基于改进涡方法的膜结构流固耦合研究

采用改进涡方法对膜结构的流固耦合进行模拟。将非协调边界元计算势流的方法引入到传统涡方法中,即为改进涡方法。该算法可以精确计算三维粘性、不可压缩流场。采用改进涡方法可以得到每个时间步膜结构的单元节点流场压力,通过与ansys有限元模型提取出的整体刚度矩阵联合求解得到单元节点位移,并可以由单元节点位移求解出下一时间步的流场分布。由于本文引入了高效的预处理循环型广义极小残余迭代算法(GMRES),使得边界元法的优势得到了充分发挥,大幅度节省了计算时间。完成了方形平屋盖膜结构气弹模型风洞试验。采用本文算法对膜结构流固耦合效应计算得到的位移均值大部分与风洞试验吻合,计算结果表明本文提出的方法是模拟膜结构流固耦合问题的有益尝试。     

三维弹塑性接触边界元法对摩擦的处理

本文建立了三维弹塑性接触问题的边界元法。采用两种摩擦模型计算了轧制过程中弹塑性体和弹性体的接触变形过程，并对两种摩擦模型的计算结果进行了比较。计算结果表明两种摩擦模型均能很好地反映实际情况     

C/SiC陶瓷基复合材料界面力学性能的离散元模拟

采用离散元法(DEM),用BPM(Bonded-particle model)模型分别建立并校准SiC陶瓷基体和碳纤维离散元模型,采用位移软化接触模型表征层间和纤维/基体之间的界面元损伤双线性本构关系。通过DCB试验(Doub-le cantilever beam virtual test)和微滴脱黏试验分别对其界面强度进行收敛试验,动态地观察了塑性变形、裂纹扩展及界面脱黏过程。结果表明,位移软化接触模型可以很好地表征界面损伤过程,采用离散元法可以很好地动态模拟较复杂复合材料的损坏过程。     

刚柔耦合接触动态粘合算法研究

建立一种动态粘合算法,用于多体系统中刚体与弹性体或弹性体与弹性体接触问题的仿真。该算法通过装配矩阵和界面柔度矩阵构建接触界面粘合矩阵,用来传递接触力和位移,当接触位置改变时界面柔度矩阵和装配矩阵随之变化,粘合矩阵需要动态更新。利用该方法可以将刚柔耦合系统中相互接触的结构分成独立的子系统,分别在独立的程序或平台中进行分布式仿真。本文使用该方法进行刚体与弹性体接触仿真,和统一方程的刚柔耦合仿真结果基本一致。     

有间隙多层板接触分析的广义协调元法

从有间隙多层板接触系统分区广义势能泛函出发,以广义协调理论为基础,通过建立和分析板单元区、接触单元区的势能泛函,提出求解多层板接触问题的广义协调元法;并构造了广义协调矩形板-板接触单元PZC21。数值结果表明,单元PZC21具有较好的稳定性和收敛性。     

弹塑性接触边界元法模拟轧制过程

本文用作者开发的弹塑性接触边界元法首次模拟轧制过程。轧辊为弹性体,轧件为弹塑性体,视轧制为有摩擦的弹塑性接触问题,用最少的假定模拟了轧制过程,为分析轧制过程提供了一个有效而精确的数值解法。     

边界面法数值结果的云图表征

边界面法继承了传统边界元法的优点,并将几何实体的边界曲面离散为参数空间里的曲面单元,在处理一些特殊问题如移动边界、高梯度、大变形等方面显示出特殊的优越性。但是也使得计算结果的后处理遇到困难。提出了一种基于黎曼度量推进波前法生成三角背景网格的实用边界面法计算结果后处理方法。该法对求解域剖分成三角背景网格然后将计算结果映射到网格节点上,通过区域填充获得计算结果的云图。温度场的数值算例表明该方法可靠实用。     

具有曲面接触斑弹性体滚动接触理论及其数值方法

该文基于了Kalker三维弹性体非Hertz滚动接触理论模型,考虑滚动接触物体具有曲面接触斑,利用有限元法,推导出物体柔度系数,即力与位移之间的关系,将理论模型转化为数学上的非线性规划问题。结合拉格朗日乘子法,求解非线性方程组,从而得到接触斑力学行为。该模型是考虑曲面接触斑三维弹性体滚动接触理论模型,考虑了滚动接触物体的真实几何尺寸和接触区外边界因素对滚动接触行为的影响。为解决任何几何形状弹性体滚动接触问题提供了方法。该文主要对二维问题的数值模拟,所得数据结果较为合理。并结合商业有限元软件计算结果对静态问题进行对比验证,两种模型的分析结果吻合的较好。该文的模型和数值方法进一步完善后将适用于任意曲面接触斑滚动接触问题的求解。     

