Strain-Based Geometrically Nonlinear Beam Formulation for Multibody Dynamic Analysis

The geometrically nonlinear strain-based beam formulation has the potential to analyze flexible multibody systems efficiently due to the minimum number of variables and the constant stiffness matrix. The objective of this paper is to extend the strain-based beam formulation to a generic multibody dynamic analysis. To achieve this objective, we describe the constraint equation by using the vector variables of the absolute nodal coordinate formulation that has a velocity-transformation relationship with the strain-based formulation. Then, we divide the Jacobian of the constraint equation into two terms. One term is equivalent to the velocity transformation matrix that has been implemented in the existing strain-based analysis framework. Therefore, additional programming effort and calculation are not needed. The other term is a simple constant or linear Jacobian defined by the orthonormal vectors of the absolute nodal coordinate formulation. This simple Jacobian description enables not only efficient analysis but also various choice of a time-integration method. We demonstrated that the proposed framework can be used with the explicit Runge-Kutta method and the implicit generalized-α method. The proposed strain-based multibody dynamic analysis method exhibited good agreement with and a better convergence than a conventional flexible multibody dynamic analysis method.