A dynamic explicitrigidplastic finite element formulationand its application to sheet metal forming processes

• Published in: Engineering computations Vol. 12; no. 8; pp. 707 - 722
• Main Authors: Jung, D.W., Yoo, D.J., Yang, D.Y.
• Format: Journal Article
• Language: English
• Published: MCB UP Ltd 01-08-1995
• Subjects: Dynamics; Finite elements; Rigidplastic; Sheet metal forming
• ISSN: 0264-4401
• DOI: 10.1108/02644409510104695

In the present work a rigidplastic finite element formulation using a dynamic explicit time integration scheme is proposed for numerical analysis of sheet metal forming processes. The rigidplastic finite element method, based on membrane elements, has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. The explicit scheme, in general, is based on the elasticplastic modelling of material requiring large computation time. The resort to rigidplastic modelling would improve the computational efficiency, but this involves new points of consideration such as zero energy mode instability. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM abbreviated from Bending Energy Augmented Membrane elements, are employed. Rotational damping and spring about the drilling direction are introduced to prevent a zero energy mode. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and a direct trialanderror method. Computations are carried out for analysis of complicated sheet metal forming processes such as forming of an oilpan and a front fender. The numerical results of explicit analysis are compared with the implicit results, with good agreement, and it is shown that the explicit scheme requires much shorter computational times, especially when the problem becomes more complicated. It is thus shown that the proposed dynamic explicit rigidplastic finite element enables an effective computation for complicated sheet metal processes.