声学-结构设计灵敏度分析

声学 -结构设计灵敏度分析揭示了结构振动引起的辐射声压与结构设计变量之间的关系。分别用有限元法和边界元法计算结构设计灵敏度和声学灵敏度。将两个灵敏度结合得到最终的声学 -结构设计灵敏度。在边界元计算中 ,采用退化元处理奇异积分问题 ,对特征频率不唯一问题采用CHIEF方法处理。以脉动球和箱体为例 ,验证了算法的可行性和精确性。  

A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity

 A general algorithm of the distance transformation type is presented in this paper for the accurate numerical evaluation of nearly singular boundary integrals encountered in elasticity, which, next to the singular ones, has long been an issue of major concern in computational mechanics with boundary element methods. The distance transformation is realized by making use of the distance functions, defined in the local intrinsic coordinate systems, which plays the role of damping-out the near singularity of integrands resulting from the very small distance between the source and the integration points. By taking advantage of the divergence-free property of the integrals with the nearly hypersingular kernels in the 3D case, a technique of geometric conversion over the auxiliary cone surfaces of the boundary element is designed, which is suitable also for the numerical evaluation of the hypersingular boundary integrals. The effects of the distance transformations are studied and compared numerically for different orders in the 2D case and in the different local systems in the 3D case using quadratic boundary elements. It is shown that the proposed algorithm works very well, by using standard Gaussian quadrature formulae, for both the 2D and 3D elastic problems. Received: 20 November 2001 / Accepted: 4 June 2002 The work was supported by the Science Foundation of Shanghai Municipal Commission of Education.  

任意的拉-欧边界元法解大晃动问题

本文针对可动边界问题提出了一个任意的拉格朗日-欧拉边界元法.运用该方法不仅边界上的控制点可以精确地跟踪自由面,而且可以避免单元畸变,保持良好的数值稳定性,实例计算表明这对求解大振幅晃动问题特别有效.另外文中引入了临界振幅的概念,对晃动分析中使用小振幅假设的条件进行了论证,首次给出了它的量级界限.  

用边界元法研究不同顶端声屏障的性能

交通噪声已成为城市主要污染源之一.目前控制交通噪声的主要措施是采用声屏障结构.考虑各种变化因素（表面声学特性、频率等） 的影响,应用边界元方法对不同顶端结构的声屏障降噪性能进行了计算研究.通过数据的对比分析,结果表明：作全吸收处理的树杈形声屏障整体降噪效果最好.  

用边界元法计算声辐射时高次奇异积分的处理方法

边界元法应用于计算辐射声场时，由于奇积分的存在，会影响以计算结果的精度，本文描述了处理带有１／ｒ奇异积分和１／ｒ＾２二次奇异积分处理方法，包括数学证明和数值积分方法，计算结果表明这种方法能提高精度。  

论Helmholtz方程的一类边界积分方程的合理性

本文导出了Helmholtz 方程超定边值问题有解的一个充要条件,和用非解析开拓法证明了文[1]中的Helmholtz 方程在外域中的解的边界积分表示式的合理性,并将此类边界积分表示式推广用于带空洞的有限域。这样就比较严密而又浅近地证明了基于该表示式建立起来的间接变量和直接变量边界积分方程的合理性。  

弹性地基板广义边值问题的边界元法

本文利用Ｈａｎｋｅｌ变换导出了弹性地基板弯曲问题的基本解，该基本解对于Ｗｉｎｋｌｅｒ地基、Ｐａｓｔｅｒｎａｋ地基和弹性半空间地基模型具有统一的表达形式。在此基础上，建立了适用于弹性地基板广义边值问题的边界积分方程组，最后文中给出了若干数值算例。  

Observed and simulated fracture pattern in diametrically loaded discs of rock material

To investigate the influence of a tensile stress gradient on fracture initiation and fracture growth in rock material, a configuration, consisting of a diametrically loaded disc with a hole on the diameter perpendicular to the loaded diameter, is used. The maximum local tensile stresses the material is able to withstand increase as the stress gradient increases. Depending on the diameter and the eccentricity of the hole, the disc splits along the loaded diameter or macro-fracturing starts at the hole. However, the tensile stresses at the top and the bottom of the hole are for nearly all cases considerably higher than the stress along the loaded diameter and than the macroscopic tensile strength of the material, determined by conventional Brazilian tests. To better understand this particular fracturing behaviour, numerical simulations of the experiments are conducted using the boundary element code DIGS, which allows the incorporation of weak elements (flaws), representing defects and weaknesses in the rock material. It is shown that the influence of the stress gradient on the stress concentration at the tip of mobilised defects lies at the origin of the particular fracturing behaviour in the diametrically loaded disc with a hole. The study of the new configuration leads also to a number of conclusions with regard to the failure in diametrically loaded discs in general. Based on the flaw model, fracture initiation in the Brazilian test has to be attributed to fracture growth of a mobilised defect, situated in the area close to one of the platens.  

复合材料层合板智能结构主动振动控制的边界元法

利用边界元法模拟智能结构的振动控制，推导出具有压电传感器及致动器的复合材料层合板的边界积分方程，应用负速度反馈控制律，研究了复合材料层合板智能结构主动振动控制问题，算例分析证明该方程的正确性。  

非均匀材料破坏过程数值模拟的边界元法研究

用格子模型和统计分布模拟非均匀材料性质的初始分布,针对二维非均匀材料格子模型建立了重复多子域边界元法求解方程。通过把各行子域集成为亚子域,然后对链状排列的亚子域应用域转移矩阵法进行求解。由于使用的域转移矩阵法对内存的要求仅略大于一个亚子域的求解,以及重复多子域法只需要进行一次系数矩阵积分,因而可以大大提高求解的规模和效率。在此基础上,对非均匀脆性材料在简单载荷作用下的破坏过程进行了数值模拟。采用重复多子域法和域转移矩阵法,可以得到子域内高精度的连续应力分布,为进一步研究非均匀材料裂纹萌生、扩展和破坏过程提供了基础。