基于应力约束全局化策略的板壳结构强度拓扑优化

应力约束下板壳结构的拓扑优化设计由于应力约束难以显式化和约束条件数量庞大等问题,存在建模和求解的困难。为了解决这些困难,首先,该文通过类比独立连续映射(Independent Continuous and Mapping, ICM)方法中的过滤函数,在实体各向同性材料惩罚(Solid Isotropic Material Penalization, SIMP)方法中引进了单元重量惩罚函数和材料许用应力惩罚函数,实现了对SIMP方法惩罚函数概念的拓广。然后,该文移植了ICM方法中行之有效的应力约束全局化策略,基于拓广后的SIMP方法,构造了代替应力约束后的结构畸变能约束的近似显式化函数,建立了多工况下板壳结构拓扑优化模型。最后,采用对偶序列二次规划算法求解该优化模型,并基于Python语言在ABAQUS软件平台进行了程序实现。数值算例都取得了很好的结果,这表明该文提出的方法是可行而有 效的。     

追究根基的结构拓扑优化方法

结合作者在结构拓扑优化方面的研究工作,围绕了ICM(独立、连续、映射)方法涉及的基本概念上的突破,叙述了将本质上为0-1离散变量的拓扑优化问题转化为连续变量优化问题的具体做法,其中介绍了若干要点:以阶跃函数把离散问题化为连续问题即完成关键的等价性转换是第一步;定义磨光函数逼近阶跃函数的可操作的近似是第二步;引入作为磨光函数反函数的过滤函数实现映射性建模是第三步;采用某些光滑算法求解连续变量模型则是第四步。通过连续体结构的典型数值算例说明了将结构拓扑优化的模型转化为独立层次的拓扑优化过程。该方法对于纯数学的0-1离散变量优化的求解也适用,方法与数值都表明了这一点。     

基于变频率区间约束的结构材料优化设计

针对频率约束的结构材料优化问题,基于结构拓扑优化思想,提出变频率区间约束的结构材料优化方法。借鉴均匀化及ICM(独立、连续、映射)方法,以微观单元拓扑变量倒数为设计变量,导出宏观单元等效质量矩阵及导数,进而获得频率一阶近似展开式。结合变频率区间约束思想,获得以结构质量为目标函数、频率为约束条件的连续体微结构拓扑优化近似模型;采用对偶方法求解。通过算例验证该方法的有效性及可行性,表明考虑质量矩阵变化影响所得优化结果更合理。     

基于ICM方法的层合板结构流固耦合频率约束拓扑优化

该文基于独立、连续、映射(independent continuous mapping, ICM)的拓扑优化方法,针对层合板结构频率约束下流固耦合的拓扑优化问题进行了建模与求解。利用格林公式与瑞利商,进行了优化模型频率约束的显式化,并基于泰勒线性近似的方法推导了设计灵敏公式,同时采用对偶序列二次规划求解了该模型。另外,通过引入修正的Heaviside函数对拓扑变量进行了离散化处理。利用PCL(Patran Command Language)二次开发平台对现有MSC.Patran软件进行二次开发,并通过MSC.Nastran软件求解器,实现了优化算法。数值算例证明了该文程序与算法的有效性与可行性。     

基于对数型Heaviside近似函数作为过滤函数的动力响应结构拓扑优化ICM方法

应用ICM(Independent Continuous and Mapping)方法, 建立了以重量最小为目标函数, 以连续频率带或离散点频率的简谐激励下的响应振幅为约束的拓扑优化模型. 引入了对数型Heaviside近似函数作为过滤函数, 并做了敏度分析, 利用对偶二次规划进行优化模型的求解, 并运用敏度过滤的方法处理动力响应数值不稳定的问题. 数值算例比较了利用对数型函数和幂函数作为过滤函数时对拓扑结构的影响, 结果显示利用对数型函数较幂函数结构优化迭代次数更少, 收敛更快.     

结构畸变比能处理的应力约束全局化的连续体结构拓扑优化

该文根据von Mises强度准则的畸变比能本质,计算单元畸变比能替代应力约束;依照应力全局化策略,定义结构畸变比能约束概念,求解应力约束下重量最小的连续体结构拓扑优化问题,急剧地减少了应力约束。构造许用应力和结构最大应力的比值含参数幂函数,对约束限进行动态修正。基于ICM(Independent Continuous and Mapping,独立、连续、映射)方法,采用指数型快滤函数建立了结构在畸变比能约束下的结构拓扑优化模型,并选取精确映射下的序列二次规划进行求解。数值算例表明:采用修正的结构畸变比能的应力全局化策略,对于结构拓扑优化问题的求解是有用和高效的。该文提出的方法对解决工况间存在病态载荷的问题也是有益的。     

