| A reliable and efficient formulation for the dynamic simulation of multibody systems within a finite element framework is presented. This approach allows the modeling of complex multibody systems with arbitrary configurations in a very systematic and modular way. This is accomplished through the assembly of basic components that include rigid and nonlinear elastic bodies as well as various joint types.; A novel constrained optimization approach is introduced to impose joint constraints between rigid bodies. The basic idea of the new method is to condense the augmented system resulting from a Lagrange multiplier formulation into a reduced system by perturbing zero diagonal terms with small penalty parameters. An optimal penalty parameter that minimizes the total error of the perturbed system is proposed. The fact that we use an inconsistent tangent matrix is justified by using a quasi-Newton method to solve the resulting nonlinear system. To deal with coupled flexible-rigid systems, a new family of explicit-implicit time integration schemes is developed. For the time-consuming flexible part, an explicit mid-point rule is applied, whereas an implicit mid-point energy-momentum conserving scheme is adopted for the rigid part. Each rigid body involves only six parameters, thus solution of the rigid body part using an implicit scheme remains very efficient for most practical problems.; The proposed algorithm has some remarkable features. First, it can efficiently handle a very general class of multibody systems with arbitrary topology. A sparse formulation introduced in this dissertation enables linear-time simulation for open loop systems. In classical Lagrange multiplier methods, singular configurations may exist which often result in failure of the solution process. The new approach overcomes this main drawback of the Lagrange multiplier method and leads to numerical systems with a full-rank coefficient matrix. Additionally, no stabilization technique is necessary since the joint constraints are exactly satisfied. Finally, the explicit-implicit scheme is shown to be linear and angular momentum conserving with good satisfaction of energy for the Hamiltonian systems considered. Several examples are presented to assess the performance and applicability of the algorithm. |
