以孔边绝对值最大的切向应力最小为优化准则的孔洞形状优化

提出了一个新的孔形优化准则－－孔边绝对值最大的切向应力最小，并给出了了基于这种优化准则寻找最优孔形的方法，在所得的孔洞周边，应力集中程度最小。     

基于固定网格和拓扑导数的结构拓扑优化自适应泡泡法

为继承传统拓扑优化泡泡法变量少、精度高等优点,并克服其网格重划频繁、孔洞合并操作繁琐等不足,提出了一种基于固定网格和拓扑导数的自适应泡泡方法.该方法的主要特点是:(1)采用有限胞元固定网格分析方法计算结构力学响应,在优化过程中无需网格更新和重划分,就能保证较高的分析精度;(2)根据拓扑导数信息指导结构区域中孔洞的引入,不仅消除了优化结果对孔洞初始布局的依赖性,还能有效控制设计变量的数量;(3)引入拓扑导数阈值和孔洞影响区域新概念,实现了孔洞引入频次和位置的自适应调节,保证了拓扑优化过程的数值计算稳定性;(4)采用光滑变形隐式曲线描述孔洞边界,不仅设计参数少、变形能力强,而且便于处理孔洞间的融合/分离操作以及与固定网格分析方法的有机结合.理论分析和数值算例表明,改进后的自适应泡泡法能够消除传统泡泡法因采用拉格朗日网格和参数化B样条曲线模型而存在的实施困难,采用很少的设计变量就可获得边界光滑清晰的优化结果.      

基于固定网格和拓扑导数的结构拓扑优化自适应泡泡法

为继承传统拓扑优化泡泡法变量少、精度高等优点,并克服其网格重划频繁、孔洞合并操作繁琐等不足,提出了一种基于固定网格和拓扑导数的自适应泡泡方法.该方法的主要特点是:(1)采用有限胞元固定网格分析方法计算结构力学响应,在优化过程中无需网格更新和重划分,就能保证较高的分析精度;(2)根据拓扑导数信息指导结构区域中孔洞的引入,不仅消除了优化结果对孔洞初始布局的依赖性,还能有效控制设计变量的数量;(3)引入拓扑导数阈值和孔洞影响区域新概念,实现了孔洞引入频次和位置的自适应调节,保证了拓扑优化过程的数值计算稳定性;(4)采用光滑变形隐式曲线描述孔洞边界,不仅设计参数少、变形能力强,而且便于处理孔洞间的融合/分离操作以及与固定网格分析方法的有机结合.理论分析和数值算例表明,改进后的自适应泡泡法能够消除传统泡泡法因采用拉格朗日网格和参数化B样条曲线模型而存在的实施困难,采用很少的设计变量就可获得边界光滑清晰的优化结果.     

含椭圆孔的变角度复合材料层合板的屈曲性能研究

本文利用变角度复合材料的纤维方向角可沿平面位置任意连续变化的特点,提出在孔附近采用与孔同心的椭圆曲线作为纤维铺设路径的层合板铺层方案,以改善含椭圆孔的层合板的孔边应力集中,进而提高层合板的抗屈曲性能．主要研究内容有：利用ABAQUS软件分析本文提出的孔边特殊铺层方式下变角度复合材料层合板的面内应力分布及屈曲性能,通过与传统直线铺层方式以及线性变角度铺层方式进行比较,说明了本文提出的新铺层方式的优越性,并详细分析了椭圆孔的离心率、开孔尺寸及开孔方位对层合板的屈曲临界荷载的影响．研究结果可为含椭圆孔的变角度复合材料层合板的结构设计和优化提供一定的参考．     

带孔有限宽板孔边应力集中系数的修正解法

 通过弹性力学方法可以得到带孔无限大(宽) 板应力场的理论解, 但带孔有限宽板的理论解却比较难于得到. 本文从二者孔边应力分布的相似性出发, 引入应力分布函数的修正系数, 从而建立了带孔有限宽板孔边应力集中系数的修正解法, 对于多种不同宽度的带孔板, 孔边应力集中系数的修正解与有限元数值解进行了比较, 误差在允许范围内, 修正因子具有其工程应用合理性.     