位移、应力、尺寸约束下二维连续体的形状优化

以二级控制理论为切入点,通过构造设计变量与关键点坐标之间的关系和关键点坐标与节点坐标之间的关系,得到了设计变量和节点坐标之间的关系。根据这一关系建立了目标函数跟设计变量之间的关系,采用有限差分法得到应力和位移的约束函数,建立了满足应力、位移和尺寸约束的形状优化模型,并采用序列二次规划方法求解二维连续体的形状优化问题。以MSC/Nastran软件为结构分析求解器,借助PCL语言开发了二维连续体的形状优化程序。为了有效地避免约束近似造成的迭代振荡乃至发散,在程序实现中,采用了区间因子来调整设计变量的上下限。数值算例表明程序算法的可靠性、精确性、高效性。     

结构拓扑优化ICM显式化与抛物型凝聚函数对于应力约束的集成化

对于连续体结构拓扑优化问题,该文指出:其最大求解困难除因0-1离散变量的本质造成,更因为目标函数、约束条件在理论上无法建立同0-1拓扑变量的直接联系。ICM(独立-连续-映射)方法解决了这一困难:用阶跃函数构筑了0-1变量与单元具体物理量或几何量联系的桥梁;将其逆函数(我们称之为跨栏函数)代入具体的优化表达式中,就可以显化拓扑优化模型与0-1变量的关系;其中跨栏函数用其逼近函数——过滤函数代替之,于是,不可微的结构拓扑优化规划就被可微化;进而可调常用的光滑算法进行有效的求解了。在磨光函数和过滤函数分别逼近阶跃函数和跨栏函数的同时,传统的0-1拓扑离散变量扩展为[0,1]区间上的连续变量了。由于许用应力、弹性模量、密度等材料性质被过滤函数识别,因而产生了相应的单元全程性质的概念,同理定义了单元全程几何参数的概念。基于ICM方法,利用单元全程许用应力,可以便捷地推导出结构拓扑优化应力奇异问题的ε-松弛解法的公式。提出了抛物型凝聚函数,证明了相关的定理,并且用于应力凝聚化处理的拓扑优化问题求解。另外,数值算例表明该文方法是有效的。     

模糊参数平面连续体结构的拓扑优化设计

研究了具有模糊参数的连续体结构在模糊载荷作用下的拓扑优化设计问题。利用信息熵将模糊变量转换为随机变量,构建了随机载荷作用下的随机参数的连续体结构的拓扑优化设计数学模型,以结构的形状拓扑信息为设计变量,结构总质量均值极小化为目标函数,满足单元应力可靠性为约束条件,利用分布函数法对应力可靠性约束进行了等价显式化处理。基于随机因子法,利用代数综合法导出了应力响应的数字特征的计算表达式。采用双方向渐进结构优化(BESO)方法求解。通过两个算例验证了该文模型及求解方法的合理性和有效性。     

基于动响应约束的结构材料优化设计

针对于随机荷载作用下动响应为约束的结构材料优化问题,基于结构拓扑优化思想,提出了一种变动响应约束的结构材料优化方法。采用分式有理式和幂函数识别结构材料单元特性参数,以微观单元拓扑变量倒数为设计变量,导出了频率及振型对微观单元设计变量的一阶导数,进而得到了随机荷载作用下结构均方响应的一阶近似展开式。结合变约束限的思想,建立了以结构质量作为目标函数,均方响应作为约束条件的连续体微结构拓扑优化近似模型,并采用对偶方法进行求解。对典型结构进行了考虑单个和多个动响应约束的结构材料优化设计,优化所得结果验证了该方法的有效性和可行性。     

Reliability‐based design optimization with equality constraints

Equality constraints have been well studied and widely used in deterministic optimization, but they have rarely been addressed in reliability‐based design optimization (RBDO). The inclusion of an equality constraint in RBDO results in dependency among random variables. Theoretically, one random variable can be substituted in terms of remaining random variables given an equality constraint; and the equality constraint can then be eliminated. However, in practice, eliminating an equality constraint may be difficult or impossible because of complexities such as coupling, recursion, high dimensionality, non‐linearity, implicit formats, and high computational costs. The objective of this work is to develop a methodology to model equality constraints and a numerical procedure to solve a RBDO problem with equality constraints. Equality constraints are classified into demand‐based type and physics‐based type. A sequential optimization and reliability analysis strategy is used to solve RBDO with physics‐based equality constraints. The first‐order reliability method is employed for reliability analysis. The proposed method is illustrated by a mathematical example and a two‐member frame design problem. Copyright © 2007 John Wiley & Sons, Ltd.     

