具有动应力、位移和稳定性约束的离散变量桁架结构布局优化设计算法

给出了在动应力、动位移和动稳定约束下离散变量结构布局优化设计问题的数学模型,用“拟静力”算法,将具有动应力约束、动位移约束和动稳定约束的离散变量结构布局优化设计问题化为静应力、静位移和静稳定约束的优化问题,然后利用两级优化算法求解该模型．优化过程由两级组成,拓扑级优化和形状级优化．在每一级,都使用了综合算法,并且在搜索过程中都根据两类设计变量的相对差商值进行搜索．对包含稳定约束和不包含稳定约束的优化结果做了比较,结果显示稳定性约束对优化结果产生较大的影响．     

周期性复合材料构型及结构一体化优化

在传统双向渐进结构优化(BESO)方法基础上,充分考虑微观尺度和宏观尺度之间的相互耦合作用,通过等效弹性模量和灵敏度分析将复合材料微结构胞元设计和宏观结构拓扑优化相结合,建立周期性复合材料构型及结构一体化优化设计方法.为了消除“灰色区域”,假设了材料微结构0 1属性及在宏观结构空间排列的均一性,提高了优化结果的实际工程适用性.相关算例说明该方法可以有效地在宏观结构优化的同时得到与之相对应的材料微观最佳拓扑形状,也为不同给定宏观结构的微观周期性复合材料设计提供了有效手段.     

易拉罐形状和尺寸的最优设计

从用料最省的角度研究了易拉罐的形状和尺寸的优化设计问题,首先通过多次测量取平均值的方法得到了题目所需的数据．然后就问题二和问题三分别建立了优化模型,并借助数学软件进行了求解,得到了最优设计的尺寸．最后设计出了椭球形状的易拉罐作为自己的最优设计．     

基于全概率公式的随机变量边际分布

探讨如何利用全概率公式求二维随机变量的边际分布.特别的对二维连续型随机变量的边际分布进行了形式的推导,并发现积分区域对连续型全概率公式的重要影响.通过几个典型例题着重说明了该公式对积分区域形状的依赖.     

压电曲壳结构的形状控制和优化设计

研究了使用最少和最合理的压电片布置,以及最合理的多点输入电压,对曲壳类结构实施最佳的形状控制.首先,采用HS-ANS法,构造能够克服剪切自锁、梯形自锁和厚度自锁的压电曲壳结构实壳单元.然后,利用遗传算法的组合优化,对作动器的数目和位置进行设计,进一步利用遗传算法的数值优化,对各作动器的作用电压值进行优化,并给出一般计算过程.最后的算例表明,给出的实壳单元和优化设计方法,可以非常有效地实现对曲壳类结构的形状控制.     

红细胞形状的变分解

本文从生物学和变分学两方面探讨了红细胞形状的优化设计问题,取细胞质膜和胞质的生化效益为优化目标,运用变分解法求得一簇理论优化曲面,理论解很好地模拟了人红细胞在等渗状态下的双凹形态及在低渗环境中的形态变化,同时成功地给出了蛙和蝾螈红细胞的椭圆盘状外形,文中建立的理论对于从两栖类、爬行类直至哺乳类动物红细胞形态的优化意义给出了统一的说明,为这一领域的研究提供了新的思路。     

基于iSIGHT平台的三维机翼气动优化设计

基于iSIGHT设计平台,结合CFD软件Fluent对三维机翼进行多目标优化设计,以提高其气动性能．设计过程中采用NCGA(neighborhood cultivation)——邻域培植遗传算法,NSGA-Ⅱ(non-dominated sorting)——非支配解排序遗传算法为优化算法,以N-S方程作为主控方程,对三维机翼优化．经过优化设计后结果表明,机翼的气动性能有了显著改善,该优化方法可推广用于多种翼型和机翼优化．     

中厚及薄板杂交模型的优化列式

文章把杂交元的优化设计原理应用于中厚及薄板问题,导出新的杂交应力4节点20自由度板弯曲单元.该元对各种厚度、形状板的通用性,收敛性以及对极薄板分析的适应性也一并作了考察和讨论.     

