Generalized Energy–Momentum Method for non-linear adaptive shell dynamics

Abstract

In the present study, a generalization of the Energy–Momentum Method, denoted by Generalized Energy–Momentum Method, applied to the non-linear dynamics of shells will be developed within the framework of the Generalized- α Method. This algorithmic environment contains the unconditionally stable Energy–Momentum Method and its numerically damped version as well as the classical Newmark and α-methods as special cases. In order to control the size of the time steps of the integration scheme with respect to accuracy and efficiency, an adaptive time stepping procedure based on local a posteriori error estimation will be improved for non-linear dynamical systems and applied to the proposed class of algorithms. The spatial discretization is realized by an eight noded finite shell element of Reissner/Mindlin type including an extensible shell director field permitting the application of three-dimensional material laws. The original formulation of this finite element will be developed for non-linear dynamic analysis and adapted for the employment within the introduced energy conserving/decaying time integration scheme.