二维含裂纹结构与声耦合问题研究

应用分形有限元方法结合边界元方法研究了二维含裂纹结构和声耦合问题.采用二级分形有限元方法对含裂纹的弹性结构体进行离散处理,这样可以使得自由度数大大地减少;无限大外域声场的计算使用边界元方法,可以自动满足无穷远辐射条件.数值仿真算例结果表明:结构声耦合系统的共振频率随着裂纹深度的增加而下降;裂纹附近的声场所受的影响较为明显.     

含裂纹弹性结构对声散射作用研究

研究了含裂纹的弹性结构对声的散射作用,应用分配形有限元和边界元相结合的方法于含裂纹的结构声相互作用问题,利用二级分形有限元方法对含裂纹结构进行离散,这将使得自由度大为减少;使用边界元方法计算外域散射声场,这将自动满足无限远辐射边界条件,数值结果初步表明：(1)随着裂纹深度的增加,结构声耦合系统的共振频率将下降;(2)裂纹附近的声场所受的影响更为明显。     

近场波动模拟的一种应力人工边界

采用平面波和远场散射波混合透射，引入无限介质线弹性本构关系建立了一种应力人工 边界条件. 其优点在于边界结点反应与内部有限元结点反应采用相同的积分格式计算，有限 元积分方法稳定时不存在人工边界失稳问题. 数值算例表明：边界精度高于现有黏性边 界、黏弹性人工边界，以及一、二阶透射人工边界.     

二维稳态辐射声场的光滑有限元-完美匹配层解法

针对外场声学有限元计算精度偏低的问题, 将光滑有限元技术引入到二维稳态辐射声场预测中, 提出了光滑有限元-完美匹配层解法. 该解法采用完美匹配层截断声场计算域, 并将其离散为等参四边形单元, 采用指数吸收函数实现完美匹配层内参数坐标和笛卡尔坐标的映射关系, 采用光滑声压梯度技术计算辐射声场刚度矩阵, 将形函数梯度的域内积分转换为形函数域边界积分. 某汽车二维声腔辐射声场的数值分析结果表明, 与标准有限元-完美匹配层相比, 光滑有限元-完美匹配层解法在完美匹配层内的声波吸收效果更好, 在计算域内的数值计算精度更高, 具有良好的工程应用前景.      

黏弹性人工边界等效荷载计算的改进方法

黏弹性人工边界在场地地震反应和结构-地基动力相互作用等问题的计算中已得到了广泛的应用.地震波在黏弹性人工边界中的输入是通过将地震波转化为作用于人工边界处的等效载荷来实现的.计算等效节点载荷的常规方法默认边界节点对应区域内的应力为均布力,但实际上该节点对应区域内的应力分布通常是不均匀的.本文在有限元方法结合黏弹性局部人工边界的显式时域波动方法的基础上,建立了无限域散射问题地震波等效载荷计算的一种改进方法.该方法采用细化网格与应力积分相结合的方法计算人工边界等效节点力,有效地降低了人工边界上等效节点力的计算误差.以不同角度入射地震波的二维算例为例,算例给出的波场位移云图和节点位移时程曲线验证了本文方法的有效性,其计算精度与网格尺寸和地震波入射角度密切相关,且网格越小、入射角度越小,计算精度越高.对于相同的网格尺寸,本文采用方法的计算精度明显高于常规方法,尤其是对于斜入射问题优势更为明显.     

声辐射问题的二级分形有限元方法

利用分形有限元和常规有限元相结合的方法对中低频段声辐射问题进行了分析，由于引用了分形比α和能够自动满足无限远辐射边界条件的全域插值函数，大大降低了未知量的个数，从而可以在较短的计算时间和较低的内存消耗的条件下高效地解决问题，计算实例表明这种方法对于求解无界域声场问题是有效的。     

一种模拟大规模高频声场的双层奇异边界法

大规模高频声场的数值模拟是一项非常有计算挑战性的课题.为了解决传统边界型离散方法由于全局支撑的满阵限制,不易应用于大规模高频声场模拟的计算瓶颈,本文提出了一种用于模拟大规模高频声场的双层奇异边界法.在该方法中,通过引入双层结构,细网格上的全局支撑的满阵被转化为局部支撑的大规模稀疏矩阵,传统奇异边界法模拟大规模问题时所面临的高计算量以及过度存储需求遂得以解决.其次,双层奇异边界法仅通过粗网格评估远场作用,且独立于特定的插值核函数.相较于快速多级方法,该方法具有更强的适应性和灵活性,且多层结构使该方法具有一定的预调节作用,非常适合求解具有大规模、高秩、高条件数特点的高频波矩阵.在其后的散射球模型算例中,双层奇异边界法配置10万个节点,成功模拟了无量纲波数高达160的声散射问题.在对于人头模型的声散射特性分析中,双层奇异边界法比COMSOL软件计算速度快了约78.13%.当配置8万个节点时,双层奇异边界法成功模拟了频率高达25 kHz的工况,该频率已远远超出了人耳的听力极限.     