应力强度因子计算的样条虚边界元法

含有裂纹的工程结构在荷载作用时在裂纹尖端会产生应力奇异的现象,其严重的程度可用应力强度因子来表征。采用基于Kelvin基本解的样条虚边界元法,结合位移外推法,给出了断裂问题应力强度因子的求解方法。通过对两个典型断裂问题的分析,对边界子段与虚边界元的划分、小单元的采用以及拟合点位置的确定等关键问题展开了讨论,获得了相关计算参数的选取规律,为该法在断裂问题的进一步应用打下良好的基础。     

边界元法分析中的边界切向应力差分算法

在用边界元法作弹性应力分析中,不能直接计算出弹性体边界切向应力。本文在边界元法分析的基础上,用差分法计算边界切向应力。推导出常边界单元情况下边界切向应力的差分公式。计算表明文中所述方法是可行的,并且简单实用。所研究的方法和公式也适用于高次边界单元的边界切向应力的计算。     

Scattering of acoustic waves by movable lightweight elastic screens

This paper computes the insertion loss provided by movable lightweight elastic screens, placed over an elastic half-space, when subjected to spatially sinusoidal harmonic line pressure sources. A gap between the acoustic screen and the elastic floor is allowed. The problem is formulated in the frequency domain via the boundary element method (BEM). The Green's functions used in the BEM formulation permit the solution to be obtained without the discretization of the flat solid–ground interface. Thus, only the boundary of the elastic screen is modeled, which allows the BEM to be efficient even for high frequencies of excitation. The formulation of the problem takes into account the full interaction between the fluid (air) and the solid elastic interfaces.The validation of the algorithm uses a BEM model, which incorporates the Green's functions for a full space, requiring the full discretization of the ground. The model developed is then used to simulate the wave propagation in the vicinity of lightweight elastic screens with different dimensions and geometries. Both frequency and insertion loss results are computed over a grid of receivers. These results are also compared with those obtained with a rigid barrier and an infinite elastic panel.     

Dynamic analysis of interfacial crack problems in anisotropic bi-materials by a time-domain BEM

A time-domain boundary element method (BEM) together with the sub-domain technique is applied to study dynamic interfacial crack problems in two-dimensional (2D), piecewise homogeneous, anisotropic and linear elastic bi-materials. The bi-material system is divided into two homogeneous sub-domains along the interface and the traditional displacement boundary integral equations (BIEs) are applied on the boundary of each sub-domain. The present time-domain BEM uses a quadrature formula for the temporal discretization to approximate the convolution integrals and a collocation method for the spatial discretization. Quadratic quarter-point elements are implemented at the tips of the interface cracks. A displacement extrapolation technique is used to determine the complex dynamic stress intensity factors (SIFs). Numerical examples for computing the complex dynamic SIFs are presented and discussed to demonstrate the accuracy and the efficiency of the present time-domain BEM.     

An elastostatic FEM/BEM analysis of vertically loaded raft and piled raft foundation

In this paper, a static analysis of vertically loaded raft and piled raft foundations in smooth and continuous contact with the supporting soil is presented. In this approach the finite element method (FEM) and the boundary element method (BEM) are coupled: the bending plate is assumed to have linear elastic properties and is modelled by FEM while the soil is considered as an elastic half-space in the BEM. The pile is represented by a single element and the shear force along the shaft is interpolated by a quadratic function. The plate–soil interface is divided into triangular boundary elements (soil) also called cells and finite elements (plate) and the subgrade reaction is linearly interpolated across each cell. The subgrade tractions are eliminated from the FEM and BEM algebraic systems of equations, resulting in the governing system of equations for plate–pile–soil interaction problems. Numerical results are presented and they are close to those resulting from much more elaborate analyses.     

Efficient simulation of multi‐body contact problems on complex geometries: A flexible decomposition approach using constrained minimization

We consider the numerical simulation of non‐linear multi‐body contact problems in elasticity on complex three‐dimensional geometries. In the case of warped contact boundaries and non‐matching finite element meshes, particular emphasis has to be put on the discretization of the transmission of forces and the non‐penetration conditions at the contact interface. We enforce the discrete contact constraints by means of a non‐conforming domain decomposition method, which allows for optimal error estimates. Here, we develop an efficient method to assemble the discrete coupling operator by computing the triangulated intersection of opposite element faces in a locally adjusted projection plane but carrying out the required quadrature on the faces directly. Our new element‐based algorithm does not use any boundary parameterizations and is also suitable for isoparametric elements. The emerging non‐linear system is solved by a monotone multigrid method of optimal complexity. Several numerical examples in 3D illustrate the effectiveness of our approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Development of circular arc boundary elements method

The boundary element method (BEM) is a popular technique to solve engineering problems. We compare the circular arc elements (CAE) discretization to both linear and quadratic discretizations. The main aim of this paper is to determine analytical expressions for the discretization error in 2D BEM for the Laplace equation using CAE discretization. The results are validated by numerical examples.     

