A RECURSIVE ABSOLUTE NODAL COORDINATE FORMULATION WITH O(n) ALGORITHM COMPLEXITY

Compared with the tradition floating frame of reference formulation, the absolute nodal coordinate formulation (ANCF) has a natural advantage in solving nonlinear large deformation problems. However, the mathematic model established by ANCF is always converted to differential algebraic equation (DAE) based on analytical mechanics methods, which leads to an O(n²) or O(n³) algorithm complexity and position or speed constraint violation during the solution procedure. In order to solve these problems, this paper proposes a recursive absolute nodal coordinate formulation (RANCF) with O(n) algorithm complexity. Firstly, the flexible bodies are described by RANCF. Secondly, a kinematic and dynamic recursive relationship between adjacent elements in the flexible multibody system is established based on the articulatedbody algorithm (ABA). The equation obtained by RANCF is an ordinary differential equation (ODE), and the system generalized mass matrix is a tridiagonal block matrix. Thus, a recursive solution of the equation by element could be obtained through an appropriate matrix processing. On this basis, a particular algorithm flow of RANCF is provided with the efficiency of each step analyzed in detail, which proves the RANCF is an O(n) complexity algorithm. The RANCF maintains the advantage of ANCF that can accurately solve large deformation multibody problem, and vastly improves the computational efficiency of ANCF. In addition, because the ANCF avoids the constraint violation problems of DAE, it also has a higher algorithm accuracy. Finally, the validity and effciently of this method is verified by the MSC.ADAMS software, the energy conservation test and the DOF-CPU time test.