一种有限元-边界元耦合分域算法

提出了一种有限元-边界元耦合分域算法．该算法将所分析问题的区域分解成有限元和边界元子域,在满足两子域界面上位移和面力协调连续的条件下,通过迭代求解得到问题的解．在迭代求解过程中,引入动态松弛系数,使收敛得以加速．该方法在两子域界面上有限单元结点和边界单元结点的位置相互独立,无需协调一致,对诸如裂纹扩展过程的模拟具有独特的优势．用所提出的耦合算法分析算例,得到的结果与有限元法、边界元法和另一种耦合算法的数值计算结果一致,验证了这种算法的正确性和可行性．     

水下爆炸气泡与复杂弹塑性结构的相互作用研究

计及结构的弹塑性,将边界元法(BEM)与有限元法(FEM)耦合提出了气泡与弹塑性结构耦合动力学计算方法,并开发了全套的三维水下气泡分析程序（UBA）,计算值与实验值之间误差在10%以内．以水面舰船为例,将三维计算程序工程化．并分析了水下爆炸气泡载荷作用下船体的弹塑性响应,从船体结构典型单元上的应力时历曲线可以看出,在气泡坍塌时出现应力峰值,证实了气泡坍塌压力及射流引起的压力对舰船等结构造成严重毁伤．从气泡与舰船的相互作用中可以看出,舰船低阶垂向振型被激起,在气泡作用下呈鞭状运动,同时舰船随着气泡的膨胀和收缩作升沉运动,通过本文的分析得到了适合于工程应用的规律及结论．     

薄体结构温度场的高阶边界元分析

分析了二维问题边界元法3节点二次单元的几何特征,区分和定义了源点相对高阶单元的Ⅰ型和Ⅱ型接近度.针对二维位势问题高阶边界元中奇异积分核,构造出具有相同Ⅱ型几乎奇异性的近似核函数,在几乎奇异积分单元上分离出积分核中主导的奇异函数部分.原积分核扣除其近似核函数后消除几乎奇异性,成为正则积分核函数,并采用常规Gauss数值方法计算该正则积分;对奇异核函数的积分推导出解析公式,从而建立了一种新的边界元法高阶单元几乎奇异积分半解析算法.应用该算法计算了二维薄体结构温度场算例,计算结果表明高阶单元半解析算法能充分发挥边界元法优势,显著提高计算精度.     

计入气穴的水下爆炸作用下结构流固耦合三维数值模拟

水下爆炸在结构物面附近产生的气穴现象,严重影响水下爆炸作用下的流固耦合动响应,是舰船水下爆炸领域的难点,传统的边界元方法、有限元方法(FEM)难以解决水下爆炸气穴现象这类强非线性问题．针对此问题,计及流体中的气穴现象,考虑流体的可压缩型,忽略流体粘性,建立水下爆炸瞬态强非线性流固耦合三维数值模型,采用流体谱单元方法(SEM)和结构有限元方法求解该模型．计算结果表明:相对有限元法,谱单元法具有更高的计算精度,且谱单元解与解析解、试验值吻合良好．在此基础上,结合ABAQUS软件,分别探讨三维球壳、船体板架在水下爆炸作用下的瞬态流固耦合机理,给出气穴区域及其对水中结构物动响应的影响特征,旨在为舰船水下爆炸瞬态流固耦合问题的相关研究提供参考．     

正交各向异性半平面内作用集中载荷的弹性解及边界元法常单元基本公式

本文采用镜相法,推导出了正交各向异性半平面作用集中载荷的理论解,给出了常单元系数矩阵表达式,为采用边界元法求解半平面问题提供了必要的公式.特解表达形式简洁,对边界元间接法常单元和高次单元各积分均可求出其原函数,可避免计算程序中的定积分数值计算过程.     