圆柱壳大开孔问题——单圆孔的理论解

从Ｄｏｎｎｅｌｌ圆柱壳方程出发，利用复变函数与保角映射的方法，将圆柱壳展开面上的开孔边界线保角晨射成单位圆，并在映射平面上给出了逼近大开孔圆柱壳方程解答的完备函数逼近序列，进而利用边界条件和正交函数展开的方法得到了自由孔边应力集中系数的表达式，最后，对具有开孔率的圆柱壳在不同荷载条件下的自由孔口边界上的应力集中的系数进行了计算，此种方法，同时研究圆柱壳开非圆大孔和接管等问题提供了可能性。     

无限大板开孔弹性波的散射及动应力集中

采用弹性平板理论及复变函数理论，对含孔无限大平板弹性波的散射及动应力集中问题进行了分析研究，建立了求解平板开孔动应力集中问题的复变函数方法。若同时采用映射变换，就为求解平板开任意形状孔的动应力集中问题提供了一种规范而有效的方法。为说明问题，本文给出了平板开圆孔及椭圆孔动应力集中因子的数值结果。     

高炉炉壳开孔位置对应力集中的影响

考虑到冶金行业中高炉炉壳开孔的实际情况，本文应用有限元分析的方法研究受远场均匀拉伸载荷，二维有限区域内菱形分布的圆孔中间不同开孔位置下的应力分布，得到最大应力集中系数随孔位置变化的三维变化曲面。此外，孔沿座标轴及沿原孔边缘位置变化对应力集中系数的影响被详细研究，从而为合理设计炉壳开孔提供了理论依据。     

钢桥塔斜拉索锚固区壁板的多孔应力集中特性

针对钢桥塔斜拉索锚固区连续布置椭圆形过索孔易产生的应力集中现象,对开任意多个椭圆孔无限大平面的力学模型建立了复应力函数,采用最小二乘边界配点法对应力场进行了求解,并与单个椭圆孔的理论解相比较,误差小于1%。结果表明:孔边应力集中系数随孔洞纵向间距增大而增大,随孔洞横向间距增大而减小,并最终都趋于定值。基于有限元分析,讨论了板件长宽比、开孔率、孔洞间距等参数对开单排和双排连续椭圆孔有限大板应力集中系数的影响情况;进一步在无限大平面计算结果基础上引入板宽修正系数,给出了便于工程应用的应力集中系数计算公式。     

双向固定网格渐进结构优化方法

近年来发展的渐进结构优化方法是一种有前途的结构拓扑和形状优化方法.本文在渐进结构优化方法的框架内建立了统一敏感度的概念,并基于固定网格有限元技术,发展了一种新的增加材料技术,提出了双向固定网格渐进结构优化方法.将该方法应用于复合材料壳结构开孔形状优化,以孔周等Tsai-Hill强度值作为优化目标,可以得到合理的最优解,证明了双向固定网格渐进结构优化方法的适用性.不同的初始点能得到几乎相同的最优解,展示了本文方法良好的全局最优性.     

Optimum shape and topology design using the boundary element method

A procedure is developed for simultaneous shape and topology design optimization of linear elastic two-dimensional continuum structures. An intuitive approach is presented to treat such topological problems whereby material is eliminated from within the structure (by introducing holes at regions of low stress) through a sequence of shape optimization processes. A mathematical programming technique coupled with the boundary element (BE) method of response and sensitivity analyses enables the optimal positioning of these holes plus optimization of the overall structural shape. The analytical derivative BE formulation is explained together with the use of appropriate design velocity fields, and example problems are solved to demonstrate the optimization procedure.     

Sensitivity analysis for fixed-grid shape optimization by using oblique boundary curve approximation

The remesh-free property is the most attractive feature of the various versions of fixed-grid-based shape optimization methods. When the design boundary curves do not pass through the predetermined analysis grids, however, the element stiffness as well as the stress along the curves may be computed inaccurately. Even with the popular area-fraction-based stiffness evaluation approach, the whole optimization process may become quite inefficient in such a case. As an efficient alternative approach, we considered a stiffness matrix evaluation method based on the boundary curve approximation by piecewise oblique curves which can cross several elements. The main contribution of this work is the analytic derivation of the shape sensitivity for the discretized system by the fixed-grid method. Since the force term in the sensitivity equation is associated only with the elements crossed by the design boundary curve, we only need the design velocities of the intersecting points between the curve and the fixed mesh. The present results obtained for two-dimensional elasticity and Poisson’s problems are valid for both the single-scale standard fixed-grid method and the multiscale fictitious domain-based interpolation wavelet-Galerkin method.     

