A Parallel, Hierarchical Approach for the Solution of Flexible Multibody Dynamics Problems

摘要

A novel approach is proposed for parallel computation in flexible multibody dynamics, based on a sub-domain decomposition technique.In this approach, the computational domain is divided into non-overlapping sub-domains and kinematic constraints are used to enforce the continuity of the displacement field over the entire structure. These kinematic constraints are enforced via fields of Lagrange multipliers that act at the interface between the sub-domains and can be interpreted as the interface connection forces. The proposed approach relies on a novel strategies for the enforcement of the kinematic constraints at the interface between sub-domains. The traditional approach [1] is to use global Lagrange multipliers to enforce all constraints.In the proposed approach, all constraints are enforced using local Lagrange multipliers and an interface mesh is defined as a byproduct.Furthermore, an augmented Lagrangian formulation is used in conjunction with with the local Lagrange multipliers. The penalty terms stemming from the augmented Lagrangian formulation provide a natural conditioning of the interface problem expressed in terms of the local Lagrange multipliers.In fact, as the penalty factor increases, the condition number of the interface problem flexibility matrix tends to unity. This advantage, however, comes at the expense of the solution of a large sized coarse mesh problem. To solve this latter problem, it is shown that the use of local Lagrange multipliers leads to an interface problem that can itself be decomposed into nonoverlapping sub-domains. This contrasts with the traditional approaches for which this is not possible.Clearly, the proposed approach leads to a hierarchical decomposition of the problem, in which each decomposition leads to an new interface problem, of ever decreasing size.At the end, the overall problem can be solved without resorting to iterative solvers, achieving great computation efficiency and stability.Examples of application of the procedure will be presented for flexible multibody systems.