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It’s crucial for process engineers to determine optimal value and combination of process parameters in the design of sheet metal forming. The multi-objective genetic algorithm (MOGA) based on Pareto approach and numerical simulation codes were integrated in this paper to fulfill the optimal formability in the sheet metal forming. Three objective functions of local formability on fracture, wrinkling and insufficient stretching were presented based on the strains state at the end of the forming process on the Forming Limit Diagram. By using Pareto-based MOGA, the optimal global formability which represents the trade-off between different local formability was decided. For the efficiency and accuracy of optimization procedure, both inverse and incremental finite element analysis were used to evaluate the value of objective functions. This method was applied to a complex engineering optimization problem: an engine hood outer panel, the optimal blank holder force and draw bead restraining forces were determined to satisfy the given objective functions for the forming of the auto body panels. The approach proposed in this paper has been shown to be a powerful tool than manual numerical simulation procedure. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed. [ABSTRACT FROM AUTHOR]

Coupling optimisation algorithms to Finite Element Methods (FEM) is a very promising way to achieve optimal metal forming processes. However, many optimisation algorithms exist and it is not clear which of these algorithms to use. This paper investigates the sensitivity of a Sequential Approximate Optimisation algorithm (SAO) proposed in [1–4] to an increasing number of design variables and compares it with two other algorithms: an Evolutionary Strategy (ES) and an Evolutionary version of the SAO (ESAO). In addition, it observes the influence of different Designs Of Experiments used with the SAO. It is concluded that the SAO is very capable and efficient and its combination with an ES is not beneficial. Moreover, the use of SAO with Fractional Factorial Design is the most efficient method, rather than Full Factorial Design as proposed in [1–4]. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

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. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The design of addendum surfaces in sheet forming process is very important for the product quality, but it is very time-consuming and needs tedious trial-error corrections. In this paper, we propose a methodology to automatically generate the addendum surfaces and then to optimize them using a forming modelling solver. The surfaces’ parameters are taken as design variables and modified in course of optimization. The finite element mesh is created on the initial addendum surfaces and mapped onto the modified surfaces without remeshing operation. The Feasible Sequential Quadratic Programming (FSQP) is adopted as our algorithm of optimization. Two objective functions are used: the first one is the thickness function to minimize the thickness variation on the workpiece ; the second one is the appearance function aiming to avoid the scratching defects on the external surfaces of panels. The FSQP is combined with our “Inverse Approach” or “One Step Approach” which is a very fast forming solver. This leads to a very efficient optimization procedure. The present methodology is applied to a square box. The addendum surfaces are characterised by four geometrical variables. The influence of optimization criteria is studied and discussed. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper describes an efficient method that integrates finite element analysis (FEA), mesh morphing and response surface based optimization in order to implement an automated and flexible software tool to optimize stamping tool and process design. For FEA, a robust and extremely fast inverse solver is chosen. For morphing, a state of the art mesh morpher that interactively generates shape variables for optimization studies is used. The optimization algorithm utilized in this study enables a global search for a multitude of parameters and is highly flexible with regards to the choice of objective functions. A quality function that minimizes formability defects resulting from stretching and compression is implemented. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper presents several approaches for preform shape optimization in 3D forging. The process simulation is carried out using the FORGE3® finite element software, and the optimization problem regards the shape of initial axisymmetrical preforms. Several objective functions are considered, like the forging energy, the forging force or a surface defect criterion. Both deterministic and stochastic optimization algorithms are tested for 3D applications. The deterministic approach uses the sensitivity analysis that provides the gradient of the objective function. It is obtained by the adjoint-state method and semi-analytical differentiation. The study of stochastic approaches aims at comparing genetic algorithms and evolution strategies. Numerical results show the feasibility of such approaches, i.e. the achieving of satisfactory solutions within a limited number of 3D simulations, less than fifty. For a more industrial problem, the forging of a gear, encouraging optimization results are obtained. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The paper is concerned with the comparison of optimization methods (OM) and control algorithms (CA) and their applications in tube hydroforming. Two sensitivity methods, the finite differentiation method and the direct differentiation method are also compared for the computation of the gradient of the objective functions in the case of optimization method. The results demonstrate that both methods could be applied for hydroforming optimization and control, but it is clearly demonstrated that control algorithms lead to better results in terms of accuracy and computational time than optimization methods. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]