APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.     

具有动应力和动位移约束的离散变量结构形状优化设计方法

讨论了动应力、动位移约束下离散变量状优化设计问题。首先用拟静力算法,将结构惯性力极值作为静载荷施加到结构上,求得结构的动位移和动内力,然后将考虑动应力约束和动作移约束的离散变量结构优化设计问题化为静应力和静位移约束的优化问题。在求解过程中,将单元内力作了一阶近似,并将多约束问题转化为单约束问题,然后利用两类变量统一考虑的离散变量结构形状优化设计的综合算法进行求解。     

Topology optimization design of continuum structures under stress and displacement constraints

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平面膜结构拓扑优化的有无复合体方法

将作者对桁架在应力约束下结构拓扑优化的有无复合体模型发展到平面膜结构在应力、位移约束下结构拓扑优化的建模与求解。同时提出了该模型的有效解法,获得了令人满意的数值结果。本文工作表明独立连续拓扑变量的提出对于结构拓扑优化的研究是有意义的。     

应力和位移约束下桁架拓扑优化的有无复合体方法

按照独立连续拓扑变量的思想,将有无复合体模型由构造应力约束问题发展为应力与位移约束问题,用于桁架结构拓扑优化．基于该文提出的位移约束与拓扑变量关系的近似显式,建立了具有应力、位移约束下桁架结构拓扑优化的有无复合体模型,用序列二次规划算法求解．数值结果令人满意．这一工作表明独立连续拓扑变量的提出对于结构拓扑优化的研究是有价值的。     

基于ICM方法的刚架拓扑优化

将ICM(独立、连续、映射)优化方法应用于刚架结构，建立了以重量为目标函数、考虑多工况下应力和位移约束的刚架结构拓扑优化模型。借助于磨光函数和过滤函数，实现了离散变量和连续变量之间的相互转换。考虑多工况应力拓扑解之间、应力和位移约束下拓扑解之间的协调，得到了合理的结果。文中给出的刚架结构拓扑优化算例表明，刚架结构的拓扑结构不同于桁架或连续体。     

连续体结构考虑离散性目标的ICM方法

为了使求解位移和应力约束下重量最轻的连续体结构拓扑优化问题的ICM(独立连续映射)方法得到更清晰的拓扑形式,引入拓扑变量离散性条件作为目标之一,与原目标组成多目标规划模型,使拓扑变量向0或1两端靠近,减小了删除率对结果的影响;用图形处理方法消除了棋盘格现象及网格依赖性;通过初选准有效约束及选择设计区域等,提高了求解效率。算例表明:改进后的算法虽然迭代次数比原算法略多,但更稳键,更实用。     

DYNAMIC RESPONSE OPTIMIZATION DESIGN FOR ENGINEERING STRUCTURES BASED ON RELIABILITY

IntroductionTheoptimumdesignofstructuraldynamicresponseisoneoftheimportantcontentsinthestructuraloptimizationdesign ,inwhichtherespondedphysicalquantityofstructuresunderdynamicexcitationaretakenasobjectorconstraintfunctions.Fortheproblemcomesdownsimultaneouslytothedynamiccharacteristicanalysisandthedynamicresponseanalysisaswellastheoptimumdesign ,itismoredifficultandcomplicatedthantheproblemofstructuralstaticoptimumdesign[1].However,therestillcomeoutsomeresearchproductionsinpastyears.Forexampl…     

The ICM method with objective function transformed by variable discrete condition for continuum structure

ICM (Independent Continuous Mapping) method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm. The project supported by the National Natural Science Foundation of China (10472003), Beijing Natural Science (3002002) and Beijing Educational Committee Foundations (KM200410005019) and Suspensoried by American MSC Company. The English text was polished by Keren Wang.     

多工况应力和位移约束下连续体结构拓扑优化

将文「１」所提出的对拓扑变量的独立连续映射（ＩＧＭ）的拓扑估化方法应用于连续体结构,从而建立了统一的以重量为目标,考虑应力和位移约束的连续体结构拓扑优化模型。通过对位移－应力拓扑解和各工况下应力拓扑解的综合协调,进而对于协调拓扑解按照阈值完成从离散到连续的反演,并且采用分层与加权策略克服了“荷载病态”困难。给出的经典的二维平面问题和三维连续体结构拓扑优化算例表明,这种统一的模型由骨架结构发展到连续     

统一骨架与连续体的结构拓扑优化的ICM理论与方法

技术了基于ＩＣＭ方法的结构拓扑优化新模型并应用于骨架与连续体结构。ＩＣＭ方法意指独立、连续变量与映射及其反演。新模型将两种结构统一建立了具有重量目标函数和多工况下应力与位移约束下的优化问题,提出的过滤函数是ＩＣＭ方法的关键技术之一。说明了优化策略与算法。     

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.The project supported by the National Natural Science Foundation of China (10472003) and Beijing Natural Science Foundation (3042002) The English text was polished by Yunming Chen.     

