On optimization of metal forming with adaptable characteristics

In the present paper we consider a problem of choosing the rational way to carry on the metal processing (the problem of stochastic optimization) and the problem of determing the unknown characteristics of parameters described with random variables.     

Reliability analysis of the metal forming process

In this paper, we propose a reliability–mechanical study combination for treating the metal forming process. This combination is based on the augmented Lagrangian method for solving the deterministic case and the response surface method. Our goal is the computation of the failure probability of the frictionless contact problem. Normally, contact problems in mechanics are particularly complex and have to be solved numerically. There are several numerical techniques available for computing the solution. However, some design parameters are uncertain and the deterministic solutions could be unacceptable. Thus, a mechanical contact study is an important subject for reliability analysis: the augmented Lagrangian method coupled with the first order reliability method, and we use the Monte Carlo method to obtain the founding results. The metal forming process is treated numerically to validate the new approach.     

Numerical investigation of microstructure evolution in metal forming processes

Grain size evolution and phase transformation during metal forming processes is investigated numerically by means of the Finite element method. Appropriate microstructure models are involved into the FEM code MSC.MARC. Material characteristics obtained by means of own experiments are used. Hot closed die forging and rod rolling are considered. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of optimal metal flow in incremental sheet forming

Sheet metal forming processes are manufacturing processes in which a piece of sheet metal is shaped to a specified geometry, e.g. a car door. A promising new forming process is incremental sheet metal forming, in which the deformation is imposed by a progressive, localised plastic deformation induced by a pin-like forming tool that moves under numerical control along a pre-defined trajectory. This process offers the possibility to control the metal flow by adjusting the trajectory of the forming tool. Mathematically, sheet metal forming processes can be considered as a mapping between the initial, undeformed sheet metal and the final, deformed state. In most applications the surface area of the sheet metal is enlarged during the deformation. In this case, an ideal mapping would produce a homogeneous stretching of the sheet metal such that the final sheet thickness is the same everywhere. In this work, we analyze the following question: for each point in the initial configuration, what must be its location on the final geometry such that the thickness is the same everywhere? We construct a special type of surface evolution that combines flow along the surface normal with appropriate tangential velocity corrections, and show that the flow yields a constant sheet thinning on a sheet metal. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design optimization and forming methods for toroidal composite shells

Based on the example of a toroidal membrane, a model for calculating the winding trajectory and the shape of a shell billet and its transformation into given surface elements, as well as for calculating the shape of the membrane under an internal pressure loading, is developed. The problem of choosing optimum design variables and manufacturing parameters of the membrane is also investigated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 147–164, March–April, 2006.     

Finite element simulation for dynamic large elastoplastic deformation in metal powder forming

In this paper, a transient dynamic analysis of the powder compaction process is simulated by a large displacement finite element method based on a total and updated Lagrangian formulation. A combination of the Mohr–Coulomb and elliptical yield cap model, which reflects the stress state and degree of densification, is applied to describe the constitutive model of powder materials. A Coulomb friction law and a plasticity theory of friction in the context of an interface element formulation are employed in the constitutive modelling of the frictional behaviour between the die and powder. Finally, the powder behaviour during the compaction of a plain bush, a rotational flanged and a shaped tip component are analysed numerically. It is shown that the updated Lagrangian formulation, using a combination of the Mohr–Coulomb and elliptical cap model, can be effective in simulating metal powder compaction.     

Mixed-integer models for topology optimization in sheet metal design

Topology optimization lies at the heart of many design tasks in mechanical engineering. For those sheet metal products that consist of a bundle of separate channels (such as conduits) we formulate the design task as a linear mixed-integer optimization problem. The design goal is to find a topology where each channel has a given cross section area, using a minimum amount of sheet met al. In addition to a light-weight design, stiffness should also be taken into account. The entire approach is demonstrated in the design of a conduit with five separate channels. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Development of an inverse isogeometric methodology and its application in sheet metal forming process

This paper proposes an inverse isogeometric analysis to estimate the blank and predict the strain distribution in sheet metal forming processes. In this study, the same NURBS basis functions are used for drawing a final part and analysis of the forming process. In other words, this approach requires only one modeling and analysis representation, in contrast to inverse FEM. This model deals with minimization of potential energy, deformation theory of plasticity, and infinitesimal deformation relations with considering a new non-uniform friction model. One advantage of the presented methodology is that the governing equations are solved in two-dimensional space without concerning about pre-estimation results. As a result, the convergence is guaranteed and the computation time decreases significantly which is important at the initial stages of design. Furthermore, by employing this model at the forming design stage, the effects of changing the final part geometry and material property can be simultaneously observed on the formability of the part. Moreover, the effects of isogeometric element size can be automatically studied on the solution accuracy. The capability of this method is demonstrated by presenting three examples including blank estimation of cylindrical cup, square box, and weld line movement in forming of tailor welded blanks. The results obtained by the presented model and those obtained by the forward FEM reveal reasonable accuracy with decreased computational costs.     