基于自适应交叉近似边界元法的快速声学灵敏度分析

基于自适应交叉近似边界元法构造一组快速声学灵敏度分析方法,其中,声学灵敏度分析分别采用直接微分法和伴随变量法;而自适应交叉近似算法被用以克服常规边界元法的高计算量和高存储量的固有缺点。自适应交叉近似算法在迭代求解之前对边界元系数矩阵进行压缩存储,可以在降低存储量的同时提高求解效率。在声学灵敏度分析中,通过直接使用求解未知边界状态值时保存的压缩系数矩阵,可以进一步提高求解效率。数值算例验证了所构造的方法的计算精度和求解效率,以及在大规模声场问题的最优化分析中的应用潜力。     

比例边界有限元二阶灵敏度设计及断裂力学分析

比例边界有限元是一种只需在边界上划分网格且无需基本解的半解析方法,能有效处理应力奇异性和无边界问题.论文提出了一种比例边界有限元的二阶灵敏度分析方法,可以准确而高效地求解响应关于参数的二阶梯度.首先通过建立仅需右特征向量的哈密顿矩阵特征灵敏度分析方程,发展了一种改进的比例边界有限元一阶灵敏度分析方法;其次,进一步通过构建二阶哈密顿矩阵特征灵敏度分析方程,并对比例边界有限元系统方程进行一系列二次直接微分,提出了一种半解析形式的比例边界有限元二阶灵敏度分析方法.该方法被应用于线弹性裂纹结构的形状灵敏度分析和不确定性传播分析.最后,给出了两个数值算例验证论文方法的有效性.     

基于人工弹簧模型的周期结构带隙计算方法研究

能量法具有将求解微分方程边值问题转化为泛函极值问题的优点,故而在结构动力学分析中被广泛使用, 近年来也被引入到周期结构带隙计算中. 然而,由于周期结构边界条件相对复杂,采用传统能量法(如Rayleigh-Ritz法)分析时位移函数构造难度大;且由于位移函数中包含波数项,扫描波数计算带隙的过程中质量、刚度矩阵需不断重算, 导致计算量较大. 鉴于此,本文对传统能量法进行改进,通过引入人工弹簧来模拟包含周期边界在内的各类边界条件,可将边界约束转化为人工弹簧的弹性势能,故而各能量分部中仅有周期边界弹性势能包含波数项,扫描波数时仅需重新计算与其对应的刚度矩阵,其余的质量、刚度矩阵只需要计算一次, 继而显著降低了计算量. 研究结果表明,本文方法准确、可靠, 且相较于传统能量法, 本文方法的计算效率更高,随着结构质量、刚度矩阵的维度增大, 或者扫描波数点数的增多,本文方法计算效率优势更加明显. 此外, 人工弹簧模型使用灵活、便捷,可进一步地拓展到更为复杂的周期性组合结构带隙分析中.      

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.     

Structural–acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme

The complete interaction between the structural domain and the acoustic domain needs to be considered in many engineering problems, especially for the acoustic analysis concerning thin structures immersed in water. This study employs the finite element method to model the structural parts and the fast multipole boundary element method to model the exterior acoustic domain. Discontinuous higher‐order boundary elements are developed for the acoustic domain to achieve higher accuracy in the coupling analysis. Structural–acoustic design sensitivity analysis can provide insights into the effects of design variables on radiated acoustic performance and thus is important to the structural–acoustic design and optimization processes. This study is the first to formulate equations for sound power sensitivity on structural surfaces based on an adjoint operator approach and equations for sound power sensitivity on arbitrary closed surfaces around the radiator based on the direct differentiation approach. The design variables include fluid density, structural density, Poisson's ratio, Young's modulus, and structural shape/size. A numerical example is presented to demonstrate the accuracy and validity of the proposed algorithm. Different types of coupled continuous and discontinuous boundary elements with finite elements are used for the numerical solution, and the performances of the different types of finite element/continuous and discontinuous boundary element coupling are presented and compared in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

pFFT快速边界元方法模拟三维声散射

研究了用pFFT快速边界元方法模拟声散射问题的关键技术。采用Burton—Miller方程消除了声学边界元方法中外问题解的不唯一现象。为此,文中研究了采用常量元时该方程中超奇异积分的计算方法。最后,通过对平面声波的刚性圆球声散射的数值模拟,验证了建立的声学pFFT快速边界元方法。     

边界元特征值分析及Burton-Miller法探究BEM eigenvalue analysis and the investigation of the Burton-Miller method

运用围道积分方法将边界元非线性特征值问题转化为规模很小的广义特征值问题,从而构造出一种边界元特征值分析方法。数值算例验证了该方法的求解精度。针对外声场问题,通过对常规、法向导数和Burton‐Miller边界积分方程的虚假特征频率的计算和比较,揭示了Burton‐Miller法规避虚假特征频率的本质,并对其中的叠加常数的最优取值给出了一种新的解释。     

Artificial boundary method for the exterior Stokes flow in three dimensions

In this paper, the artificial boundary method is considered for the numerical simulation of the exterior Stokes flow in three dimensions. First, an exact relation between the normal stress and the velocity field is obtained on a spherical artificial boundary. With the relation specified on the artificial boundary, the original problem is reduced to a new one only defined on a finite domain. After that, an variational problem equivalent to the reduced problem is derived. By truncating the series term in the formulation, a sequence of approximate variational problems are obtained, which can then be solved with a suitable finite‐element scheme. Finally, a numerical example is presented to show the performance of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.