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<p>To address challenges in unified matrix integration and computational complexity for arbitrary cross-sectional beams in the Absolute Nodal Coordinate Formulation (ANCF), this study introduces Monte Carlo integration into the framework of fully parameterized 3D ANCF beam elements. A unified element matrix numerical integration scheme for beams with arbitrarily shaped cross-sections is developed. Further optimizations include the separation of axial and cross-sectional integrations: Gaussian quadrature is applied along the axial direction, while a quasi-Monte Carlo method with low-discrepancy sequences is adopted for cross-sectional integration. These enhancements significantly improve both accuracy and computational efficiency. Additionally, the proposed method is extended to multi-layer cross-sectional beams, enabling the modeling of structures such as sandwich beams with fillers and composite transmission lines, where material properties vary across layers. Static and dynamic numerical validations demonstrate good relative agreement between the proposed beam models and theoretical solutions or finite-element benchmarks. Among them, the dynamic prediction accuracy of the proposed double-layer cross-section beam element reached 98.61%. Results confirm the feasibility of this unified approach for constructing ANCF beam elements with arbitrary cross-sections.</p>

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Absolute nodal coordinate formulation beam element with arbitrary cross-section based on Monte Carlo integration

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Li Shuo,
  • Zhang Hongsheng,
  • Yu Zuqing,
  • Wang Yue

摘要

To address challenges in unified matrix integration and computational complexity for arbitrary cross-sectional beams in the Absolute Nodal Coordinate Formulation (ANCF), this study introduces Monte Carlo integration into the framework of fully parameterized 3D ANCF beam elements. A unified element matrix numerical integration scheme for beams with arbitrarily shaped cross-sections is developed. Further optimizations include the separation of axial and cross-sectional integrations: Gaussian quadrature is applied along the axial direction, while a quasi-Monte Carlo method with low-discrepancy sequences is adopted for cross-sectional integration. These enhancements significantly improve both accuracy and computational efficiency. Additionally, the proposed method is extended to multi-layer cross-sectional beams, enabling the modeling of structures such as sandwich beams with fillers and composite transmission lines, where material properties vary across layers. Static and dynamic numerical validations demonstrate good relative agreement between the proposed beam models and theoretical solutions or finite-element benchmarks. Among them, the dynamic prediction accuracy of the proposed double-layer cross-section beam element reached 98.61%. Results confirm the feasibility of this unified approach for constructing ANCF beam elements with arbitrary cross-sections.