中文摘要：

大多数使用壳单元的一步法公式都会借助初始构型为平板这一条件略去初始构型的曲率计算，并消去转动自由度，简化终态构型曲率和弯曲刚度矩阵的计算，以保持计算效率，但这也限制了一步快速模拟的应用范围。为此，引入无转动自由度的BST（Basic shell triangular）壳单元，通过单元片内四个相邻单元，方便地计算出初始和终态构型的曲率而无需简化。在此单元基础上，使用对数应变描述大变形，采用考虑厚向异性的全量弹塑性本构关系，通过极值功原理，推导出新的可用于非平面初始构型的一步法公式，将一步法应用范围拓展到一般的壳体成形。给出一个矩形管纯弯曲的算例，特别考察其断面畸变问题，并将新一步法模拟的结果与增量分析和试验的结果做比较，验证了其正确性。

英文摘要：

Most of one-step formulations using shell elements leave out the changes of curvatures in initial blank, wipe off rotation DGFs 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-fi＇ee 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.