Stress resultant geometrically nonlinear shell theory with drilling rotations—Part II. Computational aspects Original Research Article

In this work we discuss some details of the numerical implementation of the geometrically nonlinear shell theory presented in Part I. Two possibilities to represent finite rotations, with an orthogonal matrix and with a rotation vector, are examined in detail, along with their mutual relationship in both spatial and material description. The issues pertinent to the consistent linearization procedure corresponding to these rotation parameterizations are also carefully considered. The geometrically nonlinear method of incompatible modes is extended to the nonlinear shell theory under consideration, and used to provide a 4-node shell element with enhanced performance. A rather extensive set of numerical examples in nonlinear elastostatics is solved in order to corroborate the non-locking performance of the incompatible-mode-based shell elements. The examples include not only analyses of simple shell structures undergoing very large displacements and rotations, but also cases of strong practical interest, such as non-smooth shell structures and shell structures with stiffeners.