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A New Nonlinear Shell Element Taking the Normal Stress in Thickness Direction into Account for Simulation of Sheet Metal Forming

A New Nonlinear Shell Element Taking the Normal Stress in Th...

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The Sixth World Congress on Computational Mechanics in Conjunction with the Second Asian-Pacific Congress on Computational Mechanics

作者： koichi Ito koichi kazama Y.Nagai Graduate School of Information Science Tohoku University 04 Aramaki-Aoba Aoba-ku Sendai 980-8589 Japan Press Kogyo Co. Ltd Engineering Department 2003-1 Endo Fujisawa Kanagawa Japan Press Kogyo Co. Ltd Engineering Department 2003-1 Endo Fujisawa Kanagawa Japan

In simulation of sheet metal forming, the prediction of springback, which is a major defect, is not accurate. One reason for this is that the distributions of internal stresses are not predicted accurately. The conventional degenerated shell elements based on Mindlin-Reissner's theory of plates are usually used to simulate sheet metal forming process. The degenerated sh ell element uses the assumption that the thickness of the element remains constant and the normal stress in thickness direction is zero. These lead to problems in simulation of sheet metal forming, especially in prediction of springback. In this paper, we present a new nonlinear shell element that takes the normal stress in thickness direction into account which allows for large deformation. Two pseudo nodes, which have only one degree of freedom, are introduced on the top surface and bottom surface respectively. As a result, the normal strain in thickness direction can be calculated and the normal stress in thickness direction can be calculated using constitutive relation directly. It's possible to treat the boundary condition that pressure acts on top surfaces and bottom surface is simultaneously constrained. The element is tested in several numerical examples. The simulation results show that stress prediction is improved. The normal stress in thickness direction exhibit agreement with that calculated by surface loads and bending moment decreases as normal stress in thickness direction increases, which indicates that the element can simulate the effect of bottoming, i.e. sheet metal is stamped with a great vertical load after the punch reaches dead point in the process of V-type bending to reduce springback.

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