On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3D geometrically exact beam model Original Research Article

In this work, we discuss the finite element implementation of the internal constraints in a three-dimensional (3D) geometrically exact beam model which can be formulated as holonomic constraint relationships. Model problems chosen for a more detailed consideration include a general joint constraint between beams and the beam connected to a rigid component. Appropriate modifications of the standard form of the geometrically exact beam element arrays are carried out in order to impose explicitly these kinds of constraints into time-integration schemes for nonlinear dynamics. Consequently, only the minimum number of unknowns is retained for the global set of nonlinear equations to be solved, thus avoiding the use of the extra variables (the Lagrange multipliers) and the pertinent difficulties in integrating the system of differential–algebraic equations. A number of numerical simulations considering dynamic analysis of multibody systems with rigid–flexible components and joint constraints are presented in order to illustrate versatility of the proposed procedure.