A NONLINEAR QUADRILATERAL SHELL ELEMENT WITH DRILLING DEGREES OF FREEDOM

A bending theory for thin shells undergoing finite deformations is presented, and its associated finite clement model is described. The kinematic assumptions are of Reissner-Mindlin type. The formulation is based on the introduction of a mixed functional with independent in-plane rotation field and skew-symmetric part of membrane forces. The resulting Euler-Lagrangian equations yield the equilibrium of stress resultants and the couple resultant with respect to the surface normal. Furthermore, the equality of the independent rotation field with the displacement dependent rotation field is enforced. Hence, the symmetry of the stress resultants is fulfilled in a weak sence. Naturally, the development of a quadrilateral finite element includes drilling degrees of freedom. The displacement field is approximated using an Allman-type interpolation.