A formulation of the non linear discrete Kirchhoff quadrilateral shell element with finite rotations and enhanced strains - Dammak, Fakhreddine; Abid, Said; Gakwaya, Augustin; Dhatt, Gouri (European Journal of Computational Mechanics, 2005)
This paper presents a new formulation of the non-linear discrete Kirchhoff quadrilateral shell element applicable for the analysis of geometrically nonlinear structures undergoing finite rotations. The shell director is directly interpolated and the exact linearization of the discreet form of the equilibrium equations is derived in closed form. The consistent tangent stiffness matrix is symmetric and is given explicitly in this paper. Two or three rotational variables are used at each node. To improve the in-plane deformation enhanced incompatible modes are introduced. The formulation is then illustrated by a comprehensive set of numerical experiments selected from the literature.