非连续边界元——有限元耦合方法分析

对边界元－有限元耦合方法进行了分析，采用非连续元离散边界积分方程，解决了耦合分析中自由度约束问题，给出了非连续边界元同有限元耦合的具体实施步骤，通过对二维弹性力学和流＝固耦合问题分析，表明了该文方法的有效性。     

三维弹性力学边界元多域缩聚法分析

采用超参非连续元离散三维弹性力学问题边界积分方程，借助三角极坐标变换方法处理奇异积分。将超参非连续元用于多域边界元分析，解决了自由度约束问题。提出了二次缩聚的概念，提高了多域缩聚边界元法的求解效率。通过数值算例表明了本文方法的可行性和有效性。     

h-自适应边界元方法的插值残差计算及误差估计

本文提出了一种用于估计ｈ－自适应边界元过程解误差的新方法,这种方法基于ｈ－自适应边界元过程生成的离散网络,通过计算近似解的插值残差,以此作为误差估计的数据。此外,这种误差分析方法易于程序化,可以很方便地接入现有ｈ－自适应边界元计算机程序（简单细分或分层细分）,而对原程序不作大的改动。通过对二个经典的弹性静力学问题的分析表明：本文的方法能较好地估计边界元解的误差,并使ｈ－自适应边界程序的分析更加有效     

二维边界元奇异积分和多域缩聚法分析

基于基本解的一种新的表达式，对二维边界元分析中奇异积分的精确求解进行了讨论，从几何方面对基本解的奇异性进行了分析，给出了超参非连续元离散位势和弹性力学问题边界积分方程时奇异积分计算的精确式，从而为判断各种近似方法的优劣和间接方法的精度提供了依据，也为精确地分析了大规模问题提供了一条有效的途径。     

三维非规划非均匀边界元网格的简便的高精度算法

对三维直接边界元中一阶奇异积分，一阶近奇异积分以及非奇异积分进行统一处理，给出了一种提高积分计算精度的简便有效的方法，对非规则非均匀边界元网格可获得比一般方法高得多的计算精度，非常适合边界形状比较复杂的三维实际问题的边界元分析。     

三维非规则非均匀边界元网格的简便的高精度算法

对三维直接边界元中一阶奇异积分、一阶近奇异积分以及非奇异积分进行统一处理，给出了一种提高积分计算精度的简便有效的方法，对非规则非均匀边界元网格可获得比一般方法高得多的计算精度，非常适合边界形状比较复杂的三维实际问题的边界元分析．     

位势问题非连续边界元分析

本文推导了二维位势问题超参非连续边界元分析的公式，证明了利用曲边单元对位势问题进行分析时，Ｃａｕｃｈｙ型奇异积分可以直接确定，没有必要采用通常的常位势方法．通过数值算例对非连续边界元分析中最优配点问题进行了说明．     

三维Laplace方程边界元中线性单元的精确积分法

边界元中的边界积分计算影响计算精度和计算速度。非奇异积分一般采用数值积分，当配置点接近积分单元时，计算精度降低。未知函数线性插值得到的解是连续解，但计算难度增大。本文采用积分区域变换，将三维Laplace问题的二维积分化为一维积分，这样奇异积分和非奇异积分能采用精确积分的方法计算，使求解精度，计算速度都得到提高。     

非连续边界元积分的精确表达式及相关问题

以二维位势问题边界元分析为例,给出了利用线性非连续边界元离散边界积分方程时系数矩阵积分计算的精确表达式,通过和利用Gauss积分方法计算系数矩阵所得数值结果的比较表明：配位点选择不同对数值计算结果精度影响的主要原因是积分计算的精度,尤其当配位因子选择较大时,存在的准奇异积分（Nearly Singular Integrals)很难利用常规Gauss积分方法准确求得。     

三维非线性有限元与弹性边界元耦合数值方法

本文系统地讨论了以下三个问题:(1) 有限元与边界元耦合中的几个数值问题,其中包括:边界积分方程的凝聚、等效刚度矩阵的对称化及面力不连续的处理;(2) 弹塑性有限元与弹性边界元的耦合;(3) 弹粘塑性有限元与弹性边界元的耦合及数值计算稳定性条件。     

Kinked crack analysis by a hybridized boundary element/boundary collocation method

