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。     

边界积分方程——非连续边界元度散方法及其应用

利用非连续元离散边界积分方程,有效地解决了“角点效应”问题,对影响非连续元精度和分析效率的几个问题从数值计算的角度进行了讨论,将非连续边界元用于自适应边界元分析,给出了自适应边界元误差指示确定的一种方法,通过对具体实例分析表明了给所方法的可行性,。》     

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。     

线性蠕变问题的摄动边界元-有限元方法

本文将摄动、边界元、有限元方法结合起来,提出一种求解线性蠕变问题的新方法。该方法不采用一般增量法中在一个时段内各物理量保持不变或作线性变化的假设,加大了计算步长提高了精度。文中构造了边界元摄动格式,构造了包含钢筋在内的边界元有限元耦合摄动格式,并给出了满意的数值结果。     

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。     

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．     

一种改进格林元方法及在渗流问题中的应用

采用格林公式和基本解推导出直接边界积分方程来求解渗流问题.边界积分方程数值离散基于格林元方法(Green element methond),改进了原方法中压力和压力导数的求解方法,命名为混合边界元方法(Mixed boundary element method).相较于格林元类方法,该方法显式考虑了求解节点的外法向流量值和压力值,并使求得的数值解在求解区域上能够连续,符合实际的物理过程,在不增加额外未知数的情况下提高了计算精度.分析了不同网格类型对模拟计算结果的影响,并对稳定渗流问题、非稳定(瞬态)渗流问题和非稳态问题进行了实例计算,结果显示改进方法提高了计算精度,并对各类渗流问题有较好的适应性.     

薄板振动特征值问题的一种改进积分方程解法

本文根据一种改进的边界元/有限元混合法求解薄板振动固有频率问题,既避开了标准的边界元法所导致的求解非代数特征值方程的困难,亦能够基本上消除通常的边界元/有限元混合法结果精度受区域内部单元划分影响较大的弊端。文中讨论了迭代算法的收敛问题,并用于薄板固有频率分析。数值结果表明,即便是在域内单元很粗疏划分的情况下,本文的方法仍能给出相当满意的结果。     

轴对称组合弹性体初应力分析的边界元传递矩阵法

基于边界元与传递矩阵法耦合基础上，提出了一种分析轴对称组合弹性体初应力的新方法。利用边界元和传递矩阵进行分域计算轴对称组合弹性体的初应力，无需在整个结构上进行矩阵组装，只需在轴对称子午面的边界上进行离散。故该方法具有输入数据少，计算精度高及所需计算机内存小等优点，适合在微机上求解大型复杂轴对称组合结构问题。文中给出了一个组合厚壁圆筒的计算实例，分别与有限元解和理论解进行比较；结果表明：本文所提出的     

FEM‐BEM coupling for the exterior Stokes problem with non‐conforming finite elements and an application to small droplet deformation dynamics

A non‐conforming, discontinuous Galerkin finite element–boundary element coupling procedure is presented for the exterior planar Stokes problem. The novel coupled formulation is developed using that for the conforming case as a guide to the introduction of extra mortar variables used to couple a discontinuous interior finite element solution with a continuous exterior boundary element solution. Convergence results for the new scheme are presented, for a range of different interior penalties, on computational domains discretized with regular structured meshes. To illustrate an application, the excitations required to model two‐phase droplet deformations in an extensional flow, under simple surface tension, with the new scheme are also presented. For a selection of different drop viscocities and exterior flows, with and without a rotational component, the progression to a steady‐state deformation of initially undeformed circular drops is calculated and the results compared with those from both a conforming FEM‐BEM equivalent scheme and from a small perturbation analysis where available. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Coupling of assumed stress finite element and boundary element methods with stress-traction equilibrium

In this study, the stress based finite element method is coupled with the boundary element method in two different ways. In the first one, the ordinary distribution matrix is used for coupling. In the second one, the stress traction equilibrium is used at the interface line of both regions as a new coupling process. This new coupling procedure is presented without a distribution matrix. Several case studies are solved for the validation of the developed coupling procedure. The results of case studies are compared with the distribution matrix coupling, displacement based finite element method, assumed stress finite element method, boundary element method, ANSYS and analytical results whenever possible. It is shown that the coupling of the stress traction equilibrium with assumed stress finite elements gives as accurate results as those by the distribution matrix coupling.     