改进的NSGA-Ⅱ算法研究风力机叶片多目标优化

将一种采用精英控制策略和动态拥挤方法用于快速非支配排序遗传算法（NSGA-Ⅱ）,并应用到风力机叶片的优化研究中,获得了一种新颖的风力机叶片多目标优化设计方法．作为应用算例,以设计风速下的功率系数最大和叶片质量最小为优化目标,用该方法设计了5 MW大型风力机叶片．优化结果表明,此算法在处理风力机多目标优化问题取得了良好的效果,给出的是一个Pareto最优解集,而不是传统优化方法追求的单个最优解,为风力机多目标优化设计提供新的思路和通用的算法．     

“五制约”搞定圆锥曲线离心率的范围

圆锥曲线的离心率,是描述曲线形状的重要参数,是圆锥曲线的重要性质之一,当然也是高考的一个重要知识点．本文对离心率的取值范围问题作一探讨,并通过例题加以说明．     

The Asymptotic Behaviour of a Curved Line Source Plume within an Enclosure

A line source of heat is situated in an enclosure with inletsand an outlet for the contained fluid. The convection plumeformed must take a curved shape because of the asymmetry ofthe enclosure. We show how boundary-layer theory can be usedto find this shape in the case where the plume's deflectionis small. Two effects govern the shape of the curve; a buoyancyeffect and an inertial effect due to the bounding walls. Bysolving the outer potential flow problem, both effects can beincluded in the model. Finally, a stability analysis is carriedout for steady plumes which shows that any steady solution withan inflection point, as well as several other solutions, isunstable. A comparison is made with previous work which doesnot include all these effects, and with some experimental results.     

Advances in concrete arch dams shape optimization

This paper presents an efficient methodology to find the optimum shape of arch dams. In order to create the geometry of arch dams a new algorithm based on Hermit Splines is proposed. A finite element based shape sensitivity analysis for design-dependent loadings involving body force, hydrostatic pressure and earthquake loadings is implemented. The sensitivity analysis is performed using the concept of mesh design velocity. In order to consider the practical requirements in the optimization model such as construction stages, many geometrical and behavioral constrains are included in the model in comparison with previous researches. The optimization problem is solved via the sequential quadratic programming (SQP) method. The proposed methods are applied successfully to an Iranian arch dam, and good results are achieved. By using such methodology, efficient software for shape optimization of concrete arch dams for practical and reliable design now is available.     

Archetypal shapes based on landmarks and extension to handle missing data

Archetype and archetypoid analysis are extended to shapes. The objective is to find representative shapes. Archetypal shapes are pure (extreme) shapes. We focus on the case where the shape of an object is represented by a configuration matrix of landmarks. As shape space is not a vectorial space, we work in the tangent space, the linearized space about the mean shape. Then, each observation is approximated by a convex combination of actual observations (archetypoids) or archetypes, which are a convex combination of observations in the data set. These tools can contribute to the understanding of shapes, as in the usual multivariate case, since they lie somewhere between clustering and matrix factorization methods. A new simplex visualization tool is also proposed to provide a picture of the archetypal analysis results. We also propose new algorithms for performing archetypal analysis with missing data and its extension to incomplete shapes. A well-known data set is used to illustrate the methodologies developed. The proposed methodology is applied to an apparel design problem in children.     

Parametric study of the class-shape-refinement-transformation method

The application of a novel parametrization technique to the optimization of aircraft shapes is presented. This class-shape-refinement transformation (CSRT) technique combines an analytical function (class function), a set of Bernstein polynomials (shape function) and a B-spline (refinement function) and can be used to model various aircraft components. It allows for both global and local control of a shape and forms a very efficient and intuitive way of mathematically describing aircraft parts. A parametric study was performed that shows the behaviour of the shape as a function of a number of different parameters, such as total number of shape variables and Bernstein/B-spline coefficient ratio. The CSRT method was used to approximate a typical aircraft wing cross-section and the results showed a very non-linear relationship between the number of shape variables and the error of the approximation, expressed in terms of a correlation factor. This behaviour has been thoroughly analysed. Additionally, optimization results were obtained that show that the CSRT method was successfully coupled to an aerodynamic flow solver. The objective of the optimization runs was to maximize lift-to-drag ratio, but in principle any objective function could be used as long as its input follows from the aerodynamic analysis. The optimization algorithm is capable of largely removing the shock wave on an airfoil at a typical cruise Mach number.     

