带法线自转自由度的板壳有限变形单元

FINITE DEFORMATION ELEMENT OF PLATE AND SHELL WITH DRILLING DOF

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。

Because the conventional plate and shell element is restricted to being moment load free in thd direction of drilling degree of freedom, an finite deformation theory for plate and shell with drilling degree of freedom (DDOF) is proposed. Firstly, based on the deformation gradient's polar decomposition Gd = RU, non-symmetric Blot strain tensor is introduced and the virtual work principle, which is suitable for the construction of plate and shell element with DDOF, is established. Then, the FE formulation based on the exact theory is deduced with TL method. Numerical examples show the validity of the theory.