Nonlinear dynamics of flexible beams in planar motion: formulation and time-stepping scheme for stiff problems

摘要

In this work we present a systematic development for dealing with nonlinear dynamics of multi-body systems in planar motion. The model problem addressed is the 2 d beam theory of Reissner, featuring a simple quadratic form of the kinetic energy and a convenient spatial form of the strain measures which simplifies the strain energy expression. Special care is dedicated to constructing a time-stepping scheme adequate for multi-body systems with large difference in stiffness between different system components or different deformation modes, yet referred to as stiff problems. Several numerical simulation are presented to illustrate an excellent performance of the proposed method.