On sorting triangles in a delaunay tessellation

In a two-dimensional Delaunay-triangulated domain, there exists a partial ordering of the triangles (with respect to a vertex) that is consistent with the two-dimensional visibility of the triangles from that vertex. An equivalent statement is that a polygon that is star-shaped with respect to a given vertex can be extended, one triangle at a time, until it includes the entire domain. Arbitrary planar triangulations do not possess this useful property which allows incremental processing of the triangles.This work was partially supported by the National Science Foundation's US-Italy Collaborative Research Program under Grant INT-8714578 and Information, Robotics, and Intelligent Research Grant IRI-8704781.     

Constitutive modelling and numerical simulation of multivariant phase transformation in superelastic shape‐memory alloys

This work concerns the micromechanical constitutive modelling, algorithmic implementation and numerical simulation of polycrystalline superelastic alloys under multiaxial loading. The model is formulated in finite deformations and incorporates the effect of texture. The numerical implementation is based on the constrained minimization of the Helmholtz free energy with dissipation. Simulations are conducted for thin tubes of Nitinol under tension–torsion, as well as for a simplified model of a biomedical stent. Copyright © 2004 John Wiley & Sons, Ltd.     

Applications of the discrete element method in mechanical engineering

Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples. Commemorative Contribution.     

Mesh data structure selection for mesh generation and FEA applications

The data structure representing a mesh and the operators to create and query such a database play a crucial role in the performance of mesh generation and FE analysis applications. The design of such a database must balance the conflicting requirements of compactness and computational efficiency. In this article, 10 different mesh representations are reviewed for linear tetrahedral and hexahedral meshes. A methodology for calculating the storage and computational costs of mesh representations is presented and the 10 data structures are analysed. Also, a system for ranking different data structures based on their computational and storage costs is devised and the various mesh representations are ranked according to this measure. Copyright © 2002 John Wiley & Sons, Ltd.     

《周培德三角剖分不是最小权三角剖分》一文商榷——反例不成立

周培协三角剖分是否能得到最小权三角剖分，周培德在《周培德三角部分不是最小权三角剖分》一文撰写之前已有新的结论，本文还指出《周培德三角剖分不是最小权三角剖分》一文所举反例不成立。     

主动约束层阻尼板结构动力学建模研究

将有限元法和GHM法相结合，给出了建立主动约束层阻尼（ACLD）板结构动力学模型的新方法。建模时，考虑到粘弹材料（VEM）的纵向位移影响，采用GHM方法描述VEM的本构关系，解决了VEM的力学特性随温度和频率变化的难点，避免因VEM的复杂本构关系而产生的微分积分方程。算例表明本文给出的建模方法是准确的，ACLD结构能够有效控制结构振动。     

基于改进PSO算法的结构损伤检测

结构的损伤检测常转化为求解约束优化问题,针对粒子群算法容易出现早熟问题,增大算法后期的粒子位置的改变量,从而增加粒子位置的差异,因而能够增强其在求解约束优化问题时抵抗局部极小的能力。两层刚架单损伤和多损伤识别的数值结果和收敛曲线表明了改进后的粒子群算法优于传统的带惯性因子的粒子群算法。三层框架结构的4种损伤工况的试验研究进一步说明了该算法应用于结构损伤检测领域的有效性。     

共晶强制性熔化的界面形态

对透明共晶系ＣＢｒ４－８．４ｗｔ－％Ｃ２Ｃ１６生长的典型层片共晶组织强制熔化进行实时实地观测．表明相对于强制生长时的“界面滞后”现象，熔化界面温度高于静止时界面温度，熔化界面比静止界面更靠近热端，称为“界面超前”．随熔化速度增大，“界面超前量”增大；共晶组织分层熔化，出现两个熔化界面，α和β相熔化秩序不同，α，β相分别单独熔化，两熔化界面的相对位置由α，β相成分，熔化速度和共晶相间距等因素决定．     

A faster divide-and-conquer algorithm for constructing delaunay triangulations

An easily implemented modification to the divide-and-conquer algorithm for computing the Delaunay triangulation ofn sites in the plane is presented. The change reduces its (n logn) expected running time toO(n log logn) for a large class of distributions that includes the uniform distribution in the unit square. Experimental evidence presented demonstrates that the modified algorithm performs very well forn2¹⁶, the range of the experiments. It is conjectured that the average number of edges it creates—a good measure of its efficiency—is no more than twice optimal forn less than seven trillion. The improvement is shown to extend to the computation of the Delaunay triangulation in theL _p metric for 1<p.This research was supported by National Science Foundation Grants DCR-8352081 and DCR-8416190.