In this research a two dimensional displacement discontinuity method (which is a kind of indirect boundary element method) using higher order elements (i.e. a source element with a cubic variation of displacement discontinuities having four sub-elements) is used to obtain the displacement discontinuities along each boundary element. In this paper, three kinds of the higher order boundary elements are used: the ordinary elements, the kink elements and the special crack tip elements.The boundary collocation technique is used for the calculation of the displacement discontinuities at the center of each sub-elements. Again a special boundary collocation technique is used to treat the kinked source elements occur in the crack analysis. Considering the two source elements (each having four sub-elements) joined at a corner (kink point). The collocation points in the cubic element model which are outside of the kink point are moved to the crack kink then the displacement discontinuities on the left and right sides of the kink are calculated. The displacement discontinuities of the kink point are obtained by averaging the corresponding values of its left and right sides. The special crack tip elements are also treated by the boundary displacement collocation technique considering the singularity variation of the displacements and stresses near the crack tip. Some simple example problems are solved numerically by the proposed method. The numerical results are compared with the corresponding results obtained by the previous methods cited in the literature. This comparison shows a very good agreement between the results and verify the accuracy and validity of the proposed method.     

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.     

A numerical implementation using mid-node collocation for the hypersingular boundary contour method

A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional problems does not require any numerical integration at all. In another development, a boundary contour implementation of a regularized hypersingular boundary integral equation (HBIE) using quadratic elements and end-node collocation was proposed and the technique is termed the hypersingular boundary contour method (HBCM). As reported in that work, the approach requires highly refined meshes in order to numerically enforce the stress continuity across boundary contour elements. This continuity requirement is very crucial since the regularized HBIE is only valid at collocation points where the stress tensor is continuous, while the computed stress at the endpoints of a boundary contour element, which is a non-conforming element, is generally not. This paper presents a new implementation of the HBCM for which the regularized HBIE is collocated at the mid-node of a boundary contour element. As the computed stress tensor is continuous at these mid-nodes, there is no need for unusually refined meshes. Some numerical tests herein show that, for the same mesh density, the HBCM using mid-node collocation has a comparable accuracy as the BCM.     

自由单元法及其在结构分析中的应用

通过吸收有限元与无网格法的优点,提出了一种新的数值方法------自由单元法.此方法在离散方面,采用有限元法中的等参单元,表征几何形状和进行物理量的插值;在算法方面,采用单元配点技术,逐点产生系统方程.主要特点是,在每个配置点只需要一个和周围自由选择的节点而形成的一个独立的等参单元,因而不需要考虑物理量在单元之间的相互连接关系与导数连续性问题. 本文介绍强形式与弱形式两种自由单元法,前者直接由控制方程和边界条件直接产生系统方程,后者通过在自由单元上建立控制方程的加权余量式产生弱形式积分式,并通过像传统有限元法中的积分过程建立系统方程组.本文提出的方法是一种单元配点法,对于域内点为了获得较高的导数精度,需要采用至少具有一个内部点的等参单元,为此除了可使用各阶次的拉格朗日四边形单元外, 还 给出了七节点三角形等参单元,用于模拟较为复杂的几何形状问题.      

双材料基本解弹塑性边界元法

提出并研究采用双材料基本解的弹塑性边界元法,得到了内点应力公式中有关奇点塑性应变自由项的完整表达式,并利用非连续边界单元和非连续区域单元解决了当奇点位于界面上时该自由项难于确定,以及计算区域Cauchy主值积分的常塑性应变场法在与界面相连的奇异区域单元上无法实施的困难．采用双材料基本解的弹塑性边界无法针对双材料的结构特点,特别适于分析有关弹塑性双材料界面及界面裂纹问题．     

非网格重剖分模拟宏观裂纹体的扩展有限单元法(2:数值实现)

探讨了扩展有限单元法的具体实现过程,包括裂纹体几何结构的拓扑分析、广义节点的选取及详细的单元数值计算。并针对前文提出的扩展有限单元平衡方程的统一矩阵实现模式,提出了采用虚拟层合元的思想来处理被裂纹横贯单元的子域积分问题,自然地解决了原方法中由于特殊的位移插值场在裂纹两侧不连续造成的单元刚度阵求解困难。同时依托比较成熟的虚拟层合单元法,可以方便地考虑域内及裂纹面上分布载荷影响。此外,一、二维算例较高精度的数值结果验证了本文算法的有效性和精度。     

动态断裂力学的无限相似边界元法

对弹性动力学的相似边界元法进行了进一步研究,推导了相应的计算公式,并在此基础上提出了动态断裂力学的无限相似边界元法.与传统的边界元法相比,相似边界元法由于只需在少数单元上进行数值积分,大大减少了计算量.对动态断裂力学问题,无限相似边界元法由于在裂纹尖端的边界上设置了逼近于裂纹尖端的无限个相似边界单元,可直接得到裂纹尖端具有奇异性的应力,而不需要设置奇异单元,从而突破了奇异单元对应力奇异性阶次的局限.另外,还讨论了无限相似边界元法得到的无限阶的线性代数方程组的求解方法.