透射边界结合隐式有限元方法的计算精度探讨  

A study on calculation accuracy of transmission boundary combined with the implicit finite element method

作　　者：倪同健 丁海平[1] 于彦彦[1] 陈姚杰 NI Tongjian;DING Haiping;YU Yanyan;CHEN Yaojie(Jiangsu Key Laboratory of Structure Engineering,SUST,Suzhou 215011,China)

机构地区：[1]苏州科技大学江苏省结构工程重点实验室,江苏苏州215011

出　　处：《苏州科技大学学报（工程技术版）》2020年第4期1-6,共6页Journal of Suzhou University of Science and Technology（Engineering and Technology Edition）

基　　金：国家自然科学青年基金项目(51808371)。

摘　　要：详细推导了采用隐式有限元与MTF结合进行地震作用下结构-地基系统的动力反应数值模拟方法,并选取了3种地形的二维场地模型,进行了地震波作用下的场地响应模拟。通过对比不同网格划分的数值模拟结果与精确解的差异,得到如下结果:对于有限元分析常采用的每个波长λ取10个单元的情况,一般可以得到较好的计算精度,但提高λ/Δx的数目,可以提高数值模拟的精度;时间步距Δt的减小对精度同样有所改善,只是较之空间步长而言,时间步距的改变对于精度的影响没有那么明显;对于复杂地形,建议取λ/Δx=20,并采用二阶MTF,这样可以大大地提高地震作用下场地响应的数值模拟精度。In this paper,the method of the numerical simulation of the dynamic response of structure-foundation systems under earthquakes is derived in detail by combining the implicit finite element and MTF,and the two-dimensional site models of three kinds of terrain are selected to simulate the site response under the action of seismic wave.By comparing the difference between the numerical simulation results and the exact solution under the different mesh division,the following results are obtained that??for the case that 10 elements are taken for each wavelength commonly used in finite element analysis,the better simulation precision can be obtained generally.But increasing the number can improve the precision of numerical simulation?".The change of time step also improves the accuracy,but compared with the space step,the change is not so obvious for the improvement of accuracy;for general topography,it is recommended to take and use the second-order MTF,which can greatly improve the calculation precision of the site response under the action of earthquakes.

关 键 词：隐式有限元 多次透射公式MTF 网格划分 地震响应 数值模拟精度 

分 类 号：P315.9[天文地球—地震学]