基于高频连分式与有限元法的水下结构瞬态分析方法

Transient analysis method of submerged structure based on high frequency continued fraction formulation and FEM

本文针对水下结构与无限声学水域的流固耦合问题,建立了基于比例边界有限元法(SBFEM)连分式和有限元法(FEM)的瞬态分析方法。该方法分别采用SBFEM高频连分式和FEM方程模拟无限水域和水下结构等有限域。基于其耦合项,建立了连分式与FEM耦合公式。通过数值算例,讨论了连分式阶数对计算精度的影响,比较了连分式法和SBFEM卷积积分的计算效率。数值结果表明高频连分式可准确模拟无限水域的高频特性,并随着连分式阶数的增多,可合理模拟无限水域低频特性。该方法继承SBFEM的精度高、离散单元少等特点,又避免了其卷积积分,提升了计算效率,为水下结构瞬态响应分析提供了一种高效方法。

Aiming to fluid-structure interaction problems between a submerged structure and an infinite acoustic fluid,a transient analysis method based on the scaled boundary finite element method(SBFEM)con tinued fraction formulation and finite element method(FEM)was proposed.This method used SBFEM high frequency continued fraction formulation and FEM to model an infinite fluid and a bounded domain(a sub merged structure),respectively.Based on a coupling term,the continued fraction formulation and FEM cou pling formulation were proposed.Through numerical examples,the effect of the continued fraction formula tion’s order on calculation precision was discussed and the calculation efficiency between the continued frac tion formulation and SBFEM convolution integral was compared.Numerical results showed the high frequen cy continued fraction formulation can accurately model the high frequency characteristic of infinite fluid and reasonably model the low frequency characteristic of infinite fluid with its order increasing.The proposed method inherits advantages of SBFEM such as high accuracy and few discretized elements,and avoids convolution integral,which results in efficiency improvement and provides an approach with a high efficiency for a submerged structure transient response analysis.