Energy conserving/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations

摘要

In this work we present an extension of time 0-integration energy conserving scheme which introduces desirable properties of controllable energy decay, as well as numerical dissipation of high-frequency contribution to total re- sponse. Finite element implementation details are given for the chosen model problem of geometrically exact beam undergoing finite rotations. Several numerical simulations illustrate a very satisfying performance of the proposed time- stepping scheme.