Strain-Based Geometrically Nonlinear Beam Formulation for Rigid–Flexible Multibody Dynamic Analysis

Abstract

Geometrically nonlinear strain-based beam formulation has the potential to analyze flexible slender components in multibody systems efficiently owing to the minimum number of variables and constant stiffness matrix. The objective of this study is to develop a multibody dynamic analysis framework based on the strain-based beam formulation. To this end, we describe the constraint equation using the vector variables of the absolute nodal coordinate formulation that exhibits a velocity-transformation relationship with the strain-based formulation. Subsequently, we divide the Jacobian of the constraint equation into two terms. One term is equivalent to the velocity transformation matrix that is currently implemented in the existing strain-based analysis framework. The other term is a simple constant or linear Jacobian defined based on the orthonormal vectors of the absolute nodal coordinate formulation. This simple Jacobian description integrates the strain-based beam formulation with multibody dynamic theories to handle open- and closed-loop joints. The obtained numerical results validate that the proposed strain-based multibody dynamic analysis method concurs well with and exhibits a better convergence than the conventional flexible multibody dynamic analysis method.