基于组合时间积分算法的碰撞问题振荡现象修正

该文提出了一种能够有效改善碰撞问题振荡现象的修正方法。基于有限元方法，采用Lagrange乘子法施加接触约束条件，并与一种无条件稳定的隐式组合时间积分算法相结合对无摩擦动接触问题进行求解。通过引入附加Lagrange乘子对组合时间积分算法得到的速度和加速度进行修正，使其能够满足速度和加速度形式的接触约束的一致性条件。数值算例结果表明：该文提出的修正方法能够有效地改善碰撞问题中初始接触时速度、接触力等的振荡现象，进一步提高了碰撞问题的求解精度。     

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。     

求解摩擦接触问题的IGA-B可微方程组方法

该文将等几何分析(Isogeometric analysis,简称IGA)和B可微方程组方法相结合,提出了求解弹性摩擦接触问题的IGA-B可微方程组方法。其中,接触边界的几何形状由非均匀有理B样条(NURBS)精确描述;接触条件则表示成B可微方程组的形式,可被严格满足,且在一定条件下求解该方程组的算法收敛性有理论保证。数值算例验证了该文方法用于求解弹性摩擦接触问题的有效性,计算精度较高,通过与ANSYS软件中的接触模型相比,计算自由度数可以大量节约。     

显式有限元方法求解二维壳体塑性大变形接触问题

本文系统论述了二维壳体塑性大变形接触问题的显式有限元求解方法，包括退化壳单元理论、弹塑性本构方程、应力回映算法、接触搜寻法及计算接触力的拉格朗日乘子法。本文方法已成功地应用到薄板成形过程的有限元分析之中，文中给出了几个计算实例，计算结果与实验结果相当吻合。     

动接触问题及其数值模拟的研究进展

本文试图对近二十年来,动接触问题的理论及数值计算方法进行全面系统地总结。动接触问题是接触力学领域里的新课题。近年来出现了许多关于这个问题的数值计算方法,包括：（１）Ｌａｇｒａｎｇｅ乘子法,罚方法,振动Ｌａｇｒａｎｇｅ乘子法,增广Ｌａｇｒａｎｇｅ乘子法;（２）线性补偿方法;（３）接触单元法：（４）动接触力法：（５）冲量模型,动接触模型,初始位移法等。本文首先总结了动接触问题的基本控制方程和动接触条件,然后—一陈述了上述方法的基本思想,展示其数值计算结果,并进行评述。最后对进一步的研究工作和工程应用提出了几点建议。     

基于线性互补问题的多体系统接触/碰撞动力学研究

多体系统往往包含大量的接触/碰撞行为,这些非光滑事件的存在造成了动力学方程的不连续或分段连续,给数值求解带来了很大的困难。为综合考虑平顺接触与碰撞,采用基于线性互补问题的非光滑动力学方法,首先在当前时刻为起点的短时间内对对缝隙函数进行均匀化,然后与法向接触力建立标准线性互补方程,最后将线性互补方程改造为一组非线性代数方程,通过非线性迭代可直接求解接触力。算例结果表明,采用该方法不需在接触状态发生改变时切换模型,且严格满足互补关系,保证了接触力的非负性。研究成果可成为求解多柔体系统接触/碰撞问题的新途径。     

钢筋混凝土异形柱双向偏心承载力高效算法与程序设计

异形柱结构的发展需要一种高效、精确的承载力求解方法。目前常用的数值积分方法是将截面剖分成二维网格来进行求解,这种方法虽然比较精确,但往往存在计算速度与计算精度之间的矛盾,尤其是计算包含大量构件的结构体系。针对这一问题提出了新的截面数值积分算法。新算法采用特殊的单元剖分技术,实现了有限元法与单元内部解析求解法的有机结合,并且通过构造新的迭代变量加速了迭代运算的过程。与以往算法的对比分析表明,新算法具有更高的运算速度、运算精度以及更为广泛的适用性。     

改进迭代过程的车轨耦合振动数值解法及应用

针对列车-轨道耦合振动迭代求解过程,结合Newmark-β积分格式,提出一种基于有限元法与非线性接触理论的改进迭代过程数值解法。考虑分别建立车辆系统和轨道系统振动方程,在耦合和解耦迭代过程中,构造松弛因子函数和收敛准则函数,简化轮轨界面协调适应条件,利用轮轨相互作用力在两子系统之间的快速迭代实现动态耦合关系的高效求解。此算法增强了对迭代收敛精度、迭代过程稳定性的控制,同时也减小了程序设计的难度。应用此算法分别对竖错和路基沉降两类典型线路缺陷引起的车轨振动响应进行了算例对比和分析,计算结果表明,改进解法在迭代速度和迭代稳定性上具有优势,可广泛应用于高速铁路车辆运行和轨道结构动力学问题的分析中。     

