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Bulk-metal forming processes from computational modelling via sensitivity analysis to tool shape optimization

Antunez H. J.

Prace Instytutu Podstawowych Problemów Techniki PAN

2001

nr 1

3-207

Within the proceding framework, the present work is a collection of developments performed at the Institute of Fundamental Technological Research of the Polish Academy of Science. All of them are concerning one specific way of modelling metal forming processes; this is especially suited for hot forming condition, and has conceived for steady-state processes, although it can be applied in transient ones as well. The naturally suited application of this model is extrusion; however, it can be used also in free forging, cutting and rolling (including seamless tube rolling), for which results are shown as well. Stationary and transient processes are separately presented here; not only for the sake of clarity of the exposition and for historical reasons, but to show the analysis problem, sensitivity analysis and shape optimization as successive steps within a logical line of thinking. Essentially this process was followed in the computer simulation of metal forming, feeding into each step all the results obtained in the proceding ones. In this work, the steady state is presented first, starting by the flow approach. Following, the descretization by finite elemtens is given. Here the different features accounted for in the model are explained. One the analysis model is complete, the sensitivity is ready to be introduced. First, parametric sensitivity is discussed, what is incidentally useful to show the available methods for sensitivity analysis. Shape sensitivity is considered next, followed by the optimization algorithm which finds, according to given criteria and design restrictions, the optimum design. Afterwards transient processes are considered. A full transient formulation is concidered and used to obtain an incremental method that makes use of linear elements due to a proper time-step splitting. Attention is focused on the full explicit version. Further, sensitivity analysis within such model and discretization is shown. In addition, the pseudo-concentration method is briefly revisited and used in connection to Fourier series expansion of the problem of seamless tube rolling. Some additional -but significant- topics are discussed in the course of the main presentation. The simulation of almost perfect plasticity poses the problem of uniqueness (or its lack), and this is discussed in the context of cutting simulation. Pressure stabilization is necessary to apply a friction model based on a Coulomb-type law. In this context a bilinear interpolation is introduced, which takes advantages of a method for similar pressure stabilization used in fluid mechanics. Sensitivity analysis suggests that its results can have an additional application in evaluating the effect on the solution of numerical parameters needed in some models. This is the case of the upwind parameters in coupled thermo-mechanical problems and the time step in time integration of transient processes. The introduction of shape sensitivity analysis of fomring processes gives the occasion to consider the extension to large displacements of the two available methods. In the shape optimization part, the problem of shape parameterization requires special attention. Two different techniques of interpolating points in the discretized domain in terms of the design parameters are proposed.

Sensitivity analysis of transient metal forming with incompressible linear elements

Antunez H. J.

Computer Assisted Mechanics and Engineering Sciences

2000

Vol. 7, No. 4

449-460

On the basis of a recently developed method which allows the use of linear elements for metal forming simulation within the flow approach, sensitivity analysis is carried out. Aiming at large, industrial problems, attention is focused on the explicit version, which is considered more effective for such problems, although implicit time integration is possible as well. By time step splitting a stabilization sub-matrix is obtained, which allows the use of equal interpolation for velocity and pressure. Specifically, linear triangles and tetrahedra have been used, which are easily generated by automatic meshers. Sensitivity analysis is carried out by the Direct Differentiation Method, with which similar analyses have been performed by the author for the flow approach within a direct solution scheme.