一种高阶精度人工边界条件:出平面外域波动问题  

A HIGH-ORDER ACCURATE ARTIFICIAL BOUNDARY CONDITION:OUT-OF-PLANE EXTERIOR WAVE PROBLEM

作　　者：赵密[1,2] 杜修力[1] 刘晶波[2] 

机构地区：[1]北京工业大学城市与工程安全减灾教育部重点实验室,北京100124 [2]清华大学土木工程系,北京100084

出　　处：《工程力学》2012年第4期7-14,共8页Engineering Mechanics

基　　金：973计划项目(2007CB714203);国家自然科学基金项目(90715041;90715035;51008170);中国博士后科学基金项目(20100470363)

摘　　要：针对无限外域中的出平面波动问题,提出一种用于近场波动有限元分析的高阶精度人工边界条件。首先,采用变量分离法求解远场初边值问题,建立了时空全局的精确动力刚度人工边界条件;然后,发展了一种由有理函数近似和辅助变量实现构成的时间局部化方法,并将其应用于动力刚度人工边界条件,得到时间局部的高阶精度人工边界条件;最后,沿人工边界离散高阶精度人工边界条件,并将其与近场集中质量有限元方程耦合,形成对称的时间二阶常微分方程组,采用一种新的显式时间积分方法进行求解。数值算例表明:提出的高阶精度人工边界条件精确、高效、稳定并且容易在现有的有限元代码中实现。A high-order accurate artificial boundary condition（ABC） for the finite element analysis of near-field wave motion problems is proposed.The out-of-plane wave propagation problem on an unbounded exterior domain is considered.First,an exact dynamic-stiffness ABC that is global in space and time is constructed by solving the initial boundary value problem of a far field using the separation of variables.Second,a temporal localization method that consists of the rational function approximation and the auxiliary variable realization is developed and applied to the dynamic-stiffness ABC,leading to a high-order accurate ABC that is local in time but global in space.Third,the resulting high-order accurate ABC is discretized along the artificial boundary and coupled with the standard lumped-mass finite element equation of a near field.A symmetric second-order system of ordinary differential equations in time is obtained.A new explicit time integration algorithm in structural dynamics is used to solve this system.Finally,numerical examples demonstrate that the proposed ABC is accurate,efficient,stable and easy to implement into the existing finite element codes.

关 键 词：近场波动问题 显式有限元法 人工边界条件 出平面波动 无限外域 

分 类 号：O34[理学—固体力学]