杨浩文, 吴斌, 潘天林, 谢金哲. Timoshenko梁能量守恒逐步积分算法[J]. 工程力学, 2019, 36(6): 21-28. DOI: 10.6052/j.issn.1000-4750.2018.01.0033
引用本文: 杨浩文, 吴斌, 潘天林, 谢金哲. Timoshenko梁能量守恒逐步积分算法[J]. 工程力学, 2019, 36(6): 21-28. DOI: 10.6052/j.issn.1000-4750.2018.01.0033
YANG Hao-wen, WU Bin, PAN Tian-lin, XIE Jin-zhe. ENERGY-CONSERVING TIME INTEGRATION METHOD FOR TIMOSHENKO BEAMS[J]. Engineering Mechanics, 2019, 36(6): 21-28. DOI: 10.6052/j.issn.1000-4750.2018.01.0033
Citation: YANG Hao-wen, WU Bin, PAN Tian-lin, XIE Jin-zhe. ENERGY-CONSERVING TIME INTEGRATION METHOD FOR TIMOSHENKO BEAMS[J]. Engineering Mechanics, 2019, 36(6): 21-28. DOI: 10.6052/j.issn.1000-4750.2018.01.0033

Timoshenko梁能量守恒逐步积分算法

ENERGY-CONSERVING TIME INTEGRATION METHOD FOR TIMOSHENKO BEAMS

  • 摘要: 该文提出了Timoshenko梁非线性动力分析的能量守恒逐步积分算法。采用共旋技术考虑结构的几何非线性,空间离散采用相关插值形式,避免了剪切锁定现象。在时间离散时利用多参数修正方法对等效的节点动力平衡方程进行修正,实现了离散系统在保守荷载作用下的能量守恒。算法具备二阶局部精度,与已有的平均加速度方法和隐式中点方法相比,具有更好的数值稳定性。在二维情形下与Simo方法对比,指出了Simo方法在受保守外弯矩作用时系统能量不守恒。最后,通过三个数值模拟算例验证了算法的性能和能量守恒特性。

     

    Abstract: An energy-conserving time integration method is proposed for the nonlinear dynamic analysis of Timoshenko beams. Co-rotational techniques are used to consider its structural geometric nonlinearity, and a linked interpolation form is adopted in the spatial discretization to avoid shear-locking phenomenon of a beam. The multi-parameter correction method is used to modify the equivalent nodal dynamic equations in the time discretization, which results in the energy conservation of the discrete system under conservative loading. The method has second-order local accuracy and shows better numerical stability, compared to the average acceleration method and the implicit midpoint method. The proposed method is compared to the Simo's method in two-dimensional cases and it is found that the Simo's method does not conserve system energy under a conservative external moment. Finally, the excellent performance and energy-conserving characteristic of the algorithm are verified by three numerical simulations.

     

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