弹性约束下大型钢结构应变位移重构方法

Strain-displacement reconstruction method for large steel structures under elastic constraints

  • 摘要: 针对大型钢结构在弹性约束条件下,传统模态转换分析方法(modal transformation analysis, MTA)因未考虑刚体模态信息而导致重构精度不足的问题,提出一种弹性约束下的模态转换分析(elastic-constrained modal transformation analysis, EMTA)方法。通过引入有限测点位移信息构建复合误差函数,采用最小二乘法优化求解出包含刚体与弹性模态的广义模态坐标,利用该坐标及模态振型叠加重构出结构全场位移。结合数值仿真和试验表明,在3种不同载荷工况下,MTA在3种工况下重构的表面位移拟合优度都低于0.5,而EMTA重构的表面位移拟合优度均超过0.9;MTA方法位移重构最小平均误差为36.56%,最大平均误差为56.32%,而EMTA方法位移重构最小平均误差为8.01%,最大平均误差为11.42%,且最大绝对误差不超过0.25 mm。因此EMTA重构精度和稳定性均显著优于传统MTA,为大型钢结构位移监测与控制提供了有效技术支撑。

     

    Abstract: To address the reconstruction inaccuracies in traditional modal transformation analysis (MTA) for large steel structures under elastic constraints—arising from the omission of rigid-body modal information, an elastic-constrained modal transformation analysis (EMTA) method is proposed. By incorporating finite measurement point displacement data to construct a composite error function, the generalized modal coordinates—encompassing both rigid-body and elastic modes—are optimized using the least-squares method. These coordinates are then combined with modal shape superposition to reconstruct the full-field displacement of the structure. Numerical simulations and experiments demonstrate that under three distinct loading conditions, MTA yields surface displacement fitting accuracies below 0.5, whereas EMTA consistently achieves accuracies exceeding 0.9. The minimum mean displacement error for MTA is 36.56%, with a maximum mean error of 56.32%. In contrast, the EMTA method achieves a minimum mean displacement error of 8.01% and a maximum mean error of 11.42%, with the maximum absolute error not exceeding 0.25 mm. Consequently, the EMTA method demonstrates significantly superior reconstruction accuracy and stability compared to traditional MTA, providing effective technical support for displacement monitoring and control in large-scale steel structures.

     

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