In analysis of metal forming processes by the finite element method, there appear many numerical instabilities such as element locking, hourglass mode, and shear locking, which arise from incompressible condition and geometric constraint. These instabilities may have a bad effect upon accuracy and convergence of the solution.
The present work is concerned with the improvement of stability and efficiency in the two-dimensional finite element method. In order to investigate the behavior of elements, analyses for various type of elements such as triangular and quadrilateral element and elements of different orders to include linear, quadratic, and transition elements have been carried out. For the sake of comparison among different numerical integration schemes, some problems are subjected to analyses by employing different integration schemes such as full integration, reduced integration, selective reduced integration and directional reduced integration.
As metal forming examples, upsetting and backward extrusion are taken for comparison among the methods: various element types and numerical integration schemes. Comparison is made in terms of stability and efficiency in element behavior and computational efficiency and a new scheme of adaptive directional reduced integration is introduced for finite element analysis of bulk metal forming processes. Through the proposed scheme, it has been shown that the finite element computation is stabilized from the viewpoint of computational time, convergency, and numerical instability.
