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普通的板壳有限元无法承受法线自转方向的力矩外载，使其应用受到了限制。为了解决该问题，以变形梯度的极分解为理论基础，构造非对称Ｂｉｏｔ应变张量，提出了带法线自转自由度的 ＤＤＯＦ（Ｄｒｉｌｌｉｎｇ ｄｅｑｒｅｅ ｏｆ ｆｒｅｅｄｏｍ）板壳有限变形理论并给出了基于 ＴＬ（Ｔｏｔａｌ Ｌａｇｒａｎｇｅ）算法的有限元列式。数值算例证明了这些理论和方法的正确性。
Ordinary shell and shell finite element can not withstand the normal direction of rotation of the torque load, so that its application has been limited. In order to solve this problem, based on the pole decomposition of the deformation gradient, the asymmetric Biot strain tensor was constructed and the finite deformation theory of DDOF (Drilling deqree of freedom) with normal rotation degree of freedom was proposed. Based on TL (Total Lagrange) finite element method. Numerical examples demonstrate the correctness of these theories and methods.