有限元/边界元耦合方法在海洋生物目标强度特性研究的应用*

目标强度特性是海洋生物声学识别与资源量评估的重要依据,其中,基于近似几何体和声阻抗特性的理论模型法是研究海洋生物目标强度的重要手段。由于对几何形态近似处理以及数值求解方法的限制,传统理论模型对声波频率、入射方位以及目标声阻抗、形态尺寸等均有各自不同的适用范围,单一模型难以满足不同种类或同一种类但不同尺寸海洋生物的目标强度求解。本文尝试将逐渐见诸应用的有限元/边界元耦合方法用于海洋生物目标强度特性研究,分别以球形生物、纺锤形鱼类尾明角灯鱼(Ceratoscopelus warmingii)和细长形浮游动物南极大磷虾(Euphausia superba)为例进行仿真计算,并与相适应的经典理论模型进行对比分析。结果表明,对于球形生物,有限元/边界元耦合方法与解析模型的目标强度频响曲线完全吻合;对于纺锤形鱼类,有限元/边界元耦合方法可有效弥补基于模态级数解的形变圆柱体模型在中低频和两端入射时的准确性问题;对于细长形浮游动物,有限元/边界元耦合方法与畸变波玻恩近似模型高度吻合。综上,有限元/边界元耦合方法对多种海洋生物目标强度求解均具有较好的适用性,未来有待进一步结合实验测定进行验证。     

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

The paper presents a non-element method of solving boundary problems defined on polygonal domains modeled by corner points. To solve these problems a parametric integral equation system (PIES) is used. The system is characterized by a separation of the approximation of boundary geometry from the approximation of boundary functions. This feature makes it possible to effectively investigate the convergence of the obtained solutions with no need of performing the approximation of boundary geometry. The testing examples included confirm high accuracy of the solutions.     

液体调谐减振器的分析

本文利用Ｌａｍｂ变换，考虑液体的粘性，略去二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程中的非线性预后，建立了频域内Ｎａｖｉｅｒ－Ｓｔｏｋｒｅｓ方程的边界积分表达式，完整地处理了边界条件（包括自由面边界条件和固壁边界条件）并且给出了液体随结构振动时的附加质量与阻尼的计算表达式。     

两斜交圆柱壳应力分析的边界元法

本文研究了两斜交圆柱壳的边界元法。提出了用板的基本解叠加级数形式的修正项构成圆柱壳的基本解,提高了计算精度,缩短了计算时间。对区域积分进行特殊处理,从而避免了内部网格的划分,大大减少了数据准备工作量和占机内存。并编制了FORTRAN计算程序,进行了数值计算。     

一种新的摄动粘弹性边界元法

本文在拉普拉斯变换空间中,运用摄动理论和“弹性-粘弹性”对应性原理,提出了一种新的粘弹性问题边界元求解法。文中结合广义变分原理,导出了摄动粘弹性边界元方程,并给出了摄动粘弹性问题的基本解。最后,详述了一阶摄动的求解过程,并给出了算例。     

ANALYSIS ON ACOUSTICAL SCATTERING BY A CRACKED ELASTIC STRUCTURE

The acoustical scattering by a cracked elastic structure is studied. The mixed method of boundary element and fractal finite element is adopted to solve the cracked structure-acoustic coupling problem. The fractal two-level finite element method is employed for the cracked structure, which can reduce the degree of freedoms (DOFs) greatly, and the boundary element method is used for the exterior acoustic field which can automatically satisfy Sommerfeld‘s radiation condition. Numerical examples show that the resonance frequency is lower with the crack‘s depth increase, and that the effect on the acoustical field by the crack is particularly pronounced in the vicinity of the crack tip. This mixed method of boundary element and finite element is effective in solving the scattering problem by a cracked structure.     

适合于求解边界元方程组的GMRES算法的实用化和并行化研究

为了将GMRES算法应用于大型边界元方程组的求解，采用预条件技术和重正交技术相结合的方法实现了该算法的实用化，然后在实用化的基础上针对迭代算法具有良好并行性的特点，研究了该算法在网络机群环境下的并行化技术。数值试验和分析表明所用的这些技术是行之有效的，对于提高求解速度和增大求解问题的规模是有意义的。     

Application of ‘Operational Quadrature Methods’ in Time Domain Boundary Element Methods

The usual time domain Boundary Element Method (BEM) contains fundamentalsolutions which are convoluted with time-dependent boundary data andintegrated over the boundary surface. Here, a new approach for theevaluation of the convolution integrals, the so-called OperationalQuadrature Methods developed by Lubich, is presented. In thisformulation, the convolution integral is numerically approximated by aquadrature formula whose weights are determined using the Laplacetransform of the fundamental solution and a linear multisep method. Tostudy the behaviour of the method, the numerical convolution of afundamental solution with a unit step function is compared with theanalytical result. Then, a time domain Boundary Element formulationapplying the Operational Quadrature Methods is derived. For thisformulation only the fundamental solutions in Laplace domain arenecessary. The properties of the new formulation are studied with anumerical example.     

夹层板的复变边界元解法

本文用全纯函数表示微分方程△f(x,y)-λ(~2)f(x,y)=0的一般解,粮据全纯函数的Bekya积分表示法,建立了复数域内的边界积分方程并针对各种边界条件下Reissner型夹层板、Hoff型夹层板进行了数值求解。     

任意外型薄板非线性后屈曲问题的边界元解

本文就薄板后屈曲问题建立一组新型的边界元计算公式，用这组公式求解能方便处理各种边界问题，另外文中将面内应力分解成基本部份和附加部份，并利用微分算子分解理论导得了挠度的一个不同形式的基本解，由于计算公式中，实现了面内位移和挠度的解耦，从而使迭代过程得到简化，文末还对圆板后屈曲路径进行了计算，得到了满意的结果。