The discontinuous profile method for simulating two‐phase flow in pipes using the single component approximation

Godunov‐type algorithms are very attractive for the numerical solution of discontinuous flows. The reconstruction of the profile inside the cells is crucial to scheme performance. The non‐linear generalization of the discontinuous profile method (DPM) presented here for the modelling of two‐phase flow in pipes uses a discontinuous reconstruction in order to capture shocks more efficiently than schemes using continuous functions. The reconstructed profile is used to define the Riemann problem at cell interfaces by averaging of the components of the variable in the base of eigenvectors over their domain of dependence. Intercell fluxes are computed by solving the Riemann problem with an approximate‐state solver. The adapted treatment of boundary conditions is essential to ensure the quality of the computational results and a specific procedure using virtual cells at both extremities of the computational domain is required. Internal boundary conditions can be treated in the same way as external ones. Application of the DPM to test cases is shown to improve the quality of computational results significantly. Copyright © 2001 John Wiley & Sons, Ltd.     

裂缝分析的比例边界有限元与有限元耦合的虚拟结构面模型

比例边界有限元法SBFEM(Scaled Boundary Finite Element Method)是一种半解析数值方法,在裂缝分析特别是强度因子计算上具有相当高的精度。本文提出了一种用于裂缝分析的基于虚拟结构面的SBFEM与常规FEM的耦合分析方法。首先选取裂缝周边一定范围的计算域,并将结构分成不含裂缝区域和含裂缝区域两部分。然后,对不含裂缝区域,采用FEM进行网格离散;对含裂缝区域,采用SBFEM进行网格离散;两者相互独立,在这两个域内,分别采用各自相应的位移模式。最后通过在SBFEM网格的外边界设置虚拟耦合结构面的模式,实现有限元网格和比例边界有限元网格的耦合。通过两个经典的含裂缝平板的算例研究,探讨了本文方法在I型开裂和混合型开裂分析中,影响应力强度因子精度的因素。算例表明,SBFEM具有的降维和半解析性质,使本文方法在裂缝分析中的前处理简单易行,且计算结果具有相当高的计算精度。     

近场动力学最小二乘和有限元耦合方法研究

准确高效地对损伤和断裂问题进行建模是计算力学中的关键研究课题之一。将近场动力学最小二乘在处理含裂纹等非连续问题上的优势和有限元计算效率高及便于施加边界条件的优势结合,提出了近场动力学最小二乘和有限元耦合方法。将裂纹及其可能扩展区域划分为近场动力学区域,边界及其他区域划分为有限元区域,并将其中的结点类型分为近场动力学结点和有限元结点。有限元结点仅与同单元中的其他结点产生作用,近场动力学结点则与其族内的所有结点产生作用。将以上的单元刚度矩阵和质量矩阵进行组装得到整体刚度矩阵和整体质量矩阵。本文的耦合方法数值实现简单有效,相对于键基和常规态基近场动力学,该耦合方法包含了应力和应变的概念,同时不受零能模式的影响。一维和二维静态和动态问题的研究,验证了本文的耦合方法的有效性和准确性。     

有限覆盖径向点插值方法理论及其应用

数值流形方法能够统一地处理连续与非连续变形问题,有限覆盖技术是这种方法的核心。无网格方法前处理过程比较简单,径向点插值法是其中的一种计算格式。本文将有限覆盖技术与径向点插值方法相结合发展了有限覆盖径向点插值无网格方法,综合了数值流形方法与点插值方法的各自优点,能够有效地处理连续与非连续性问题,由此所构造的形函数具有Kronecker δ-函数属性,能够有效地处理位移边界条件。本文在阐述了这种方法基本原理的基础上,通过算例分析与数值计算论证了本文所建议方法的可靠性及其有效性。     

VISCOUS FLOWFIELD BASED ON DISCONTINUOUS BOUNDARY ELEMENT METHOD AND VORTEX METHOD

基于非协调边界元方法和涡方法的联合应用, 模拟了二维和三维黏性不可压缩流场. 计算中利用离散涡元对漩涡的产生、凝聚和输送过程进行模拟, 并将整体计算域分解为采用涡泡模拟的内部区域和用涡列模拟的数字边界层区域. 计算域中涡量场的拉伸和对流由Lagrangian涡方法模拟, 用随机走步模拟涡量场的扩散. 内部区域涡元涡量场速度由广义Biot-Savart公式计算, 势流场速度则采用非协调边界元方法计算. 非协调边界元将所有节点均取在光滑边界处, 从而避免了法向速度的不连续现象; 而对于系数矩阵不对称的大型边界元方程组,引入了非常高效的预处理循环型广义极小残余(the generalized minimum residual, GMRES)迭代算法, 使得边界元法的优势得到了充分发挥, 同时, 在内部涡元势流场计算中对近边界点采用了正则化算法, 该算法将奇异积分转化为沿单元围道上一系列线积分, 消除了势流计算中速度及速度梯度的奇异性. 二维、三维流场算例证明了所用方法的正确性, 也验证了该算法可以大幅度提高模拟精度和效率.