Abstract: Because the conventional plate and shell element is restricted to being moment load free in the 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 Biot 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.

Key words: Deformation, Drilling degree of freedom, Nonlinear Finite element method, Plate and shell, TL method