An Energy Preserving Scheme For Constrained Flexible Nonlinear Multibody Systems

Abstract

An energy conserving algorithm which was presented in previous works, is now being
extended to flexible problems by developing the formulation of a nonlinear large rotations beam.
Although the general formulation in previous works included flexibility, only rigid multibody
dynamics problems were tested. Flexibility is dealt with easily in energy conserving algorithms
only for finite element models with displacement degrees of freedom. However, beam models
which have rotation degrees of freedom, are more cumbersome to be handled. The beam model
which we introduce in this paper has been simplified and lead to quite compact expressions of
its different terms. The time integration algorithm proves now to be able to deal with flexible
multibody dynamics problems. This kind of algorithms have many advantages, both theoretical
and practical, because of its unconditional stability which is warranted even in the nonlinear
regime.