Improved Formulation of One-Step Approach Suitable for Initially Non-Flat Configurations and Forward Simulation

For the traditional one-step formulations of using shell elements, the computations of the curvature variation and bending stiffness matrix were simplified by omitting the rotational DOFs (degrees of freedom) on the basis of initial flat blank and fully known final configuration. They were highly efficient but not suitable either for the forming processes with non-flat initial configurations or for one-step forward and multistep analyses. Thus, a one-step formulation based on the rotation-free BST (Basic Shell Triangle) element was presented. In this formulation, the penalty method was adopted to deal with contacts in the forming processes.