STRESS RESULTANT GEOMETRICALLY NONLINEAR SHELL THEORY WITH DRILLING ROTATIONS .2. COMPUTATIONAL ASPECTS

In this work we discuss some details of the numerical implementation o f the geometrically nonlinear shell theory presented in Part I. Two po ssibilities to represent finite rotations, with an orthogonal matrix a nd with a rotation vector, are examined in detail, along with their mu tual 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 ge ometrically nonlinear method of incompatible modes is extended to the nonlinear shell theory under consideration, and used to provide a 4-no de shell element with enhanced performance. A rather extensive set of numerical examples in nonlinear elastostatics is solved in order to co rroborate the non-locking performance of the incompatible-mode-based s hell 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 structur es and shell structures with stiffeners.