ANCF reference node for multibody system analysis

摘要

The objective of this short communication is to introduce the important concept of the absolute nodal coordinate formulation reference node (ANCF-RN), a concept that can be used effectively to develop new and complex multibody system (MBS) models. The ANCF-RN allows for defining constraints and joints using linear algebraic equations, can be used to define local linear elastic problem in the case of small deformations, and ensures an optimum sparse matrix structure of the MBS dynamic equations of motion. Using this concept, complex systems such as tank cars filled with fluid or tire assemblies can be modeled using one mesh (subsystem) developed using ANCF finite elements (FE). This new FE mesh, which allows for arbitrarily large displacements including rotation and deformation, has a constant inertia matrix and zero Coriolis and centrifugal forces. Constraints at the mesh interfaces and boundaries are imposed at a preprocessing stage using linear constraint equations, thereby allowing for the elimination of dependent variables before the start of the simulation. The reference node, which is not associated with a particular finite element, can be used to define a rigid triad that serves as the ANCF mesh reference. The inertia coefficients associated with the reference node gradients is defined at a preprocessing stage, thereby allowing for the development of a constant positive definite inertia matrix for the ANCF mesh. A Cholesky transformation can be used to obtain an identity generalized inertia matrix, leading to an optimum sparse matrix structure of the MBS dynamic equations. Regardless of the complexity and dimension of the ANCF mesh or subsystem, only six nonlinear algebraic equations are required in order to define an ANCF-RN coordinate system. These algebraic equations are introduced to the dynamic formulation using the technique of Lagrange multipliers in order to preserve the ANCF desirable features.