基于填充函数与DCD的全局优化算法及其反演

岩土工程中以监测位移为已知信息的反演问题可通过带未知变量约束空间的优化模型去求解.该模型中的优化函数常具有非线性、非凸性等特点,使得反演结果容易陷入局部最优的困境.为了应对在运用优化算法反演此类问题时存在的困境,并提高其算法效率,依据填充函数优化思想与DCD(Dynamic Canonical Descent)思想在反...     

基于傅里叶级数的汽轮机叶根轮槽结构设计

提出了一种基于傅里叶级数的枞树型叶根轮槽的优化设计方法。在叶根轮槽构型表征方面,采用傅里叶级数-直线法,与传统的圆弧-直线法相比,不但具有高保真度和完备性,还扩大了优化的搜索空间,减少了设计变量数目,有效降低计算代价。在优化设计方面,为避免以最小化峰值应力为目标函数引起的迭代震荡和不收敛现象,采用KS函数凝聚应力值,降低了优化问题的非线性程度,保证优化快速稳定收敛。以三齿枞树型叶根轮槽为实例,优化结果表明,傅里叶级数-直线法和KS凝聚法优化可有效降低汽轮机叶根轮槽的应力水平,提高汽轮机结构的可靠性。同时,提出的结构表征和优化设计方法具有较高的通用性和实际工程应用价值,可方便扩展至其他工程结构型线设计。     

基于应变能与频率灵敏度的静动力双目标ESO

当前在运用渐进结构优化(ESO)时,大多仅设定了单一的静力或动力目标,难以满足工程结构设计的需求。为此,将单目标优化常用的应变能灵敏度和频率灵敏度进行无量纲处理,再与多目标优化理论结合,开发出静动力双目标ESO。通过多个不同边界条件的深受弯构件数值算例,证实了新方法的运行稳定性和普遍适用性,同时还得到了静力优化与动力优化间的权重系数比取值建议。有限元对比分析结果表明,该新方法相较于传统的单目标优化,能够兼顾结构的静动力性能,使结构耗材减少但静力刚度基本维持,同时材料利用率和一阶固有频率还能不断提升。     

Optimum blank design for sheet metal forming based on the interaction of high- and low-fidelity FE models

This paper deals with an optimization methodology for the design of the sheet-metal-forming process. In this study, a new design optimization system is developed which employs an iterative optimization technique and numerical simulation of a sheet-metal-forming process. The main feature of this new optimization method is that it is based on the interaction of high- and low-fidelity simulation models in order to reduce overall computing time. In the iterative optimization procedure, only the corrected low-fidelity model is used. The high-fidelity model, which requires much longer computing time, is used only for the correction of the low-fidelity analysis and validation of the final solution. To demonstrate the developed optimization method on a practical application, it is applied to the optimum blank design for deep-drawing process of a rectangular box. In deep-drawing, the flange of the drawn product is usually trimmed off to obtain the desired product geometry, and the trimmed material is wasted. Therefore, the formulation of the optimization problem is to determine the optimum initial blank geometry which minimizes the amount of the trimmed material, that is, the waste of material. It is confirmed that the blank design was optimized successfully in remarkably short computing time by the developed optimization method.     

基于解析解和新准则的深埋隧道断面形状优化

针对深埋隧道断面形状优化问题,考虑复杂受力下洞周可能存在拉应力情况,提出基于摩尔-库伦屈服准则的新的优化准则,基于解析解用模拟退火法获得洞周最小破坏范围的最优断面形状．优化模型中,以断面映射函数系数为优化的设计变量,利用混合罚函数使优化孔形满足一定的约束条件,设立孔边最大有效应力（与屈服准则相关）最小的优化准则．针对存在内压的深埋隧道断面形状优化问题,对不同内压、不同侧压系数、不同宽高比限制等情况进行优化计算,并对比两种优化准则在该情况下优化结果的异同．结果表明,对压应力主导优化的情况,新准则与原准则没有差别;对可能出现拉应力的复杂应力情况,新准则有更好的适应性,可以获得更优断面形状．     

Shape optimization and its extension to topological design based on isogeometric analysis

In most of structural optimization approaches, finite element method (FEM) has been employed for structural response analysis and sensitivity calculation. However, the approaches generally suffer certain drawbacks. In shape optimization, cumbersome parameterization of design domain is required and time consuming remeshing task is also necessary. In topology optimization, design results are generally restricted on the initial design space and additional post-processing is required for communication with CAD systems. These drawbacks are due to the use of different mathematical languages in design or geometric modeling and numerical analysis: spline basis functions are used in design and geometric modeling whereas Lagrangian and Hermitian polynomials in analysis. Isogeometric analysis is a very attractive and promising alternative to overcome the limitations resulting from the use of the conventional FEM in structural optimization. In isogeometric analysis, the same spline information such as control points and spline basis functions which represent geometries in CAD systems are also used in numerical analysis. Such unification of the mathematical languages in CAD, analysis and design optimization can resolve the issues mentioned above. In this work, structural shape optimization using isogeometric analysis is studied on 2D and shell problems. The proposed framework is extended to topology optimization using trimming techniques. New inner fronts are introduced by trimming spline curves in topology optimization. Trimmed surface analysis which was recently proposed to analyze arbitrary complex topology problems is employed for topology optimization. Some benchmarking problems in shape and topology optimization are treated using the proposed approach.     

