一种模拟弹性波在层状地基中传播的简化高阶双渐近透射边界  

A simplified high order doubly asymptotic open boundary for modeling elastic wave propagation in layered foundation

作　　者：高毅超[1] 徐艳杰[2] 金峰[2] SONG ChongMin 

机构地区：[1]华侨大学土木工程学院,厦门361021 [2]清华大学水沙科学与水利水电工程国家重点实验室,北京100084 [3]Department of Civil and Environmental Engineering, University of New South Wales, Sydney 2052, Australia

出　　处：《中国科学：技术科学》2016年第5期527-534,共8页Scientia Sinica(Technologica)

基　　金：国家自然科学基金(批准号:51409107,41274106);博士后自然科学基金(批准号:2014M551832)资助项目

摘　　要：在强烈地震作用下,层状地基与结构之间的动力相互作用将对结构的动力响应产生重大影响,其难点是模拟波动在无限层状地基中传播引起的辐射阻尼效应.基于比例边界有限单元法(SBFEM)构建的层状介质标量波高阶双渐近透射边界能够在全频范围内快速收敛到准确解,具有很高的计算精度和计算效率,并且具有良好的数值稳定性.以二维水平等高层状地基为研究对象,将弹性动力学方程强行解耦得到两个独立的标量波方程,基于解耦的标量波方程构建了一种层状地基弹性波传播模拟的简化高阶双渐近透射边界.同标量波高阶双渐近透射边界一样,该透射边界具有良好的计算性能.数值算例结果表明,该透射边界对底部为固定边界条件的水平层状地基具有良好的模拟精度.Dynamic structure-layered foundation interaction has great contribution to the seismic response of structure subjected to strong earthquake. The main difficulty in this area lies in accurately modeling the radiation damping caused by the wave propagation in the infinite layered foundation. Based on the scaled boundary finite element method, a high order doubly asymptotic open boundary for modeling the scalar wave propagation in the semi-infinite layered medium has been developed. This open boundary is capable of accurately mimicking the unbounded layered medium over the entire frequency range. It converges to the exact solution quickly as its order increases and has high computational efficiency as well as good numerical stability. In this paper, the elastic wave equation for layered foundation is decoupled, leading to two independent scalar wave equations. The scalar wave high order doubly open boundary is applied for each independent scalar wave equation. As a result, a simplified high order doubly asymptotic open boundary for elastic waver propagation in layered foundation is developed. Numerical example results demonstrate that this proposed open boundary is suitable for modeling the elastic wave propagation in the layered foundation with fixed bottom boundary condition.

关 键 词：透射边界 层状地基 双渐近 比例边界有限单元法 

分 类 号：O347.41[理学—固体力学]