Primary DOF Selection via QR Pivoting for Physical-Type Dynamic Condensation and Substructuring

The selection of primary degrees of freedom (DOF) plays an important role in the accuracy of physical-type dynamic condensation and substructuring methods. Conventional DOF-selection strategies usually rely on engineering judgment or quantitative criteria such as stiffness-to-mass ratios or modal energy measures. However, these approaches often fail for structures with complex geometry or strong spatial non-uniformity. As a result, their reliability is limited in many-query engineering analyses such as optimization or uncertainty quantification. To address this, we propose a systematic selection procedure based on QR factorization with column pivoting (QRCP). The method uses a subset of global or component normal modes, computed once via a single sparse eigendecomposition, to identify spatial coordinates that best preserve dominant dynamic behavior. Numerical examples on representative finite element models show that QR pivoting yields higher modal fidelity and better transient predictions. Moreover, it improves stability of non-converging iterative schemes such as the iterative order reduction (IOR) method. The proposed approach requires fewer primary DOF, and the additional QRCP step adds only minimal computational overhead.