applicable optimisation algorithm. The strategy is applied to solve manufacturing problems for an industrial deep drawing process

On the use of local max-ent shape functions for the simulation of forming processes

In this work we review the opportunities given by the use of local maximum-\ud entropy approximants (LME) for the simulation of forming processes. This approximation can\ud be considered as a meshless approximation scheme, and thus presents some appealing features\ud for the numerical simulation of forming processes in a Galerkin framework.\ud Especially the behavior of these shape functions at the boundary is interesting. At nodes\ud on the boundary, the functions possess a weak Kronecker-delta property, hence simplifying the\ud prescription of boundary conditions. Shape functions at the boundary do not overlap internal\ud nodes, nor do internal shape functions overlap nodes at the boundary. Boundary integrals can be\ud computed easily and efficiently compared to for instance moving least-squares approximations.\ud Furthermore, LME shapes also present a controllable degree of smoothness.\ud To test the performance of the LME shapes, an elastic and a elasto-plastic problem was\ud analyzed. The results were compared with a meshless method based on a moving least-squares\ud approximation

The influence of curvature on FLC’s of mild steel, (A)HSS and aluminium

In literature the influence of curvature on formability has been reported. This\ud paper shows results for four materials when an FLC is measured with increasing curvature. It shows the FLC increases for sharper curvature most notably with 20 [mm] tool diameter. The increase is negligible on the left hand side, moderate on the right hand side and large on the plane strain axis. It is thought that contact pressure plays a role here and preliminary simulations indicate that this is quite possible

Modelling of yield point phenomenon in bake-hardening grade steel

In this study the yield point phenomenon in Bake-Hardening grade steel is predicted using a physically based thermo-mechanical model. A modified Taylor equation is proposed with a physically based dislocation density evolution approach. The softening that follows the higher yield point is incorporated with a Voce type decaying exponential function. The strain rate dependency of the plastic hardening is also incorporated in the model. The yield point in the decay function is also strain rate dependent but does not follow the same dependency of plastic hardening. This was solved by making the decay function strain rate dependent by adding a modified strain rate stress term to the exponential function. This parameter is calculated based on tensile experiments. Due to the softening behavior of the material, the numerical model is mesh size sensitive. Hence, a lower order strain gradient enhanced approach is implemented. The gradient is in a form of an additional hardening term assigned in the locally strained bands based on the plastic strain gradient. Hill48 yield criterion is used to assimilate the anisotropy in the steel grade. The numerical results show good correspondence with experimental tensile tests. The regularization significantly reduced the mesh size dependency of the numerical results.</p

A comparative study on the performance of meshless approximations and their integration

The goal of this research is to study the performance of meshless approximations and their integration. Two diffuse shape functions, namely the moving least-squares and local maximum-entropy function, and a linear triangular interpolation are compared using Gaussian integration and the stabilized conforming nodal integration scheme. The shape functions and integration schemes are tested on two elastic problems, an elasto-plastic problem and the inf-sup test. The elastic computation shows a somewhat lower accuracy for the linear triangular interpolation than for the two diffuse functions with the same number of nodes. However, the computational effort for this interpolation is considerably lower. The accuracy of the calculations in elasto-plasticity depends to great extend on the used integration scheme. All shape functions, and even the linear triangular interpolation, perform very well with the nodal integration scheme and locking-free behavior is shown in the inf-sup test

The construction of confidence intervals for frequency analysis using resampling techniques

International audienceResampling techniques such as the Bootstrap and the Jack-knife are generic methods for the estimation of uncertainties in statistics. When applied in frequency analysis, resampling techniques can provide estimates of the uncertainties in both distribution parameters and quantile estimates in circumstances in which confidence limits cannot be obtained theoretically. Test experiments using two different parameter estimation methods on two types of distributions with different initial sample sizes and numbers of resamples has confirmed the utility of such methods. However, care is necessary in evaluating the skewness of the resampled quantiles, especially with small initial sample sizes. Keywords: Bootstrap, Jack-knife, frequency analysis, maximum likelihood method, maximum product of spacings metho