一种新的几何约束系统参数取值范围的计算方法

在利用参数化CAD系统进行图形设计的过程中,通过修改图形对象的可变参数重新生成图形是最常见的一种操作。但用户在改变参数的过程中,由于事先并不知道有效的参数值,也没有任何引导信息,导致了用户只能盲目地不断输入参数值,通过反复输入参数值来满足约束关系的需要。该文将结构约束引入参数有效取值范围求解的范畴,并提出了确定一类常用的二维参数化CAD模型中参数的有效范围的计算方法和算法。算法复杂度为O（n2）。     

Locality constraints within multiscale model for non‐linear material behaviour

This paper presents a two‐scale approach for the mechanical and numerical modelling of materials with microstructure‐like concrete or fibre‐reinforced concrete in the non‐linear regime. It addresses applications, where the assumption of scale separation as the basis for classical homogenization methods does not hold. This occurs when the resolution of micro and macro scale does not differ ab initio or when evolving fluctuations in the macro‐fields are in the order of the micro scale during the loading progress. Typical examples are localization phenomena. The objective of the present study is to develop an efficient solution method exploiting the physically existing multiscale character of the problem. The proposed method belongs to the superposition‐based methods with local enrichment of the large‐scale solution ū by a small‐scale part u ′. The main focus of the present formulation is to allow for locality of the small‐scale solution within the large‐scale elements to achieve an efficient solution strategy. At the same time the small‐scale information exchange over the large‐scale element boundaries is facilitated while maintaining the accuracy of a refined complete solution. Thus, the emphasis lies on finding appropriate locality constraints for u ′. To illustrate the method the formulation is applied to a damage mechanics based material model for concrete‐like materials. Copyright © 2006 John Wiley & Sons, Ltd.     

Unit load and material-handling considerations in facility layout design

The effectiveness of a layout design cannot be completely measured if the operational characteristics of the manufacturing system are ignored. There is, therefore, a need to develop integrated manufacturing system design models. In this paper, the integration of unit load and material-handling considerations in a facility layout design is presented. This integration is based on a stochastic model that captures the operational characteristics of the manufacturing system and a nonlinear mixed-integer program that incorporates a department formation and facility layout. The non-linear mixed-integer program is solved using a simulated annealing-based algorithm. Analytical results for different manufacturing system scenarios are presented and compared with results obtained using alternative QAP-type formulations. Based on our experiments and the characteristics of the different formulations, key observations are presented and discussed.     

几何与动力约束结合的凸轮机构基本尺寸优化

考虑凸轮与转子间最大压力角及凸轮轮廓最小曲率半径等几何约束条件的同时,结合最大接触压应力、最大剪应力等动力约束条件,对凸轮机构基本尺寸优化问题进行了研究,提出了优化方法。最后辅之实例,结果表明低速上述最小尺寸由几何约束条件控制,中速时主要受动力约束条件限制,高速时则完全由动力约束条件所主宰。     

A novel branch-and-bound algorithm for the chance-constrained resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a mixed integer linear programming (MILP) formulation that solve a sample average approximation of the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. The computational results suggest that the proposed B&B procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature.     

Effect of frictional constraints on the barreling formations in cylinder upsetting with a hollow die

The objective of this study is to investigate the material flow characteristics associated with solid cylinder upsetting using a hollow die subjected to different combinations of frictional constraints. During the upsetting process, obviously two barrels are formed along the lateral-free surface of the workpiece and correspond to some specific combination of frictional constraints. A finite element based methodology is utilized to examine the radii of curvature of the barrels and the height of the top free surface that is extruded into the aperture of the die. In addition, the effect of various combinations of interface friction at the top- and bottom- die surfaces on both the effective stress and strain distributions are also investigated.     

矢量图的参数化重建系统——VACAD

本文重点探讨了如何将矢量图形进行参数化重建，即从只具备纯几何信息的矢量图中抽取元素间的拓扑信息，从而保证尺寸变动时保持拓扑关系不变，并能对多视图进行同步处理。这一方法的最大优点是用户作图时不受约束，因为系统只处理最终图形。另外，该思想并不局限于Ａｕｔｏ ＣＡＤ环境上，可方便地推广到其它二维绘图系统中。     

带有界约束非凸二次规划问题的整体优化方法

通过研究带有界约束非凸二次规划问题，给出了求解该问题的整体最优 解的分枝定界方法及其收敛性，提出了定界的紧，松驰策略，把球约束二次规划问题作为子问题来确定原问题的整体最优值下界和上界，应用分枝定界方法达到了对原问题的求解。     

Critical chain project buffer sizing based on resource constraints

Project scheduling is a complex process involving many types of resources and activities that require optimisation. The resource-constrained project scheduling problem is one of the well-known problematic issues when project activities have to be scheduled to minimise the project duration. Consequently, several methods have been proposed for adjusting the buffer size but none of these traditional methods consider buffer sizing accuracy based on resource constraints. The purpose of this paper is to develop a buffer sizing method based on a fuzzy resource-constrained project scheduling problem in order to obtain an appropriate proportionality between the activity duration and the buffer size. Specifically, a comprehensive resource-constrained method that considers both the general average resource constraints (GARC) and the highest peak of resource constraints (HPRC) is proposed in order to obtain a new buffer sizing method. This paper contributes to the research by considering several different aspects. First, this paper adopts a fuzzy method to calculate and obtain the threshold amount. Second, this paper discusses the resource levelling problem and proposes the HPRC method. Third, the proposed method uses a fuzzy quantitative model to calculate the resource requirement. The findings indicate that the project achieved higher efficiency, providing effective protection and an appropriate buffer size.