A time domain boundary element method for poroelasticity

The development of a general boundary element method (BEM) for two- and three-dimensional quasistatic poroelasticity is discussed in detail. The new formulation, for the complete Biot consolidation theory, operates directly in the time domain and requires only boundary discretization. As a result, the dimensionality of the problem is reduced by one and the method becomes quite attractive for geotechnical analyses, particularly those which involve extensive or infinite domains. The presentation includes the definition of the two key ingredients for the BEM, namely, the fundamental solutions and a reciprocal theorem. Then, once the boundary integral equations are derived, the focus shifts to an overview of the general purpose numerical implementation. This implementation includes higher-order conforming elements, self-adaptive integration and multi-region capability. Finally, several detailed examples are presented to illustrate the accuracy and suitability of this boundary element approach for consolidation analysis.     

Receding contact problem involving large displacements using the BEM

A new algorithm is presented for the boundary element analysis of the two-dimensional contact problem between elastic solids involving large displacements. The contact constraints are not applied node-on-node but node-on-element, using the element shape functions to distribute the geometry, displacements and tractions on each element in the contact zone. Thus, the discretizations performed along the two surfaces in contact need not necessarily be the same. The solution procedure is based on the updated Lagrangian approach and the resulting method is incremental. The algorithm guarantees equilibrium and compatibility at the nodes in the final deformed configuration and allows us to deal with problems undergoing large displacements without it being necessary to change the initial discretization of the boundary of the bodies. Only the frictionless static problem is dealt with, and the proposed algorithm is applied to the most representative receding contact problem: a layer pressed against an elastic foundation. The results obtained when the displacements are small are in good agreement with the analytical solution. When large displacements are considered, another nonlinearity appears and its influence will be shown in this paper.     

辐板型式和轮轨接触点位置对车轮声辐射特性的影响

为了分析不同车轮辐板型式和轮轨接触点位置对车轮声辐射特性的影响,建立了车轮有限元-边界元混合振动声辐射模型。首先,根据车轮实际拓扑结构建立三维实体有限元模型,采用分块Lanzos法求解结构的特征值问题,然后采用模态叠加法计算车轮结构在法向单位力激励下的动态响应,将车轮外表面的速度处理成声学边界元的输入,计算车轮的辐射噪声。数值计算中,考虑了S型、直型和波浪型三种辐板型式和轮缘、名义滚动圆处和车轮外侧三个轮轨接触点位置。结果表明,辐板型式和轮轨接触点位置对车轮声辐射具有较明显的影响。而且,不同辐板型式车轮在不同轮轨接触点位置下的声辐射特性也不尽相同。数值分析可以为低噪声车轮的选型提供一定的参考。     

Comparison of boundary and finite element methods for moving-boundary problems governed by a potential

Three formulations of the boundary element method (BEM) and one of the Galerkin finite element method (FEM) are compared according to accuracy and efficiency for the spatial discretization of two-dimensional, moving-boundary problems based on Laplace's equation. The same Euler-predictor, trapezoid-corrector scheme for time integration is used for all four methods. The model problems are on either a bounded or a semi-infinite strip and are formulated so that closed-form solutions are known. Infinite elements are used with both the BEM and FEM techniques for the unbounded domain. For problems with the bounded region, the BEM using the free-space Green's function and piecewise quadratic interpolating functions (QBEM) is more accurate and efficient than the BEM with linear interpolation. However, the FEM with biquadratic basis functions is more efficient for a given accuracy requirement than the QBEM, except when very high accuracy is demanded. For the unbounded domain, the preferred method is the BEM based on a Green's function that satisfies the lateral symmetry conditions and which leads to discretization of the potential only along the moving surface. This last formulation is the only one that reliably satisfies the far-field boundary condition.     

An analysis of solidification problems by the boundary element method

The problem of interest in this paper is the calculation of the motion of the solid–liquid interface and the time-dependent temperature field during solidification of a pure metal. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time-dependent Green's functions and convolution integrals. The BEM approach requires discretization of only the surface of the solidifying body. Thus, the numerical method closely follows the physics of the problems and is intuitively very appealing. The formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems. Emphasis is given to two-dimensional problems. Comparison with existing semi-analytical solutions and other numerical solutions from the literature reveals that the method is fast, accurate and without major time step limitations.