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。     

弹塑性有限变接触问题的边界元法

本文建立了弹塑性有限形变（大变形，大旋转）接触（考虑界面摩擦）问题的多重非线性边界元法，并计算机模拟了弹塑性体和弹性体的接触变形过程，可应用于精密轧制，精密塑性加工及铁路，水坝基础等工程领域。     

三维弹性体移动接触边界元法的一类新方案

基于对二维弹性体移动和滚动接触边界元法的前期研究,将其中的协调离散方案推广到三维问题,提出了针对给定移动方向的三维弹性体移动接触的一种边界元协调离散方案。其中在接触面上的位移和面力都能在边界元离散意义下精确满足,因此能保持边界元法在位移计算、特别是应力计算中高精度的优势。该方案将可能接触区分成大小相等的直角三角形单元,每个直角三角形单元有6个节点,其中3个角节点是固定节点,另外在每条边上有一可动节点。可动节点的位置确定于与其接触的另一面上对应单元的固定节点及其连线的位置。在每一瞬时,每个单元可由可动节点连线分成4个三角形子单元,在每个子单元上边界位移与面力线性分布。文中给出了一些算例来验证所提出算法的有效性和高精度。     

有摩擦弹性接触问题边界元分析的一种新方法

在将切向接触力与切向相对位移的关系表为带有惩罚因子的线性互补形式后,直接利用法向接触力与法向相对位移的互补关系,结合边界元技术,本文给出了一种新的求解有摩擦弹性接触问题的数学规划法。     

模态边界元法

本文介绍了用有限区域弹性体代替传统的无限区域弹性体建立边界方程基本解的思想。文中以有限弹性体模态的线性组合表示稳态基本解,建立了积分与激励频率无关的稳态边界元的直接表达式和间接表达式。其次文中提出了求解弹性系统固有频率和振型的设想,导出了边界元法特征方程。最后,文中以一维固有特性问题为例对原理、方法的正确性和精确度进行了检验,得到了不同边界条件下的固有频率和振型。文中所给数据表明与理论值吻合良好。     

三维热弹性力学问题的混合边界元法

本本文给出了三维无限大域内点热源作用下的位移、应力场基本解。采用基于虚拟热源法的间接边界元法和直接边界元法的混合边界元法求解三维有限域热弹性力学问题,有效地避免了热弹性力学问题中域内积分的处理。数值计算表明混合边界元法求热弹性力学问题具有简单方便、精度较高的优点。     

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。     

集中荷载下的边界元法

本文应用Betti互等定理,推导出弹性体边界和体内受有限个集中荷载作用时的边界元法,弥补了常规边界元法在处理集中荷载方面的不足。算例结果表明本文方法是有效的。     

高层建筑结构分析的边界元法

首先简述弹性力学平面问题分域样条虚边界元法的计算原理，该法可用于高层建筑平面结构（如框支剪力墙，联肢墙，框架－剪力墙等）的静力分析，为了能对高层建筑进行整体分析，进一步采用分域样条虚边界元法导出高层建筑侧向刚度矩阵，据此即可对高层建筑进行整体的静力和动力分析，文中给出若干工程算例，说明了方法的可行性和实用性。     

ELASTOHYDRODYNAMIC LUBRICATION ANALYSIS OF LAYERED LINE CONTACT BY THE BOUNDARY ELEMENT METHOD

This paper presents a numerical routine to compute the contact characteristics of elastomer layered cylinders lubricated by isoviscous liquids. The indentation of the elastic layer is calculated from boundary integral equations which are solved by linear and quadratic boundary element methods for a finite plane model and a circular representation of the junction. The hydrodynamic equation is also transformed into a boundary integral equation and solved by Simpson's rule. Some factors which possibly affect numerical accuracy are examined. Examples for finite plane and circular layer are analysed with reference to parameters for printing press roller contact, in which results are obtained for the indentation, film thickness and liquid pressure, as well as internal stresses through the simultaneous solution of the elasticity and hydrodynamic equations. The results show that high precision is easily achieved and the method is efficient for such layered problems.     

用样条边界元计算振动体的三维稳态声辐射

本文采用三次Ｂ样条边界单元计算振动体的三维稳态声辐射。实际计算表明：采用样条边界元可获得较好的数值计算结果。此外，本文在计算声场内点声压的Ｈｅｌｍｈｏｌｔｚ边界积分公式的基础上，导出了计算声场内点质点振速和声强的边界积分公式。文中还给出了应用本文方法计算的算例结果。     

R-ADAPTIVE BOUNDARY ELEMENT METHOD FOR UNSTEADY FREE-SURFACE FLOW ANALYSIS

An adaptive meshing based on the r-method is developed for two-dimensional unsteady non-linear flows with a free surface. Coupling of a boundary element equation and a weighted residual formulation of the pressure equation on the free surface is employed in solving the wave problems. A mesh optimization scheme is constructed for these two matrix equations. The final mesh distribution on the free surface is determined from the weighted average of these two adaptive meshes. Through numerical analyses of a non-linear sloshing problem and solitary waves in a tank, the influence of time interval of the remeshing and the weight factor for two adaptive meshes on the accuracy and efficiency of the proposed approach is investigated.     

