Forward and inverse dynamics of flexible multibody systems

This dissertation presents new computational algorithms for the forward and inverse dynamics of flexible multibody systems. The flexible multibody components are modeled through the use of consistent isoparametric finite elements. The equations of motion are formulated through a floating frame approach derived by using Lagrange's equations for constrained systems. Dynamic equations are developed on the basis of the finite element nodal deformation coordinates as well as the modal deformation coordinates. In the forward dynamics problem, an efficient algorithm is developed to determine the resulting motion of flexible multibody systems when the actuating external forces are specified. The proposed solution to the forward dynamics problem uses an acceleration-based augmented Lagrangian penalty formulation to solve the differential-algebraic equations of motion. The proposed method yields convergent solutions with minimal constraint violations. In the inverse dynamics problem, recursive and non-recursive methods are developed to determine the actuating forces that are needed so that specific control points in the flexible multibody system follow desired trajectories. The inverse dynamics methods developed in this dissertation yield stable, non-causal (time-anticipatory) solutions to the inverse problem.