三维快速多极边界元法分析地埋管群传热问题北大核心CSCD

基于三节点三角形线性单元,为克服单元跨叶子积分难题,将三维位势问题快速多极边界元法与几乎奇异积分的半解析算法相结合,实现了三维边界元法中几乎奇异积分的准确计算,该方法适用于U型地埋管薄体结构的换热分析.在制冷、制热两种工况下研究了U型地埋管壁厚对换热量的影响,并进一步分析了管群间的热相互作用.计算结果显示,当管壁导热系数一定时,管壁越厚,对管内流体和土壤之间的换热影响越大.当钻孔间距一定时,管群中埋管数量越多,热干扰现象越强烈,提高管群换热量的主要措施是降低管群间热干扰.因准确计算了几乎奇异积分,三维快速多极边界元法可以有效计算薄体和厚体耦合的三维热传导问题.该文方法和分析结果可为地埋管换热器系统的工程应用提供参考.     

关于无界区域和非齐次问题的无限元法

<正> 无限相似单元法(简称无限元法)是一种计算有奇点的椭圆型方程的近似解的方法.如果奇点是边界上的一个角点,那末它是有界区域上的无限元法,如果奇点是无穷远点,那末它是无界区域上的无限元法.Babu(s|ˇ)ka 曾经研究过无界区域上的有限元法,由于只有有限个自由度,因此求解区域不能不是有界的,尽管这个区域可以很大.现在,我们用无限元法处理这一类问题.我们证明了在无界区域上各种无限元方法解的存在唯一性.     

插值型无单元Galerkin比例边界法与有限元法的耦合在压电材料断裂分析中的应用

插值型无单元Galerkin比例边界法是一种只需在边界上采用插值型无单元Galerkin法离散且无需基本解的半解析方法,能有效求解压电材料的断裂问题.为进一歩提高这种方法的适用性,该文提出了一种用于压电材料断裂分析的插值型无单元Galerkin比例边界法耦合有限元法(finite element method,FEM)的分析方法.裂纹周边一定范围的计算域采用插值型无单元Galerkin比例边界法离散,其余区域采用FEM离散.插值型无单元Galerkin比例边界法方程和FEM方程的耦合可利用界面两侧广义位移的连续条件方便地实现.最后,给出了两个数值算例验证了该文所提方法的有效性.     

多裂纹问题计算分析的本征COD边界积分方程方法

针对多裂纹问题，若采用常规的数值求解技术，计算效率较低.为实现多裂纹问题的大规模数值模拟，建立了本征裂纹张开位移（crack opening displacement, COD）边界积分方程及其迭代算法，并引入Eshelby矩阵的定义，将多裂纹分为近场裂纹和远场裂纹来处理裂纹间的相互影响.以采用常单元作为离散单元的快速多极边界元法为参照，对提出的计算模型和迭代算法进行了数值验证.结果表明，本征COD边界积分方程方法在处理多裂纹问题时取得较大的改进，其计算效率显著高于传统的边界元法和快速多极边界元法.     

弹性动力问题的有限元与特解边界元耦合的数值方法

导出了特解边界元法与有限元法的耦合方程。并应用自由度缩减技术,使耦合方程的自由度缩减到有限元域及其和边界元域的耦合边界上。这样得到的耦合方程不增加原有限元方程的带宽和阶数。耦合方程的求解可以引用求解有限元方程的所有方法,易于程序实现。数值算例结果表明,本文所提出的方法是正确的,是一种较为理想的耦合方法。     

Recent progresses in studies on wave-current loads on foundation structure with piles and slab?

The foundation structure with piles and slab is widely used in o?shore wind farm construction in shallow water. Experimental studies on the hydrodynamic loads acting on the piles and slab under irregular waves and currents are summarized with discussion on the e?ects of pile grouping on the wave forces and wave impact loads on the slab locating near the free surface. By applying the theoretical solution of the wave di?racted by the slab and using the Morison equation to evaluate the wave force on the piles, the e?ects of the slab on the wave forces acting on the piles are analyzed. Based on the Reynolds-averaged Navier-Stokes (RANS) equations and the volume of ?uid (VOF) method, a numerical wave basin is developed to simulate the wave-structure interaction. The computed maximum wave force on the foundation structure with piles and slab agrees well with the measured data. The violent deformation, breaking, and run-up of the wave around the structure are presented and discussed. Further work on the turbulent ?ow structures and large deformation of the free surface due to interaction of the waves and foundation structures of o?shore wind farms needs more e?cient approaches for evaluating hydrodynamic loads under the e?ects of nonlinear waves and currents.     

