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作 者:段雪良 周正华 卞祝 韩轶 赵玲 李政 廖成亮 贺家聪 刘伟 Duan Xueliang;Zhou Zhenghua;Bian Zhu;Han Yi;Zhao Ling;Li Zheng;Liao Chengliang;He Jiacong;Liu Wei(College of Transportation Engineering,Nanjing Tech University,Nanjing 210009,China)
机构地区:[1]南京工业大学交通运输工程学院,南京210009
出 处:《地震科学进展》2025年第4期197-208,共12页Progress in Earthquake Sciences
基 金:国家自然科学基金项目(U2039208)资助。
摘 要:一个时间步内外行波以人工波速走过的距离与网格尺寸往往不一致,因此在应用透射边界公式时,一般通过时间插值或空间插值的方法将透射边界的计算结点用有限元结点表示。本文导出了拉格朗日插值算法、埃尔米特插值算法以及三次样条插值算法的透射边界一次透射插值公式,探讨不同插值算法对透射边界数值模拟结果的影响。首先将弹性半空间中入射P/SV波自由场问题的数值解与解析解对比,讨论3种插值算法对计算精度的影响,然后以半圆河谷地形入射P/SV波散射问题为例,对比不同插值算法计算得到的结果。数值结果表明:不同插值算法对透射边界数值模拟结果有显著影响,在3种插值算法中,三次样条插值算法计算精度最高,其次是拉格朗插值算法,相比之下,埃尔米特插值算法计算得到的精度较低。相比于自由场,散射问题的计算结果受3种插值算法的影响较大,拉格朗日插值算法与三次样条插值算法计算结果相近,而埃尔米特插值算法的计算结果差异较大。本研究成果为在应用透射边界模拟场地动力反应时,选择合适的插值算法提供了科学依据。The distance traveled by contour wave with artificial wave velocity in a step-time is often inconsistent with the mesh size.Therefore,when the transmission boundary formula is applied,the calculation nodes of transmission boundary are usually represented by finite element nodes through the method of time interpolation or spatial interpolation.In this paper,the transmission boundary interpolation formulas of Lagrange interpolation algorithm,Hermite interpolation algorithm and cubic spline interpolation algorithm are derived,and the influence of different interpolation algorithms on the numerical simulation results of transmission boundary is discussed.Firstly,the numerical and analytical solutions of the incident P/SV wave free field problem in elastic half space are compared,and the influence of three interpolation algorithms on the calculation accuracy is discussed.Then,taking the scattering problem of incident P/SV wave in semi-circular valley terrain as an example,the results obtained by different interpolation algorithms are compared.The numerical results show that:Different interpolation algorithms have significant influence on the numerical simulation results of transmission boundary.Among the three interpolation algorithms,the cubic spline interpolation algorithm has the highest accuracy,followed by Lagrange interpolation algorithm,and the Hermite interpolation algorithm has lower accuracy.Compared with the free field,the results of scattering problem are more affected by three interpolation algorithms,and the results of Lagrange interpolation algorithm and cubic spline interpolation algorithm are similar,while the results of Hermite interpolation algorithm are different.The findings of this study can serve as a scientific foundation for the selection of an appropriate interpolation algorithm when utilizing transmission boundaries to simulate the dynamic reaction process of the site.
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