包含两类变量的离散变量桁架结构拓扑优化设计

建立了包含截面和拓扑两类变量的离散变量结构拓扑优化设计的数学模型,该模型考虑了截面变量与拓扑变量间的耦合关系,反映了拓扑优化问题的组合优化本质,可以较好地解决"极限应力"、"最优解的奇异性"等困扰结构拓外优化设计的问题．同时采用相对差商法进行离散变量桁架结构拓扑优化,直接求解包含两类变量的离散变量结构拓扑优化设计数学模型,收到了比较满意的效果．     

频率约束的三维连续体结构动力拓扑优化设计

针对频率约束和结构重量最小的动力拓扑优化问题, 基于(independent continuous mapping, ICM)独立、连续、映射方法,建立了频率约束下的三维连续体拓扑优化模型. 利用瑞利商和一阶泰勒展式对频率约束进行了显式化处理,并采用幂函数与复合指数函数作为过滤函数,将优化模型进行了标准化转换, 利用对偶理论及数学规划法进行了求解. 另外,利用质量矩阵和刚度矩阵过滤函数比值与动态约束处理了局部模态和模态交换等数值问题. 最后,通过应用两类不同过滤函数的数值算例表明了文中模型及方法在处理动力拓扑优化问题上的合理性与有效性.      

用ICM法拓扑优化静位移及频率约束下连续体结构

用ICM方法建立了静位移及频率约束下、重量最小为目标的连续体结构拓扑优化模型。采用独立于截面及形状参数的连续拓扑变量,借助于过滤函数,位移约束用莫尔定理显式化,频率约束用瑞利商求导数借助模态动能及模态应变能近似显式化。用图形过滤处理的方法解决了棋盘格及网格依赖问题。通过构造适当的过滤函数有效地防止了局部模态问题。动态引入防止模态交换的频率约束条件,使迭代过程不发生振荡。算例表明:用ICM方法建立的模型在处理多工况静位移约束、多频率约束及解决局部模态及模态交换等问题上有优势。     

FUNDAMENTAL FREQUENCY MAXIMIZATION DESIGN FOR CONTINUOUS FIBER-REINFORCED COMPOSITE STRUCTURES 1)

与传统的金属材料相比, 纤维增强复合材料在强度、刚度、抗断裂等诸多方面具备更优良的性能, 目前纤维增强复合材料已在汽车、航空航天等工业领域得到了广泛应用. 本文提出一种求解连续纤维增强复合材料结构无阻尼自由振动下的基频最大化问题的拓扑优化方法. 为了实现结构拓扑构型与纤维角度的同步优化, 建立了以准许的材料用量体积分数为约束、以结构的一阶特征值为目标函数的动力学拓扑优化模型, 该模型包括表征结构拓扑构型的密度设计变量和表征纤维方向的角度设计变量. 详细推导了特征值目标函数关于密度设计变量和角度设计变量的解析灵敏度列式, 并采用移动渐进线方法 (method of moving asymptotes, MMA) 进行了优化求解; 最后通过3个数值算例验证本文方法的有效性, 其中包括一个以刚度最大化为目标的静力学优化算例, 和两个以一阶特征值为目标的动力学优化算例. 结果表明, 所提方法优化迭代过程稳健, 收敛快, 能够在实现结构拓扑构型与纤维角度的一体化优化的同时, 有效提高结构的频率.     

桁架频率优化解存在性及其算法研究

给出桁架在给定固频约束时,动力不优化解存在性的基本理论。指出：桁架固频约束通常是决定其动力学优化解是否存在的“关键约束”。基此,给出了一种工程算法,只用到固频对设计变量的一阶导数,就可很快确定约束是否可能满足。反之,当提出的方法判定给定固频约束不能满足时,可以求出一个解存在的极限频率的狭窄范围及相应的设计变量范围,以供设计人员重新设计时参考。三个由简到繁的算例说明了所提出方法实用、有效。     

考虑性态约束时多工况桁架结构拓扑优化设计

本文提出了一种适用于桁架结构的拓扑优化设计方法。它以杆内力为设计变量,以结构重量为目标函数。该方法的主要特点是:第一,通过引入杆内力为设计变量,既克服了已有方法要求预定位移场这一主要困难,又为在拓扑优化过程中考虑应力、位移等性态约束创造了条件;第二,将多工况的拓扑优化问题描述为一个非光滑的数学规划问题,再通过一个变量代换将其转化为一般的规划为题,进而将原问题的求解又转化为几个线性规划问题的求解;第三,基于结构力学的三个基本方程,将位移与应力约束提成为线性不等式约束,这些约束同重量的目标函数一起构成了拓扑优化设计的线性规划模型。最后,将本方法应用于几个工程算例,得到了满意的数值计算结果。     

基于ICM方法三维连续体结构拓扑优化

基于ICM方法,建立了在应力和位移约束下以重量为目标的多工况下的三维连续体结构拓扑优化模型.利用von Mises强度理论,提出了应力全局化的方法,从而将局部的应力约束转化为全局的应变能约束问题,减少了约束数目,避免了敏度分析的困难;利用单位虚载荷法,将位移约束表示为设计变量的显式关系.为减小由于不同物理量在数量级上相差太大引起数值计算的误差,将应变能约束和位移约束进行无量纲化,由此建立了包含两类约束的无量纲化的优化模型.同时处理了多工况下的最佳传力路径的问题.利用对偶规划理论对模型进行了求解.另外,利用PCL语言在MSC/Patran的开发平台上实现了该文算法.数值算例表明了该方法的可行性和有效性.     

AN EFFICIENT GENETIC ALGORITHM FOR LARGE SCALE BUILT-UP STRUCTURAL OPTIMIZATION

In this paper,a new zigzag method for plate structures and a geneticalgorithm (GA) of dynamic source seed spaces are developed and a combination ofthem is used to deal with large scale built-up structural optimization.The new GAcombined with the zigzag method can work efficiently when coping with large scalestructural optimization included displacement and stress constraints.Examples showthat this GA is robust and can be used for many complex structural optimizationproblems.