A couple of issues are identified in the process to embed absolute nodal coordinate formulation (ANCF) flexible bodies in an existing multibody dynamics code. (1) The generalized coordinates of ANCF must be solved together with those of the rest of the mechanism in a combined system of the equations of motion. (2) The various constraints, joints, and forces elements supported in the multibody dynamics code must be extended to the ANCF flexible bodies without major code restructuring. This paper describes two novel techniques that were devised to solve these issues. The first is the idea of interface triad. We will demonstrate how to construct the interface triad such that all exiting constraints, joints, and forces elements are automatically supported. The second idea is to represent the equations of motion of the ANCF body as a user-defined subroutine element representing a set of implicit general state equations subroutine (GSESUB). By treating each ANCF body modularly as a user-defined subroutine, not only all existing integration options of its host solver, e.g., HHT or DAE index-1, 2, and 3, etc., are automatically supported, but also the existing features such as parallel computing and sparse matrix solution of the existing multibody dynamics software are supported with minimum programming. Numerical examples are presented to demonstrate the efficiency and the success of these two techniques.
Parallel Sparse Matrix Solution for Circuit Simulation on FPGAs
