Interpolation multipoint constraints with selection criteria of degree of freedoms for flexible multibody dynamics

•A new method is presented to extend the DOFs selection in the interpolation MPCs.•The derived formula for a matrix rank can allow a non-invertible constraint matrix.•A stable FMBD model can be more freely constructed through the suggested method. An interpolation multipoint constraints (MPCs) formulation with selection criteria of the additional degree of freedoms is proposed for the simulation of flexible multibody dynamics (FMBD). The proposed formulation, which addresses invertible condition problems, overcomes the limitations in the selection of dependent degrees of freedom (DOFs) in interpolation MPCs. For the extension of the DOF selection criteria, a new transformation matrix is essentially derived via the approximation of the series expansion by using dynamic correction, and hence the derived transformation matrix can be easily applied to construct a symmetric FMBD formulation for the numerical stability. Consequently, the proposed formulation shows an improved performance in the selection of dependent DOFs to well reflect the realistic constraints of flexible bodies and provide better numerical stability with standard time integrators. The performance of proposed method was evaluated through numerical examples.