结构形状优化设计数值方法的研究和应用

本文论述了连续体结构形状优化设计数值方法的研究和应用进展,讨论了结构模型化、灵敏度分析、优化方法改进、优化实用软件开发以及同CAD技术相结合等问题,介绍了在结构优化设计软件MCADS中采用的方法,并通过工程实例说明了结构形状优化设计的应用及其价值。     

On optimum design of structures and materials

A survey of problems of optimum design of structures and materials is presented with the main emphasis on fundamental aspects and on current methods and capabilities for topology and shape optimization.The methods are selected from conditions of versatility and suitability for integration into an engineering design optimization system which realizes the design process as an iterative solution procedure of a multicriterion optimization problem based on the concept of integration of finite element analysis, sensitivity analysis, and optimization by mathematical programming.A picture of current possibilities and the present status of the field is given through a number of examples.General invited lecture presented at the 12th Italian Congress on Theoretical and Applied Mechanics AIMETA '95, Naples, 3–6 October 1995.     

人工智能在结构拓扑优化领域的现状与未来趋势

结构优化,特别是结构拓扑优化,受到学术界和工业界的广泛关注.通过发展不同的拓扑优化算法,实现了众多具有卓越力学、热学和声学等多学科性能的最优拓扑构型创新设计.然而传统的拓扑优化方法在处理大规模的拓扑优化问题的迭代过程中往往需要多次大规模有限元分析,面临巨大计算量的挑战.近年来,以机器学习为代表的人工智能方法的迅猛发展,...     

基于拟满应力设计和遗传算法的网架截面优化方法

通过在遗传算法中嵌入拟满应力算子,提出了一种以网架结构杆件截面作为离散变量的优化设计方法,即基于拟满应力设计和遗传算法的网架截面优化方法.分析结果表明,该法能够提高遗传算法的搜索效率和获得全局最优解的可靠性,对于同时有应力和位移约束的网架等空间结构截面优化问题,这种混合算法有较高的效率.     

基于均匀材料微结构模型的热弹性结构与材料并发优化

研究由宏观上均匀多孔材料制成的结构的优化设计问题,待设计的结构受到给定的外力与温度载荷作用,优化设计旨在给定结构允许使用的材料体积约束下,设计宏观结构的拓扑及多孔材料的徼结构,使得结构柔度最小.本文提出了一种宏观结构与微观单胞构型并发优化设计的方法.在此方法中,引入宏观密度和微观密度两类设计变量,在微观层次上采用带惩罚的实心各向同性材料法SIMP(Solid Isotropic Material with Penalty),在宏观层次上采用带惩罚的多孔各向异性材料法PAMP(Porous Anisotropic Material with Pemlty),借助均匀化方法建立两个层次阃的联系,通过优化方法自动确定实体材料在结构与材料两个层次上的分配,得到优化设计;提供的数值算例检验了本文所提方法及计算模型,并讨论了温度变化、材料体积及计算参数对优化结果的影响.研究结果表明同时考虑热和机械载荷时,采用多孔材料可以降低结构柔顺性.     

相变传热问题的灵敏度分析与优化设计方法

研究了相变传热问题的优化设计及其灵敏度分析方法. 在有限元-时间差分和等效热容 法求解相变温度场的基础上,提出了相变温度场对设计变量一阶灵敏度的计算方法,给出直 接法和伴随法两种计算格式并分析了它们的特点,建立了相变温度场优化的模型和算法,在有限元分析与优化设计软件JIFEX中实现了该方法. 数值算例表明了灵敏度计算的精度和优 化方法的有效性.     

结构设计中的混沌优化方法及其改进

在变尺度混沌优化方法研究中．结合结构优化问题的特点,提出了一种改进的混沌优化求解算法,用来解决带有多种约束条件的结构优化设计问题。在有限元分析和优化设计软件JEFIX中实现了上述算法．并通过数值算例讨论了变尺度混沌优化方法在结构优化中的可行性及存在的问题,得到了一些重要结论。     

