The study is concerned with two-dimensional elastic-plastic finite element analysis of stretch forming by using the selective membrane/shell elements. Most of sheet metal working processes involve three-dimensional characteristics in geometry and deformation. The full three-dimensional analysis requires, however, tremendous computational time and thus for the handy analysis of the sheet metal forming process two-dimensional sectional analysis is introduced. That is, the three-dimensional deformation is approximated by assembling two-dimensional sectional analyses for the processes in which plane-strain condition is dominant, such as in the panel forming process.
Among various methods of analysis for sheet metal forming, the membrane analysis and the shell analysis are most often used. The membrane analysis is frequently used due to the short computational time. However, in the membrane analysis the bending effects can not be considered at all, which are important in stretching and deep drawing processes for precise determination of strain distributions. On the other hand, the shell analysis allows the consideration of bending effects, but involves too much computational time. As a practical compromise between two kinds of analyses, selective membrane/shell analysis is proposed which combines the shell elements for the local region where the bending effect should be considered and the membrane elements for the rest of the computational region where the bending effect can be safely neglected. In the proposed method of analysis, a criterion is employed in determining the elements for the shell analysis with other regions remaining for the membrane analysis.
Two-dimensional stretch forming is analyzed by the conventional membrane analysis, by the shell analysis employing the degenerated shell elements and by the proposed selective membrane/shell analysis. The selective membrane/shell elements analysis is forward to be in good agreement with the shell analysis with less than half of the computational time consumed by the full shell analysis. It is thus shown that the proposed selective membrane/shell elements analysis can be effectively applied to the two-dimensional sectional analyses of sheet metal forming processes.
