Abstract: Most of one-step formulations using shell elements leave out the changes of curvatures in initial blank, wipe off rotation DOFs and simplify the computations of bending stiffness matrix and curvatures in final configurations in virtue of initial flat blank. By this way high efficiency is kept but the applications of one-step fast simulation are limited at the same time. Therefore the rotation-free BST (Basic shell triangular) element is introduced to compute the changes of curvatures by a patch of four adjacent elements conveniently without any simplification. On the base of the BST shell element, a new one-step formulation is deduced, in which the logarithmic strain is employed to describe finite strain plasticity, Hill’s normal anisotropic yield function is adopted and the principle of extreme work is utilized. The applications of one-step approach are therewith broadened to the general shell forming process with non-flat blank. A numerical example of the pure bending of rectangular tube is inspected and the simulation results of the new one-step method are compared with those of incremental analysis and experiment, by which its correctness is verified.

Key words: BST element, Non-flat blank, One-step method