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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。
Aiming at the problem of out-of-plane fluctuations in an infinite outer domain, a high-order artificial boundary condition for near-field wave motion finite element analysis is proposed. First, the variable-separation method is used to solve the problem of initial-boundary value in the far-field and the artificial boundary condition of the precise dynamic stiffness in space-time is established. Then, a local time-localized method is constructed, which is composed of rational function approximation and auxiliary variable. Finally, along the artificial boundary, the high-order artificial boundary conditions are discretized and coupled with the finite element equation of near-field mass concentration to form the symmetrical time two Ordinary differential equations, using a new explicit time integral method to solve. Numerical examples show that the proposed high-precision artificial boundary conditions are accurate, efficient, stable and easy to implement in existing finite element codes.