AN INDIRECT BOUNDARY ELEMENT METHOD FOR PLATE BENDING ANALYSIS

An indirect Boundary Element Method is employed for the static analysis of homogeneous isotropic and linear elastic Kirchhoff plates of an arbitrary geometry. The objectives of this paper consists of a construction and a study of the resulting boundary integral equations as well as a development of stable powerful algorithms for their numerical approximation. These equations involve integrals with high-order kernel singularities. The treatment of singular and hypersingular integrals and a construction of solutions in the neighborhood of the irregular points on the boundary are discussed. Numerical examples illustrate the procedure and demonstrate its advantages. © 1997 by John Wiley & Sons, Ltd.     

虚拟裂缝模型的接触有限元法实现

沿裂缝可能开展路径设置接触点对,将求解接触问题的有限元混合自由度法进行扩展,以实现混凝土断裂力学虚拟裂缝模型的数值模拟。把作用在结构上的力系分解为外力和接触缝面上的接触力,以结构的位移为基本未知量,而以缝面局部坐标系下的结点接触力为迭代变量,将非线性接触迭代收缩在可能接触缝面上进行,提高了计算效率。计算过程中缝面接触力和开口位移可以显式地求出,故可方便地引入各种类型的混凝土软化本构关系,实现混凝土断裂力学虚拟裂缝模型的数值模拟。首先给出了有限元混合自由度法求解接触问题的基本思路,然后引入混凝土软化本构关系,最后以数值算例说明了该文方法的正确性和有效性。     

CONTINUITY AND COLLOCATION EFFECTS IN THE BOUNDARY ELEMENT METHOD

The presence of singularities in the integral operators of the boundary element methods requires that the density functions must satisfy certain continuity requirements if the displacements and stresses are to be bounded. Quite often the continuity conditions, particularly on the derivatives of the density functions, are relaxed at the element ends for the sake of simplicity in approximating the unknown density functions. In this paper, a numerical study on the effects of satisfying or violating the continuity requirements and the effect of the boundary condition collocating point on three different BEM formulations is presented. Two are indirect formulations using force singularities and displacement discontinuity singularities, and the third is Rizzo's direct formulation. The two integral operators in the direct BEM appear individually in the two different formulations of the indirect BEM. This makes it possible to study the numerical error and other problems in each integral operator and the interaction of the two integral operators in the direct BEM. The impact of the study on numerical modelling for the three BEM formulations is presented in the paper. © 1997 by John Wiley & Sons, Ltd.     

摩擦接触裂纹问题的扩展有限元法

扩展有限元法(XFEM)是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法。扩展有限元法分析闭合型裂纹时,必须考虑裂纹面间的接触问题。已有文献均采用迭代法求解裂纹面的接触问题。该文建立了闭合型摩擦裂纹问题的扩展有限元线性互补模型,将裂纹面非线性摩擦接触转化为一个线性互补问题求解,不需要迭代求解。算例分析说明了该方法的正确性和有效性,同时表明扩展有限元法结合线性互补法求解接触问题具有较好的前景。     

基于扩展有限元方法的界面接触算法

该文构建了适用于扩展有限元法(XFEM)的界面接触算法,该算法具备模拟界面上粘连、滑动和分离状态的能力.对平面摩擦问题的计算结果表明,该方法对于界面接触行为的描述能力与常规接触面单元十分接近.对平面应变压剪试样中剪切带问题的模拟分析表明,该算法合理地反映了摩擦接触的耗散机制,从而避免了零能耗散现象,能够较准确地描述平面...     

A FRICTIONAL CONTACT ELEMENT FOR STRONGLY CURVED CONTACT PROBLEMS

Based on a mixed formulation approach, a frictional contact element is proposed for the numerical solution of contact problems including strongly curved rigid obstacles. The implementation of the frictional contact element is analogous to that of a finite element. This feature facilitates its implementation in implicit finite element programmes, since the structure of the code need not be modified. For efficient modelling of the forming tool geometries by Computer Aided Geometric Design techniques and in order to achieve a high performance of the contact search, the numerical schemes of the frictional contact element operate directly on parametric polynomial surface patches. Thus, no discretization of curved contact surfaces is performed. Numerical simulations of deep drawing processes demonstrate the performance of the method in the case of large sliding increments upon curved tools and in the case of elasto-plasticity.