A study of design velocity field computation for shape optimal design

Design velocity field computation is an important step in computing shape design sensitivity coefficients and updating a finite element mesh in the shape design optimization process. Applying an inappropriate design velocity field for shape design sensitivity analysis and optimization will yield inaccurate sensitivity results or a distorted finite element mesh, and thus fail in achieving an optimal solution. In this paper, theoretical regularity and practical requirements of the design velocity field are discussed. The crucial step of using the design velocity field to update the finite element mesh in the design optimization process is emphasized. Available design velocity field computation methods in the literature are summarized and their applicability for shape design sensitivity analysis and optimization is discussed. Five examples are employed to discuss applicability of these methods. It was found that a combination of isoparametric mapping and boundary displacement methods is ideal for the design velocity field computation.     

有理线性插值曲线和曲面(英文)

构造了含参数的分段线性有理插值函数(分子、分母均为一次多项式),通过适当选择形状参数,由此函数产生的曲线一阶连续并且保单调.文中用张量积方法将此结果推广到二元矩形网格上的曲面插值,同时给出了插值函数的误差估计及数值例子.     

A new reconstruction method for a parabolic inverse source problem

In this paper, we focus on the detection of the shape and location of a discontinuous source term from the knowledge of boundary measurements. We propose a non-iterative reconstruction algorithm based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from an energy-like cost function. The unknown shape of the term source support is reconstructed using a level-set curve of the topological gradient. The efficiency of our algorithm is illustrated by some numerical simulations.     

A nonparametric approach to 3D shape analysis from digital camera images — I

This article for the first time develops a nonparametric methodology for the analysis of projective shapes of configurations of landmarks on real 3D objects from their regular camera pictures. A fundamental result in computer vision, emulating the principle of human vision in space, claims that, generically, a finite 3D configuration of points can be retrieved from corresponding configurations in a pair of camera images, up to a projective transformation. Consequently, the projective shape of a 3D configuration can be retrieved from two of its planar views, and a projective shape analysis can be pursued from a sample of images. Projective shapes are here regarded as points on projective shape manifolds. Using large sample and nonparametric bootstrap methodology for extrinsic means on manifolds, one gives confidence regions and tests for the mean projective shape of a 3D configuration from its 2D camera images. Two examples are given: an example of testing for accuracy of a simple manufactured object using mean projective shape analysis, and a face identification example. Both examples are data driven based on landmark registration in digital images.     

Exploring uses of persistent homology for statistical analysis of landmark-based shape data

A method for the use of persistent homology in the statistical analysis of landmark-based shape data is given. Three-dimensional landmark configurations are used as input for separate filtrations, persistent homology is performed, and persistence diagrams are obtained. Groups of configurations are compared using distances between persistence diagrams combined with dimensionality reduction methods. A three-dimensional landmark-based data set is used from a longitudinal orthodontic study, and the persistent homology method is able to distinguish clinically relevant treatment effects. Comparisons are made with the traditional landmark-based statistical shape analysis methods of Dryden and Mardia, and Euclidean Distance Matrix Analysis.     

The static shape control for intelligent structures

A finite element formulation is presented for modeling the plate structure containing distributed piezoelectric sensors and actuators (S/As). A new plate bending element for analysis of the plate with distributed piezoelectric S/As is developed. This element saves much memory and computation time. Using the bending plate element, a general method of static shape control for the intelligent structure is put forth. Two examples are given to illustrate the application of the method presented in this paper. The purpose of the first example is to check the accuracy of the finite element method presented in this paper. The second example is to study the problem of the static shape control for the intelligent structure. It is concluded that the shape of the intelligent structure can reach the desired shape through passive control or active control.