广义变分原理的结构形状优化伴随法灵敏度分析

提出了一种利用伴随变量进行结构形状优化灵敏度分析的新方法. 基于广义变分原理， 考虑了形状优化中位移边界条件的变化对结构响应的影响. 新方法弥补了Arora 等人所提出的形状优化灵敏度分析变分原理中的缺陷，为采用伴随法进行灵敏度分析提供了 新的框架.     

Accuracy of Finite Element Based Shape Design Sensitivity Analysis*

ABSTRACT Accuracy of finite element based shape design sensitivity analysis, for use in shape design optimization, is analyzed and tested. A shape design sensitivity formulation that uses stress averaging to treat stress constraint func-tionals is presented. A smooth boundary parameterization is introduced to avoid the "Babuska paradox" and to improve accuracy of design sensitivity analysis. Accuracy of design sensitivity analysis with displacement and hybrid stress finite element formulations is compared. Good accuracy is obtained using higher order displacement finite elements, such as linear stress triangular and 8-noded isoparametric elements.     

热结构瞬态响应的耦合灵敏度分析方法与优化设计

研究结构瞬态热变形和热应力的灵敏度分析方法及其优化设计,灵敏度计算给出了直接法和伴随法两种算法.考虑了温度场的耦合作用,在直接法中需要计算温度场对设计变量的导数,在伴随法中需要计算热载荷对温度场的导数.数值算例验证了该方法的精度.伴随法在应用程序中的实现,为大型结构优化提供了高效率的灵敏度计算方法.     

Analytic Sensitivity Analysis for Shape Optimization

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无限粘弹性平面中椭圆孔口变边界过程的复变函数解答

工程中存在一类几何边界随时间变化的变边界结构,例如土木工程中处于施工阶段的结构。本文以粘弹性岩体中隧道开挖为背景,尝试用变边界问题对应关系和平面弹性复变方法求取无限平面中椭圆孔口自相似变边界情况下的解析解答。首先建立了复变函数法求解变边界粘弹性问题的基本步骤和公式。然后通过建立逆映射函数将已知?平面复位势转至z平面,从而解耦参与拉普拉斯变换的时间与孔口映射函数所带来的时间,从而导出了粘弹性类材料的应力与位移的统一表达。作为一个例子,本文选择Boltzmann粘弹性模型,代入模型参数后得到积分形式的位移、应力解析解,通过与数值解的比较验证了该解答的可靠性,并通过一个算例分析了变边界过程对位移、应力的影响。分析结果显示,采用不同变边界过程的位移、应力变化形态和数值均有差别。本文解答可用于进行地下椭圆孔型隧道在开挖过程中的力学分析,为实际工程提供初步设计的手段。此外,本文给出的方法可用于推导任意形状孔型变边界问题的解答。     

Shape optimization of two equal holes in an infinite elastic plate

Abstract

The optimal design of the stress state in elastic plate structures with openings is a problem of great significance in engineering practice. Achieving proper shape of hole can reduce stress concentration around the boundaries remarkably. The optimal shape of a single hole in an infinite plate under uniform stresses has been obtained by complex variable method based on different optimal criteria. The complex variable method is particularly suitable for the hole shape optimization in infinite plate, in which the continuous hole boundary can be represented by the mapping function. It can also be used to solve the shape optimization problems of two or more holes. However, because of the difficulty of finding the mapping function for multi connected domain, the holes are mapped onto slits or separately mapped onto a circle. In this article, the two symmetrical and identical holes are mapped onto an annulus simultaneously by the newly found mapping function, which has a general form. The maximum tangential stress around the boundaries is minimized to achieve the optimal hole shape. And the coefficients of mapping function which describe the boundary are calculated by differential-evolution algorithm.     

A biarc-based shape optimization approach to reduce stress concentration effects

In order to avoid stress concentration, the shape boundary must be properly designed via shape optimiza- tion. Traditional shape optimization approach eliminates the stress concentration effect by using free-form curve to present the design boundaries without taking the machin- ability into consideration. In most numerical control （NC） machines, linear as well as circular interpolations are used to generate the tool path. Non-circular curves, such as non- uniform rotational B-spline （NURBS）, need other more ad- vanced interpolation functions to formulate the tool path. Forming the circular tool path by approximating the opti- mal free curve boundary with arcs or biarcs is another op- tion. However, these two approaches are both at a cost of sharp expansion of program code and long machining time consequently. Motivated by the success of recent researches on biarcs, a reliable shape optimization approach is pro- posed in this work to directly optimize the shape boundaries with biarcs while the efficiency and precision of traditional method are preserved. Finally, the approach is validated by several illustrative examples.