动力学方程的解析逐步积分法

提出了求解动力学方程的一个新型的逐步积分法。基于动力学方程的解析齐次解,构造出动力学方程解的一般积分表达式,借助于显式、自起动、预测－校正的单步四阶精度的积分算法,离散方程右端的等价荷载项,给出了一个新的解析逐步积分方法格式。如果用分块求解,其刚度阵、质量阵等将有较小的规模,将使计算效率更高。算例表明本文方法比中心差分法、Ｎｅｗｍａｒｋ、Ｗｉｌｓｏｎ－θ、Ｈｏｕｂｏｌｔ法等有较高的精度,本文结果更接近解析解。本文方法也适用于非线性,因为本计算格式是显示,因此不需要迭代求解。     

求解线接触弹流润滑完全数值解的多重网格重复合直接迭代法

本文将近来发展起来的一种新型数值计算技术一多重网格法引入求解线接触弹流润滑问题，并将求解弹流润滑中的的迭代模式－复合直接迭代模式与多重网格法相结合，使求解过程既快又稳定，精度又高，该方法可推广到其它耦合场问题的数值求解。     

Polygon‐based contact resolution for superquadrics

The representation of discrete objects in the discrete element modelling is a fundamental issue, which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems. Disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency, but they are unable to provide resistance to rolling motion. For this reason, some non‐circular/spherical objects, such as polygons/polyhedrons, superquadrics, or the clustering of disks/spheres to form irregular shapes, are introduced. When superquadrics are used as discrete elements, the bottleneck of contact resolution is associated with the searching for intersections of two non‐linear functions, which is a very expensive operation and may sometimes fail in finding the solution. In this work, an efficient and robust algorithm is proposed for contact resolution of 2D superquadrics, in which any superquadric is approximated with a convex polygon through adaptive sampling; then by clipping two polygons, an efficient linear algorithm is performed to search for intersections and overlap area of the polygons; the contact forces and directions are determined by employing a newly established corner/corner contact model. It is important to highlight that the proposed methodology can also be extended to general non‐circular discrete object cases. The performance of the algorithm is demonstrated via numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.     

A frictional spring and cohesive contact model for accurate simulation of contact forces in numerical manifold method

“Open-close iteration” is a crucial algorithm for handling complex contacts in numerical manifold method (NMM) and discontinuous deformation analysis (DDA). This algorithm has proved to be robust and efficient for decades. However, as some researchers have pointed out, the original open-close iteration may involve errors in sliding tests, especially in critical sliding tests with cohesive contacts. In this study, two major problems in the original algorithm are found to be nonconvergent contact force and early removed cohesive strength. The modifications are the following: (a) a frictional spring. By avoiding the trail value of normal contact force, we added a new frictional spring to the iteration scheme. This spring can apply accurate friction and can help ensure the convergence of contact forces. (b) A cohesive contact model. The original scheme can encounter an “early failure” in cohesive contacts. After investigating how contacts provide shear resistance, we found the cause and then provided a simple correction of the cohesive issue. The new algorithms in this article are essential for accurately simulating contacts by NMM/DDA.     

A monolithic smoothing‐gap algorithm for contact‐impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact‐impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact‐impact. The smoothed signed distance functions are constructed by a moving least‐squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright © 2002 John Wiley & Sons, Ltd.     

An accurate and robust contact detection algorithm for particle‐solid interaction in combined finite‐discrete element analysis

When applying the combined finite‐discrete element method for analysis of dynamic problems, contact is often encountered between the finite elements and discrete elements, and thus an effective contact treatment is essential. In this paper, an accurate and robust contact detection algorithm is proposed to resolve contact problems between spherical particles, which represent rigid discrete elements, and convex quadrilateral mesh facets, which represent finite element boundaries of structural components. Different contact scenarios between particles and mesh facets, or edges, or vertices have been taken into account. For each potential contact pair, the contact search is performed in an hierarchical way starting from mesh facets, possibly going to edges and even further to vertices. The invalid contact pairs can be removed by means of two reasonable priorities defined in terms of geometric primitives and facet identifications. This hierarchical contact searching scheme is effective, and its implementation is straightforward. Numerical examples demonstrated the accuracy and robustness of the proposed algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

An X‐FEM approach for large sliding contact along discontinuities

The extended finite element method (X‐FEM) has been developed to minimize requirements on the mesh design in a problem with a displacement discontinuity. This advantage, however, still remains limited to the small deformation hypothesis when considering sliding discontinuities. The approach presented in this paper proposes to couple X‐FEM with a Lagrangian large sliding frictionless contact algorithm. A new hybrid X‐FEM contact element was developed with a contact search algorithm allowing for an update of contacting surfaces pairing. The stability of the contact formulation is ensured by an algorithm for fulfilling Ladyzhenskaya‐Babuska‐Brezzi (LBB) condition. Several 2D simple examples are presented in this paper in order to prove its efficiency and stability. Copyright © 2008 John Wiley & Sons, Ltd.     