Combined unstructured and hanging-node-based remeshing with boundary control for metal forming simulations

During finite element simulation of metal forming process, the mesh which represents the workpiece undergoes extreme large deformation, which could result in highly distorted mesh and numerical failure in simulation. To overcome the problem and improve computation efficiency, advancing front quad meshing technique and non–conforming mesh refinement approach are combined to generate new mesh according to desired mesh size distribution. Application of the combined remeshing strategy to rolling simulation will be presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integer linear programming models for topology optimization in sheet metal design

The process of designing new industrial products is in many cases solely based on the intuition and experience of the responsible design engineer. The aid of computers is restricted to visualization and manual manipulation tools. We demonstrate that the design process for conduits, which are made out of sheet metal plates, can be supported by mathematical optimization models and solution techniques, leading to challenging optimization problems. The design goal is to find a topology that consists of several channels with a given cross section area using a minimum amount of sheet metal and, at the same time, maximizing its stiffness. We consider a mixed integer linear programming model to describe the topology of two dimensional slices of a three dimensional sheet metal product. We give different model formulations, based on cuts and on multicommodity flows. Numerical results for various test instances are presented.     

Application and evaluation of hyper- and hypoelastic-based plasticity models in the FE simulation of metal forming processes

Metal forming processes are usually accompanied by large plastic strains and rotations of the material elements which emphasizes the need for reliable finite strain elastoplasticity models in corresponding FE simulations. In this work, two specific finite strain hyper- and hypoelastic-based plasticity models with combined nonlinear isotropic and kinematic hardening are presented and compared in numerical FE simulations. Although both models led to remarkably different results in a shear-dominated single element deformation test, the structural simulation of a standard deep drawing process delivered nearly congruent results which suggests that both models are equally well-suited for modeling metals in common forming processes. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the stochastic optimization problems of plastic metal working processes under stochastic initial conditions

The article is devoted to mathematical modeling of problems of stochastic optimization of the plastic metal working. Classification and mathematical statements of such problems are proposed. Several calculation techniques of the single goal function are presented. The probability theory and the Fuzzy Numbers were applied for solution of the problems of stochastic optimization.     

Transformation technologies in forming composite structures

A design model of axisymmetric transformation of a helically wound shell preform into a given shape is considered. Types of design problems are determined, and examples of their solution are given. Examples of fabrication techniques for structural prototypes by using the transformation method are included.     

On forming the Romberg table

Romberg-type extrapolation is commonly used in many areas of numerical computation. An algorithm is presented for forming the Romberg table for general step-length sequence and general powers in the asymptotic expansion. It is then shown that parameters of the algorithm can be used to gain an a priori bound on propagation of rounding errors in the table.     

Optimal decision rule in forming an insurance portfolio

The paper is devoted to finding an optimal decision rule for accepting/rejecting potential insureds when the demand for the insurance provision is a stochastic variable. A criterion to be maximized is the mean-variance utility function of the insurer. It is shown that the optimal decision rule is a stopping rule with some finite protection level.     

Experimentation in optimization

The purpose of this paper is to focus on experimentation issues in optimization. In it, we examine the key factors that impact any computational experiment. Statistical methods of experimentation are reviewed and examples of their use are provided. Complicating factors that arise frequently are also discussed. At the heart of the paper are three diverse case studies which collectively illustrate a host of recurring themes. The paper should be of interest to practitioners as well as researchers.     

Robust multiobjective optimization & applications in portfolio optimization

Motivated by Markowitz portfolio optimization problems under uncertainty in the problem data, we consider general convex parametric multiobjective optimization problems under data uncertainty. For the first time, this uncertainty is treated by a robust multiobjective formulation in the gist of Ben-Tal and Nemirovski. For this novel formulation, we investigate its relationship to the original multiobjective formulation as well as to its scalarizations. Further, we provide a characterization of the location of the robust Pareto frontier with respect to the corresponding original Pareto frontier and show that standard techniques from multiobjective optimization can be employed to characterize this robust efficient frontier. We illustrate our results based on a standard mean–variance problem.     

The role of examples in forming and refuting generalizations

Acknowledging students’ difficulty in generalizing in general and expressing generality in particular, we assert that the choice of examples that learners are exposed to plays a crucial role in developing their ability to generalize. We share with the readers experiences in which examples supported generalization, and elucidate the strategies that worked for us in these circumstances, presuming that similar strategies could be helpful with other students in other settings. We further share several pitfalls and call for caution in avoiding them.