A FULLY NONLINEAR AXISYMMETRICAL QUASI-KIRCHHOFF-TYPE SHELL ELEMENT FOR RUBBER-LIKE MATERIALS

An axisymmetrical shell element for large deformations is developed by using Ogden's non-linear elastic material law. This constitutive equation, however, demands the neglect of transverse shear deformations in order to yield a consistent theory. Therefore, the theory can be applied to thin shells only. Eventually a 'quasi-Kirchhoff-type theory' emerges. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non-linear bending behaviour. Furthermore, special attention is paid to the linearization procedure in order to obtain quadratic convergence behaviour within Newton's method. Finally, the finite element formulation for a conical two-node element is given. Several examples show the applicability and performance of the proposed formulation.