惯性释放法在结构耐撞性拓扑优化中的应用和改进

惯性释放法是在飞行器设计中采用的一种近似分析方法,用于获得载荷作用下的自由-自由结构的内力响应。为了克服结构耐撞性拓扑优化问题求解的困难,探讨了惯性释放法在结构耐撞性拓扑优化中的应用和改进。将惯性释放法改进的惯性释放法、ESL(等效静力法)的优化思想与HCA(混合胞元自动机法)的材料更新规则结合,提出了一种新的高效的可用于耐撞性拓扑优化问题的混合法。数值算例结果表明,改进的惯性释放法对于多数碰撞问题均可以获得精度较高的结果,而惯性释放法对部分问题同样可以获得精度较高的结果,同时应用过程更加简便。优化算例的结果显示,新的混合法可以获得吸能性能更好的结构设计,同时有效地降低优化过程的耗时。     

渐进密度AESO方法及其在热传导结构拓扑优化中的应用

研究用于结构拓扑优化的基于材料添加策略的进化算法(AESO方法).基于进化算法的思想,利用单元材料相对密度的变化描述材料的添加(从O到1)或删除(从1到O).当某些单元满足进化准则时,单元的相对密度进行O-1交化.研究发现.基于一步变化策略的AESO方法往往不能获得正确的拓扑形式,其原因可能是,进化后的响应量是基于密度为O或很小时的敏度经线性近似获得的,与实际相差很大.这种敏度的计算误差问题在ESO、BESO等硬杀算法中都存在.本文提出将进化过程分成多步,以软杀的思想进行硬杀优化,即使材料密度逐渐由O变化到1,实现材料的逐步添加.基于该策略,提出了渐进密度AESO方法,并比较分析了这种逐步添加的做法对结果的影响.算例验证了该方法的正确性和有效性.渐进密度AESO方法为双向进化算法(BESO)提供了有效的进化(材料添加)策略.     

On the comparative optimal analysis and synthesis of four-bar function generating mechanism using different heuristic methods

In this research, optimal synthesis of function generation of four-bar linkages is investigated using different heuristic optimization methods. The novelty of this study is that we considered the five precision point’s distribution and both stroke angles of the follower and crank links as the optimization variables. Therefore, a non-linear optimization was done with seven variables. Different optimization techniques, including heuristic and gradient based methods were used for optimization and were completely compared. Finally, general solutions were found and distribution of precision points for some desired functions was rationalized. GA-Hybrid seems to be the best method in finding global optimums in cases that the problem is sorely nonlinear, and also it is fast. Even it seems that distribution of precision points is independent of stroke angles of the follower and crank links. Some precision points are out of the design domain, and they are sorted in a way that they can describe the behavior of desired function better.     

在静力与动力荷载作用下拱坝的体形优化

建立了拱坝体形优化的合理而实用的数学模型,提出了有效的求解方法,特别重视工程应用,目前已应用于近三十个实际工程,取得了巨大经济效益,并已应用于250米特高拱坝的设计。作者提出了一系列有效的求解方法,如内力展开法,设计变量指数变换法等等,并首次实现了地震荷载作用下拱坝的体形优化。     

冲击载荷下轻质夹芯拱最大刚度拓扑优化及动力响应

基于双向渐进结构优化方法（bi-directional evolutionary structural optimization,BESO）框架,将传统动态载荷优化法中的内外层迭代引入到ABAQUS-MATLAB平台集成优化中,改进动态载荷拓扑优化流程。对初速度为100 m/s的子弹冲击下的夹芯拱结构进行拓扑优化设计和动力学响应分析。优化后夹芯拱芯层的变形模式可分为3个对称的部分,跨中区域的中部和上部主要发生压缩变形,呈现类三角点阵桁架结构,边界区域上部发生拉伸变形,下部发生压缩变形,呈现C形型结构,跨中和边界之间的过渡区域以拉弯联合变形为主,呈现Y形结构。通过与两种等质量的拱结构对比,分析了3种结构在不同初速度的子弹冲击下结构的挠度以及芯层的能量吸收情况。结果表明:在相同的冲击速度下,优化后的结构挠度最小,芯层比吸能最高;当冲击速度较低时,优化后的结构的抗冲击性能优势并不明显;在所研究的冲击速度范围内,冲击速度越高,优化后结构的抗冲击性能越好。对比对称载荷与非对称载荷（冲击点偏移量为100%）下2种优化结构在不同载荷工况下的动态响应,结果表明:载荷工况不同,得到的最终优化结果也略有所不同,但在相同载荷下结构的响应相差较小,每种工况下得到的优化结果在相应工况下所展现的力学性能略优,但均明显优于传统结构。因此,在对称冲击载荷下优化所得的结构具有一定的普遍性。     

A Method for Topological Optimization of Structures with Discrete Variables under Dynamic Stress and Displacement Constraints

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悬式绝缘子的形状优化

本文将带自适应运动极限的序列线性规划法应用于悬式绝缘子瓷头的形状优化问题中。建立了优化的数学模型;给出了相应的算法;分析了优化计算的结果;为悬式绝缘子的形状优化设计提供了可行的有效手段。