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    欧拉梁单元的边界增强集中质量矩阵及其在车桥耦合分析中的应用

    A Boundary-Enhanced Lumped Mass Matrix Formulation for Euler Beam Element and Its Application to Vehicle-Bridge Interaction Analysis

    • 摘要: 尽管欧拉梁单元的分块对角质量矩阵在频率计算中具有较高精度,但由于其非正定的特点,在用于动力分析时存在数值发散问题.针对该问题,通过在分块对角质量矩阵边界单元中引入稳定项,提出了一种边界增强集中质量矩阵,有效消除了分块对角质量矩阵的负特征值,保证了矩阵半正定性,并将其用于车桥耦合计算.理论分析与数值模拟结果均表明,梁单元的边界增强集中质量矩阵不仅计算精度和临界时间步长优于包含转动惯量的传统集中质量矩阵,还有效避免了非正定分块对角质量矩阵的动力响应发散问题,因而在车桥耦合动力分析中具有良好适用性.

       

      Abstract: Although the Euler-Bernoulli beam element with block-diagonal mass matrix achieves superior frequency accuracy,its non-positive-definite property leads to noticeable numerical instability in transient finite element analysis.To resolve this issue,a boundary-enhanced lumped mass matrix is proposed in this study through introducing a stabilization term into the components of boundary entries of the block-diagonal mass matrix.It turns out that this boundary-enhanced lumped mass matrix guarantees the positive definiteness.Meanwhile,a frequency accuracy analysis based upon the perturbation theory indicates that the proposed boundary-enhanced lumped mass matrix yields a third-order accuracy for frequency computation,which is one order higher than that of the conventional lumped mass matrix with rotational inertia.Furthermore,an analytical eigenvalue analysis reveals that the critical time step corresponding to the boundary-enhanced lumped mass matrix is also larger compared with the conventional lumped mass matrix with rotational inertia,which enables a more efficient transient computation.Subsequently,the proposed boundary-enhanced lumped mass matrix is employed for the finite element analysis of vehicle-bridge interaction.Numerical results demonstrate that the proposed boundary-enhanced lumped mass matrix not only produces more favorable solution accuracy in comparison with the conventional lumped mass matrix with rotational inertia,but also effectively avoids the transient response divergence caused by the non-positive-definiteness of the block-diagonal mass matrix.Consequently,the proposed boundary-enhanced lumped mass matrix offers an efficient,accurate and stable way for the dynamic analysis for vehicle-bridge interaction.

       

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