桩基承台结构的波流力研究进展

我国近海风电场建设大多采用桩基承台结构．总结了不规则波浪和水流共同作用下桩基承台结构的波流力物理模型实验结果,得到了群桩效应系数及其变化规律,讨论了作用于近水面承台底部的波浪拍击力;从理论上分析了规则波作用下承台对桩基波浪力的影响;建立了规则波与桩基承台相互作用的数值模型,揭示了波浪在承台的上浪与爬高及其水动力特征．鉴于桩基承台结构包含多个斜桩和较大尺度的承台,在波浪与水流作用下该结构物附近的流场结构十分复杂,有必要针对结构附近的流动结构以及自由表面大变形开展细致的实验和数值模拟研究,以进一步揭示作用于这类结构的波流力变化规律及其机理.     

The stress field problem for a pre-stressed plate-strip with finite length under the action of arbitrary time-harmonic forces

In the framework of the three-dimensional linearized theory of elastodynamics the finite element modeling of the stress field problem for the pre-stressed plate-strip with finite length resting on a rigid foundation under the action of inclined linearly located time-harmonic forces is developed. The numerical results involving the normal stress acting on the interface plane of the plate-strip and the rigid foundation are presented. Moreover, the dependencies between this stress, the frequency of the arbitrary inclined linearly located external force and the initial stretching of the plate-strip are analyzed.     

Modeling of electrodynamic-mechanical coupling phenomena in smart magnetoelectroelastic materials

The coupling of electric, magnetic and mechanical phenomena may have various reasons. The famous Maxwell equations of electrodynamics describe the interaction of transient magnetic and electric fields. On the constitutive level of dielectric materials, coupling mechanisms are manyfold comprising piezoelectric, magnetostrictive or magnetoelectric effects. Electromagnetically induced specific forces acting at the boundary and within the domain of a dielectric body are, within a continuum mechanics framework, commonly denoted as Maxwell stresses. In transient electromagnetic fields, the Poynting vector gives another contribution to mechanical stresses. First, a system of transient partial differential equations is presented. Introducing scalar and vector potentials for the electromagnetic fields and representing the mechanical strain by displacement fields, seven coupled differential equations govern the boundary value problem, accounting for linear constitutive equations of magnetoelectroelasticity. To reduce the effort of numerical solution, the system of equations is partly decoupled applying generalized forms of Coulomb and Lorenz gauge transformations [1,2]. A weak formulation is given to establish a basis for a finite element solution. The influence of constitutive magnetoelectric coupling on electromagnetic wave propagation is finally demonstrated with a simple one-dimensional example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model of primary production,including circulation influences,in Lake Superior

The flow regimes of Lake Superior in 1973 have been computed by a finite difference hydrodynamical model. The results confirm the observed general anticlockwise circulations during the summer stratification period. Preliminary results from experiments using a variable wind drag coefficient are included. This coefficient depends on a number of factors, including wave age, wind-wave coupling and station exposure.A two-compartment phosphorus model was also developed. The biological model was coupled with the water transport to elucidate the observed temporal and spatial changes in the nutrient conditions and primary productivity. The simulations show that temperature and nutrient distributions are influenced by current patterns, which in turn influence biological activity.     

