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<p>This paper proposes an efficient method for dynamic analysis of large-deformation flexible beams. The method integrates the absolute nodal coordinate formulation (ANCF), differential quadrature (DQ) time integration scheme, and discrete time transfer matrix method (DTTMM), herein referred to as ANC-DQ-DTTMM. The three-node ANCF beam element is employed to model geometrically nonlinear dynamics, systematically incorporating stretching, shearing, bending, and torsional effects. Shear locking is effectively mitigated by interpolating the position vector with shape functions one order higher than those used for the gradient vector. The element-level nonlinear ordinary differential equations are converted into algebraic form via the DQ time integration scheme, which guarantees both numerical stability and high accuracy. At each time step, the resulting nonlinear algebraic system is linearized via the Newton–Raphson method, enabling iterative updating of state variables until convergence criteria are satisfied. These state vectors are propagated along topological paths via Riccati transfer matrices, a process that circumvents global matrix assembly and achieves linear time complexity (O(<i>n</i>)). Numerical validation demonstrates that ANC-DQ-DTTMM outperforms conventional methods in both computational efficiency and solution accuracy.</p>

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Efficient dynamic analysis of large-deformation beams using the differential quadrature-discrete time transfer matrix method

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Huaqing Zhou,
  • Xiaoting Rui,
  • Bin He,
  • Jiang Cui,
  • Kai Xie,
  • Jinghong Wang,
  • Feiyu Hao

摘要

This paper proposes an efficient method for dynamic analysis of large-deformation flexible beams. The method integrates the absolute nodal coordinate formulation (ANCF), differential quadrature (DQ) time integration scheme, and discrete time transfer matrix method (DTTMM), herein referred to as ANC-DQ-DTTMM. The three-node ANCF beam element is employed to model geometrically nonlinear dynamics, systematically incorporating stretching, shearing, bending, and torsional effects. Shear locking is effectively mitigated by interpolating the position vector with shape functions one order higher than those used for the gradient vector. The element-level nonlinear ordinary differential equations are converted into algebraic form via the DQ time integration scheme, which guarantees both numerical stability and high accuracy. At each time step, the resulting nonlinear algebraic system is linearized via the Newton–Raphson method, enabling iterative updating of state variables until convergence criteria are satisfied. These state vectors are propagated along topological paths via Riccati transfer matrices, a process that circumvents global matrix assembly and achieves linear time complexity (O(n)). Numerical validation demonstrates that ANC-DQ-DTTMM outperforms conventional methods in both computational efficiency and solution accuracy.