Geodesic
A numerical method of optimizing the stretch forming process for the production of panels
Numerical methods and programming, Tome 20 (2019) no. 4, pp. 386-395.

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We analyze the stretch-forming technology using a press to manufacture the double-curvature shells. The automated shaping of parts requires the development of a control program and an electronic model of a punch. The quality of the part obtained depends on the accuracy of the calculated and manufactured tools that specify the anticipated shape of the panel and on the deformation path of the sheet. Under the condition of a given tooling, an optimal control problem is formulated to find the best trajectory of movement of the clamps in the equipment. Some criteria for deformation optimization processes are introduced to ensure a minimum damage and maximum residual deformations. The calculation of the criteria is performed with the aid of modeling and analyzing the panel nonlinear deformation with contact constraints by the finite element method. The problems of inelastic deformation are solved by the finite element method. A discrete optimal control problem is formulated and solved by the methods of dynamic programming. The algorithms are implemented using the MSC.Marc package and allow us to calculate the optimal parameters of the stretch-forming press in serial and parallel modes. The obtained numerical results show the efficiency of parallel implementations on a cluster of computers.
Keywords: elasticity, plasticity, stretch-forming, finite element method, damage, discrete optimal control problem, dynamic programming method.
Mots-clés : variational principles 
@article{VMP_2019_20_4_a3,
     author = {K. S. Bormotin and A. Vin},
     title = {A numerical method of optimizing the stretch forming process for the production of panels},
     journal = {Numerical methods and programming},
     pages = {386--395},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2019_20_4_a3/}
}
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K. S. Bormotin; A. Vin. A numerical method of optimizing the stretch forming process for the production of panels. Numerical methods and programming, Tome 20 (2019) no. 4, pp. 386-395. http://geodesic.mathdoc.fr/item/VMP_2019_20_4_a3/