Dynamic modeling and analysis of wind turbine drivetrain considering the effects of non-torque loads

With the increase of the rotor diameter and the deterioration of operating conditions, modern wind turbines suffer from more and more significant time-varying non-torque loads, which increases the burden of turbine structures especially the gearbox. Based on an aeroelastic loose coupling approach and assembly of the finite element method, an integrated drivetrain coupling analysis model including blade module, aerodynamic module, and gearbox module is established in this study. This proposed model is validated by comparing the calculation results with previous literature. Taking National Renewable Energy Laboratory 5-MW wind turbine as the research object, the gearbox vibration responses, gear meshing forces and bearing forces under non-torque loads caused by blade gravity, wind shear (WS), tower shadow (TS) and yawed inflow are studied in detail. Results show that the y-direction displacements of the gearbox, sun gear 1, sun gear 2 and gear are larger than those in x-direction because F_y or M_x generated by blade gravity, WS and TS dominates the non-torque loads. The non-torque loads lead to a non-uniform planet load sharing especially for the planetary gear stage 1. Because of the fluctuations of non-torque loads, not only the rotation frequencies of the corresponding carrier but also the multiple frequencies of the carrier 1 are observed in the frequency spectrums. The non-torque loads are mainly borne by carrier 1 bearings. Except for the blade gravity, the bearing forces caused by other unsteady inflows have obvious fluctuations.     

多个同频摇荡剖面引起的水面波辐射

在内场中使用简单Green函数的边界元方法与外场的速度势特征函数展开式相结合,用于求解多个同频摇荡剖面引起的水面波辐射问题的频域解·　方法适用于外场为定深的水域以及内场的复杂边界条件,各剖面的摇荡模态、幅值和相位可以互不相同·　利用摄动展开完整地求解了流场的二阶速度势和各个剖面所受的一、二阶水动力·　与单个剖面的情况相比,数值结果证实了多个剖面辐射引起的诸如水波共振和负附加质量等水动力干扰现象,这对于多体结构的锚泊系统和其它海洋工程设施的设计是很重要的·     

Energetic BEM-FEM coupling for the numerical solution of the damped wave equation

Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for the coupling of boundary integral equations and hyperbolic partial differential equations related to wave propagation problems, we consider here an extension for the damped wave equation in layered media. A coupling algorithm is presented, which allows a flexible use of finite element method and boundary element method as local discretization techniques. Stability and convergence, proved by energy arguments, are crucial in guaranteeing accurate solutions for simulations on large time intervals. Several numerical benchmarks, whose numerical results confirm theoretical ones, are illustrated and discussed.     

Coupled FEM-BEM for elastoplastic contact problems using Lagrange multipliers

The coupling of the elastoplastic finite element and elastic boundary element methods for two-dimensional frictionless contact stress analysis is presented. Interface traction matching (boundary element approach), which involves the force terms in the finite element analysis being transformed to tractions, is chosen for the coupling method. The analysis at the contact region is performed by the finite element method, and the Lagrange multiplier approach is used to apply the contact constraints. Since the analyses of elastoplastic problems are non-linear and involve iterative solution, the reduced size of the final system of equations introduced by combining the two methods is very advantageous, especially for contact problems where the nature of the problem also involves an iterative scheme.     

Nonlinear finite element analyses of concrete bridge joint systems subjected to seismic actions

Following widespread damage to bridge joints in the San Francisco region from the 1989 Loma Prieta earthquake, the necessity for establishing an alternative method for seismic design of bridge joints was identified. Recognizing that conventional joint design practice based directly on shear forces results in congested reinforcement details, which are difficult to implement in practice, a rational design procedure was sought through large-scale testing of bridge joint systems and subsequent finite element and strut-and-tie analyses. The finite element part of the study is presented in this paper, which focuses on (a) identification of compression force flow and thus the load path across the joint, (b) examination of an efficient joint force transfer model, and (c) influence of cap beam prestressing. Combining the experimental and analytical results, a joint design method has been established in which reduction of joint reinforcement was achieved by treating joint shear as part of the complete force transfer across the joint, rather than as an independent action. The proposed design approach has been validated in a laboratory test on a full-scale multiple-column bridge bent.