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In the traditional one-step formulations using shell elements, the computations of the curvature variation and bending stiffness matrix are simplified by omitting the rotational DOFs on the basis of initial flat blank and fully known final configuration. They are highly efficient but not suitable either for the forming processes with non-flat initial configurations, or for one-step forward and multi-step analyses. Thus a one-step formulation based on the rotation-free BST (Basic Shell Triangular) element is presented here. In this formulation, the following improvements are made: 1) the curvature variation can be calculated exactly and efficiently resorting to a patch of four elements without rotational DOFs, which makes the formulation suitable for non-flat initial configurations, one-step and multi-step forward or inverse analyses, 2) The penalty method, instead of traditional sliding constraint, is employed to treat contacts in the forming processes, which makes it possible to inspect some deformation defects such as wrinkling et al directly. To verify the improved formulation, a program has been developed, and the bending process of a rectangular tube is simulated, with particular attentions paid on cross-sectional distortion. The numerical results of the one-step simulation agree with those of incremental analysis and experimental values.