Integration of topology and shape optimization for design of structural components

This paper presents an integrated approach that supports the topology optimization and CAD-based shape optimization. The main contribution of the paper is using the geometric reconstruction technique that is mathematically sound and error bounded for creating solid models of the topologically optimized structures with smooth geometric boundary. This geometric reconstruction method extends the integration to 3-D applications. In addition, commercial Computer-Aided Design (CAD), finite element analysis (FEA), optimization, and application software tools are incorporated to support the integrated optimization process. The integration is carried out by first converting the geometry of the topologically optimized structure into smooth and parametric B-spline curves and surfaces. The B-spline curves and surfaces are then imported into a parametric CAD environment to build solid models of the structure. The control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization, in which CAD-based design velocity field computations, design sensitivity analysis (DSA), and nonlinear programming are performed. Both 2-D plane stress and 3-D solid examples are presented to demonstrate the proposed approach. Received January 27, 2000 Communicated by J. Sobieski     

近似弧长参数化的三次保形插值

在构造近似弧长参数化曲线时,必须添加某些额外的数据点,以获得足够的近似弧长参数化精度,对于参数三次曲线,给出了一个“双点单位化”的近似弧长参数化公式,为如何选择这些额外数据点提供了理论依据,所给出的方法既能有效地提高近似弧长参数化精度,同时又满足了保形插值的要求。     

热轧带钢中板形的计算和控制

热轧带钢中保持良好的板形是生产过程中极其重要的问题。首先,介绍了板形的基础知识包括板形的概念和计算,以及目前生产中板形控制方面实际存在的问题。在此基础上,讨论了影响板形的因素和控制策略,并对由带钢温度引起的缺陷,经过层流冷却获得良好板形的策略做了重点的讨论。从预防的角度阐明了板形的控制方法,并且介绍了一种实际生产中热轧带钢中浪板形控制方法,即PC设定控制方法的具体流程和实际应用效果。     

Shape Morphing-Based Control of Robotic Visual Servoing

We present an approach for controlling robotic interactions with objects, using synthetic images generated by morphing shapes. In particular, we attempt the problem of positioning an eye-in-hand robotic system with respect to objects in the workspace for grasping and manipulation. In our formulation, the grasp position (and consequently the approach trajectory of the manipulator), varies with each object. The proposed solution to the problem consists of two parts. First, based on a model-based object recognition framework, images of the objects taken at the desired grasp pose are stored in a database. The recognition and identification of the grasp position for an unknown input object (selected from the family of recognizable objects) occurs by morphing its contour to the templates in the database and using the virtual energy spent during the morph as a dissimilarity measure. In the second step, the images synthesized during the morph are used to guide the eye-in-hand system and execute the grasp. The proposed method requires minimal calibration of the system. Furthermore, it conjoins techniques from shape recognition, computer graphics, and vision-based robot control in a unified engineering amework. Potential applications range from recognition and positioning with respect to partially-occluded or deformable objects to planning robotic grasping based on human demonstration.     

Geodesic Matching with Free Extremities

In this paper, we describe how to use geodesic energies defined on various sets of objects to solve several distance related problems. We first present the theory of metamorphoses and the geodesic distances it induces on a Riemannian manifold, followed by classical applications in landmark and image matching. We then explain how to use the geodesic distance for new issues, which can be embedded in a general framework of matching with free extremities. This is illustrated by results on image and shape averaging and unlabeled landmark matching. Laurent Garcin is a former student of the Ecole Polytechnique. He obtained his Ph.D. in 2004 at the Ecole Normale de Cachan, working on matching methods for landmarks and images. He is an engineer at the French National Geographic Institute. Laurent Younes is a former student of the Ecole Normale Superieure in Paris. He was awarded the Ph.D. from the University Paris Sud in 1989, and the thesis advisor certification from the same university in 1995. He works on the statistical analysis of images and shapes, and on modeling shape deformations and shape spaces. Laurent Younes entered CNRS, the French National Research Center in October 1991, in which he has been a “Directeur de Recherche" until 2003. He is now a professor at the Department of Applied Mathematics and Statistics Department and the Center for Imaging Science at Johns Hopkins University in July 2003.     

Dynamic problems of shape optimal design for shallow curved plates

The problem of optimal structural design of shallow thin-walled elements such as curved rectangular plates are formulated and solved for dynamic conditions. The distribution of the initial curvature of shallow plates in a nonstrained state is taken as the control function. Dynamic compliance is considered as the minimized performance functional. Optimality conditions are derived for the distributed parameter system considered and applied for the construction of the analytical solution. The rigorous analysis of extremum conditions and behavioural equations shows that the initial optimization problem is decomposed into several problems of classical structural analysis, which can be successfully solved analytically. Some optimal designs obtained for rectangular plates under stretching and bending, and a plate lying on an elastic foundation and subjected to lateral forces are presented. Received: November 27, 1998     

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions.     

An approach to averaging digitized plantagram curves

The averaging of outline shapes of the human foot for the purposes of determining information concerning foot shape and dimension within the context of comfort of fit of sport shoes is approached as a mathematical problem. An outline of the human footprint is obtained by standard procedures and the curvature is traced with a Hewlett Packard Digitizer. The paper describes the determination of an alignment axis, the identification of two ray centres and the division of the total curve into two overlapping arcs. Each arc is divided by equiangular rays which intersect chords between digitized points describing the arc. The radial distance of each ray is averaged within groups of foot lengths which vary by ± 2·25 mm (approximately equal to 1/2 shoe size). The method has been used to determine average plantar curves in a study of 1197 North American males (Hawes and Sovak 1993).     

改进主动形状模型算法在运动物体定位中的研究与应用

为提高彩色图像中目标物体的定位精准度和鲁棒性,改善传统主动形状模型采用的灰度模型单一搜索,提出了一种新的基于RGB色彩空间三通道的局部搜索策略.根据彩色图像的特点,充分利用目标的颜色信息,把一维灰度模型扩展成RGB空间彩色模型.结合该模型,提出一种基于各颜色分量所占比重权值的自适应综合匹配函数,并通过由粗到精的多级搜索,实现了彩色图像中运动物体的定位.实验结果表明,该方法降低了模型陷入局部最优的概率,并且提高了目标物体定位的精度和收敛速度.     

一种结合灰度和边缘信息的局部特征描述算法

针对单一特征引导图像匹配的准确度有限,提出了一种同时使用灰度和边缘信息的特征描述子。该描述子将图像的几何特征与灰度信息结合起来,首先计算每个特征点的灰度对比直方图,然后引入边缘属性以增强边缘的匹配。实验结果表明,该算法由于同时采用灰度信息与边缘信息引导图像匹配,其匹配效果好于单独使用灰度或边缘的图像匹配算法,在一定程度上降低了误匹配率,同时满足旋转和光照不变性,对图像灰度变化和噪声不敏感,具有良好的匹配性能。