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In the last years a great interest in optimization algorithms aimed to design forming processes was demonstrated by many researches. Proper design methodologies to reduce times and costs have to be developed mostly based on computer aided procedures. Response surface methods (RSM) proved their effectiveness in the recent years also for the application in sheet metal forming aiming to reduce the number of numerical simulations. Actually, the main drawback of such method is the number of direct problem to be solved in order to reach good function approximations. A very interesting aspect in RSM application regards the possibility to build response surfaces basing on moving least squares approximations (MLS) by utilizing a moving and zooming region of interest. In this paper, MLS is utilized to solve an optimization problem for a complex sheet metal forming process. The influence on the optimization results was analyzed basing on MLS peculiarities. In particular, the analysis was carried out studying the effect of weighting functions shape and of the points belonging to the design of experiments. [ABSTRACT FROM AUTHOR]

The simplified (one step) method also called “inverse approach”(IA) for the numerical analysis of the stamping process has been continuously developed by the authors since the end of the eighties (1, 2, 3, 4). In the present paper we recall the main finite element formulation aspects of a robust IA analysis code, called FAST_STAMP, for an efficient estimation of the large elastoplastic strains (in particular the thickness strains) encountered in deep drawing operations. Our results will be presented and compared with others, obtained either from experiments or from incremental codes such as ABAQUS or STAMPACK. The presentation includes “math based” optimization algorithms and strategies for process parameter design. The cost functions and constraints are mainly express to reduce or control the thickness changes, the localized necking, the wrinkling tendency, the springback effects after forming. The design variables are describing the shape of the blank and the tools, the restraining forces due to drawbeads, material properties such as anisotropy coefficient and hardening exponent. Results will be presented to show the actual capabilities of the coupled analysis and optimization strategy with application to the design of stamping parameters. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Treatment of contact between a sheet and tools is one of the most difficult problems to deal with in finite-element simulations of sheet forming processes. In order to obtain more accurate tool models without increasing the number of elements, this paper describes a new formulation for contact problems using interpolation proposed by Nagata for tool surfaces. A contact search algorithm between sheet nodes and the interpolated tool surfaces was developed and was introduced into the static-explicit elastoplastic finite-element method code STAMP3D. Simulations of a square cup deep drawing process with a very coarsely discretized punch model were carried out. The simulated results showed that the proposed algorithm gave the proper drawn shape, demonstrating the validity of the proposed algorithm. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Numerical simulation technology and optimization method have been applied in sheet metal forming process to improve design quality and shorten design cycle. While the existence of fluctuation in design variables or operation condition has great influence on the quality. In addition to that, iterative solution in numerical simulation and optimization usually take huge computational time or endure expensive experiment cost In order to eliminate effect of perturbations in design and improve design efficiency, a CAE-based six sigma robust design method is developed in this paper. In the six sigma procedure for sheet metal forming, statistical technology and dual response surface approximate model as well as algorithm of “Design for Six Sigma (DFSS)” are integrated together to perform reliability optimization and robust improvement. A deep drawing process of a rectangular cup is taken as an example to illustrate the method. The optimization solutions show that the proposed optimization procedure not only improves significantly the reliability and robustness of the forming quality, but also increases optimization efficiency with approximate model. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

A simplified (one step) method called “inverse approach” (IA) for the numerical analysis of the stamping process has been continuously developed by the authors since the end of the eighties. In the present paper we recall the main finite element formulation aspects, for an efficient estimation of the large elastoplastic strains encountered in deep drawing operations. The capabilities of the code Fast_Stamp include: fixed (imposed) initial blank, bending effects due to tool curvatures, blankholder restraining forces (including drawbeads). Considerations of bending and unbending during forming stages can improve the IA regarding stresses distribution. In this case satisfactory estimation of springback can result. Since 1996 we also developed “math based” optimization algorithms and strategies. The cost functions and constraints are mainly expressed to reduce or control the thickness changes, the localized necking, the wrinkling tendency, the springback after forming. The design variables are describing the shape of the blank, the additional (addendum) surfaces, the restraining forces due to drawbeads and the material properties such as anisotropy coefficient and hardening exponent. Optimization algorithms are mainly based on surface response techniques with moving least square approximation and SQP to find the optimum solution at each iteration. Selected results will be presented related to the design of additional surfaces. © 2005 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]