An o(n) complexity recursive algorithm for multi‐flexible‐body dynamics based on absolute nodal coordinate formulation

Abstract

SummaryA new algorithm called recursive absolute nodal coordinate formulation algorithm (REC‐ANCF) is presented for dynamic analysis of multi‐flexible‐body system including nonlinear large deformation. This method utilizes the absolute nodal coordinate formulation (ANCF) to describe flexible bodies, and establishes a kinematic and dynamic recursive relationship for the whole system based on the articulated‐body algorithm (ABA). In the ordinary differential equations (ODEs) obtained by the REC‐ANCF, a simple form of the system generalized Jacobian matrix and generalized mass matrix is obtained. Thus, a recursive forward dynamic solution is proposed to solve the ODEs one element by one element through an appropriate matrix manipulation. Utilizing the parent array to describe the topological structure, the REC‐ANCF is suitable for generalized tree multibody systems. Besides, the cutting joint method is used in simple closed‐loop systems to make sure the O(n) algorithm complexity of the REC‐ANCF. Compared with common ANCF algorithms, the REC‐ANCF has several advantages: the optimal algorithm complexity (O(n)) under limited processors, simple derivational process, no location or speed constraint violation problem, higher algorithm accuracy. The validity and efficiency of this method are verified by several numerical tests. Copyright © 2016 John Wiley & Sons, Ltd.