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Objective <p>To reduce the computation time associated with the geometrically exact beam theory (GEBT), this study proposes an efficient computational framework that avoids time integration (TI), thereby substantially increasing computational efficiency.</p> Method <p>The proposed computational framework combines component mode synthesis (CMS) and the harmonic balance with the alternating frequency/time domain (HB-AFT) method, which incorporates four contributions: (1) to parameterize the rotational operator and angular displacements of nodes using unit quaternions; (2) to derive the CMS-reduced model of the quaternion-parameterized GEBT and its partial derivatives; (3) to address the issue of stiffness matrix singularity caused by the unit quaternion constraint via the Reduced-Inversion-Restoration (RIR) Strategy proposed in this study; and (4) to solve the CMS-reduced model using the HB-AFT method and thus establish a computationally efficient computational framework for GEBT.</p> Results <p>Validation against a full-order model, TI results, commercial software, and a previously reported benchmark confirms the accuracy of the proposed framework. The resulting computational speed is approximately 15.06–50.32 times that achieved in previous research.</p> Conclusion <p>The proposed framework significantly enhances the computational efficiency of GEB systems, demonstrating potential for applications in wind turbines, microrobotics, fiber manufacturing, metamaterials, and other slender flexible engineering systems.</p>

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An Efficient Computational Framework for Geometrically Exact Beam Systems Using HB-AFT and CMS

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • Bowen Tian,
  • Hidetoshi Takeuchi,
  • Riko Ogawara,
  • Akira Heya,
  • Tsuyoshi Inoue

摘要

Objective

To reduce the computation time associated with the geometrically exact beam theory (GEBT), this study proposes an efficient computational framework that avoids time integration (TI), thereby substantially increasing computational efficiency.

Method

The proposed computational framework combines component mode synthesis (CMS) and the harmonic balance with the alternating frequency/time domain (HB-AFT) method, which incorporates four contributions: (1) to parameterize the rotational operator and angular displacements of nodes using unit quaternions; (2) to derive the CMS-reduced model of the quaternion-parameterized GEBT and its partial derivatives; (3) to address the issue of stiffness matrix singularity caused by the unit quaternion constraint via the Reduced-Inversion-Restoration (RIR) Strategy proposed in this study; and (4) to solve the CMS-reduced model using the HB-AFT method and thus establish a computationally efficient computational framework for GEBT.

Results

Validation against a full-order model, TI results, commercial software, and a previously reported benchmark confirms the accuracy of the proposed framework. The resulting computational speed is approximately 15.06–50.32 times that achieved in previous research.

Conclusion

The proposed framework significantly enhances the computational efficiency of GEB systems, demonstrating potential for applications in wind turbines, microrobotics, fiber manufacturing, metamaterials, and other slender flexible engineering systems.