A new algorithm for contact detection between spherical particle and triangulated mesh boundary in discrete element method simulations

In discrete element method (DEM) simulations of real scale, the spherical particles are commonly employed for increasing the computation speed, and the complex boundary models are represented by triangle meshes with controllable accuracy. A new contact detection algorithm has been developed to resolve the contacts between the spheres and the triangle mesh boundaries. The application of the barycentric coordinates makes this algorithm more efficient to identify contacts in the intersection test. As a particle probably collides with several triangles at the same time, the multiple contacts would be reported as face contacts, edge contacts, or vertex contacts. Moreover, the particle embedding in a triangle can be also contact with the edges or vertices of the next triangles. These contacts should be considered as invalid for updating contact forces in the DEM. To exclude invalid records from the multiple contacts, the algorithm gives attention to the mesh structure nearby contacts and analyzes all possible collision situations. Numerical experiments have been conducted to verify this algorithm by using the algorithm in the DEM simulation framework. The numerical results suggest that the algorithm can resolve all contacts precisely and stably when the spherical particles collide on the complex boundary circumstances. Copyright © 2013 John Wiley & Sons, Ltd.     

A phase-field method for modeling cracks with frictional contact

We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (i) it can represent arbitrary crack geometry without an explicit function or basis enrichment, and (ii) it does not require an algorithm for imposing contact constraints. The first feature, which is common in phase-field models of fracture, is attained by regularizing a sharp interface geometry using a surface density functional. The second feature, which is a unique advantage for contact problems, is achieved by a new approach that calculates the stress tensor in the regularized interface region depending on the contact condition of the interface. Particularly, under a slip condition, this approach updates stress components in the slip direction using a standard contact constitutive law, while making other stress components compatible with stress in the bulk region to ensure nonpenetrating deformation in other directions. We verify the proposed phase-field method using stationary interface problems simulated by discrete methods in the literature. Subsequently, by allowing the phase field to evolve according to brittle fracture theory, we demonstrate the proposed method's capability for modeling crack growth with frictional contact.     

Vertex‐to‐face contact searching algorithm for three‐dimensional frictionless contact problems

This article presents a new vertex‐to‐face contact searching algorithm for the three‐dimensional (3‐D) discontinuous deformation analysis (DDA). In this algorithm, topology is applied to the contact rule when any two polyhedrons are close to each other. Attempt is made to expand the original contact searching algorithm from two‐dimensional (2‐D) to 3‐D DDA. Examples are provided to demonstrate the new contact rule for vertex‐to‐face contacts between two polyhedrons with planar boundaries. Copyright © 2005 John Wiley & Sons, Ltd.     

Polyarc discrete element for efficiently simulating arbitrarily shaped 2D particles

A new two‐dimensional discrete element type, termed the ‘polyarc’ element is presented in this paper. Compared to other discrete element types, the new element is capable of representing any two‐dimensional convex particle shape with arbitrary angularity and elongation using a small number of shape parameters. Contact resolution between polyarc elements, which is the most computation‐extensive task in DEM simulation only involves simple closed‐form solutions. Two undesirable contact scenarios common for polygon elements can be avoided by the polyarc element, so the contact resolution algorithm for polyarc elements is simpler than that for polygon elements. The extra flexibility in particle shape representation induces little or no additional computational cost. The key algorithmic aspects of the new element, including the particle shape representation scheme, the quick neighbor search algorithm, the contact resolution algorithm, and the contact law are presented. The recommended contact law for the polyarc model was formulated on the basis of an evaluation of various contact law schemes for polygon type discrete elements. The capability and efficiency of the new element type were demonstrated through an investigation of strength anisotropy of a virtual sand consisting of a random mix of angular and smooth elongated particles subjected to biaxial compression tests. Copyright © 2011 John Wiley & Sons, Ltd.     

A 3D contact smoothing method using Gregory patches

In this work, a method is developed for smoothing three‐dimensional contact surfaces. The method can be applied to both regular and irregular meshes. The algorithm employs Gregory patches to interpolate finite element nodes and provide tangent plane continuity between adjacent patches. The resulting surface interpolation is used to calculate gaps and contact forces, in a variationally consistent way, such that contact forces due to normal and frictional contact vary smoothly as slave nodes transition from one patch to the next. This eliminates the ‘chatter’ which typically occurs in a standard contact algorithm when a slave node is situated near a master facet edge. The elimination of this chatter provides a significant improvement in convergence behaviour, which is illustrated by a number of numerical examples. Furthermore, smoothed surfaces also provide a more accurate representation of the actual surface, such that resulting stresses and forces can be more accurately computed with coarse meshes in many problems. This fact is also demonstrated by the numerical examples. Published in 2002 by John Wiley & Sons, Ltd.