A 9-node mixed shell element based on the Hu-Washizu principle

This paper proposes a new 9-node degenerated shell element based on a nonlinear mixed formulation. To avoid locking phenomena, we present a mixed formulation based on a three-field Hu-Washizu principle in which displacements, the Green strain tensors, and the second Piola-Kirchhoff stress tensors are independently assumed. In approximating strain and stress fields, covariant components of the strains and stresses measured in the element curvilinear coordinate system are interpolated by the common polynomial functions over an element. Parameter vectors of stress and strain interpolants are elementwise eliminated so that we may obtain an element stiffness matrix similar to that of the displacement model. This formulation is mathematically clear in the variational context, and can include geometrical and material nonlinearities without spoiling such clearness. Numerical results based on our approach are illustrated with satisfactory behavior of the element observed.