Geometric nonlinearity is an essential consideration in the dynamic analysis of flexible structures, and significant attention has focused on effective model order reduction to accelerate computational efficiency. This paper introduces the Iterative Improved Reduced System dynamic condensation method within the dynamic substructuring framework to establish an efficient reduced-order approach for nonlinear dynamic solution and analysis. In the dynamical model, the structure is partitioned into substructures discretized via the finite element method. Applying Hamilton’s principle yields the substructural equations of motion, where internal degrees of freedom are condensed using truncated modes. Interface degrees of freedom then assemble the condensed substructure models, followed by execution of the Iterative Improved Reduced System method’s third transformation to obtain the final structural equations of motion. The incremental harmonic balance method coupled with the arc-length method enables automatic iterative solution. Validation through variable-cross-section beam experiments confirms the accuracy of condensation method. Comprehensive numerical results demonstrate that the combined Craig-Bampton and Iterative Improved Reduced System approach maintains high computational accuracy while significantly enhancing efficiency. Applicable to finite-element-constructed structural equations of motion, this method substantially improves dynamic analysis efficiency for geometrically nonlinear structures, providing an optimized computational pathway for engineering design and optimization.
Hu et al. (Fri,) studied this question.