考虑重叠过滤及稳定性约束的桁架拓扑优化方法

从工程实际的角度来说,一般不允许结构形式中包含重叠单元。目前桁架拓扑优化的基结构法在选定基节点的情况下一般不建重叠单元,这导致可行域缩小,使优化不能找到更优解,人为增删杆件缺乏科学依据。针对该问题,该文对重叠给出准确的数学描述,建立包含重叠杆的基结构,利用Heaviside函数将拓扑变量连续化处理,使之在优化过程中可以获取目标函数、约束函数的敏度信息,同时考虑在拓扑优化中加入基频约束以避免出现机构,并加入稳定性约束防止出现压杆失稳,通过优化模型实现重叠过滤。最后通过两个案例计算证明可以找到更优解,验证了该方法的有效性。     

概率及非概率不确定性条件下结构鲁棒设计方法

提出了在概率不确定性和非概率不确定性同时存在时的约束函数鲁棒性和目标函数鲁棒性的实现策略及结构鲁棒设计方法。将传统优化设计问题的约束条件改造成为能同时反映两类不确定性量波动变化影响的约束条件,以实现约束函数的鲁棒性;在传统优化设计问题目标函数中增加若干个关于目标函数灵敏度的新目标函数,构成一个多目标函数设计问题,以实现目标函数的鲁棒性。所提方法应用于一个10杆桁架结构设计,采用宽容排序法求解。计算结果表明,在相同的结构总质量限制条件下,目标函数鲁棒性程度随着变量不确定性程度的增加而降低;在相同的变量不确定性程度条件下,增加结构总质量能提高目标函数鲁棒性的程度。     

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）。     

区间参数杆系结构非概率可靠性指标的改进仿射算法

将杆系结构中的不确定性参数用区间数表示,建立结构的非概率可靠性指标求解方程。将矩阵形式的仿射算术和递归导数信息结合,提出了改进的二元区间多项式矩阵形式的仿射上下界公式。给出了有界不确定性变量的仿射型和区间形式的相互转化,将有界不确定性变量的仿射型及结合导数信息的矩阵形式的仿射运算引入到杆系结构基于区间模型的非概率可靠性指标计算中。分别以某外伸梁和十杆桁架结构为例对该方法的可行性和有效性进行了验证。     

面向工程的专用产品参数化CAD系统的研究

 针对目前参数化CAD系统的不足，提出了面向工程的参数化思想，引入了功能约束，分析了对功能约束进行处理的3种方法．采用了基于特征的参数化造型方法，用应用层、描述层和图形层三层体系表达基于特征的参数化模型，将该模型作为参数驱动的基础．将设计中的约束分为3类：工程约束、适配约束和几何约束．通过适配约束在工程约束与几何约束间建立映射关系，使得参数化设计系统既可以受几何参数的驱动，又可以受工程参数的驱动，从而扩大了CAD技术对设计过程支持的范围。     

屈曲与应力约束下连续体结构的拓扑优化

基于ICM(独立、连续、映射)方法建立了以结构重量最小为目标,以屈曲临界力、应力同时为约束的连续体拓扑优化模型:采用独立的连续拓扑变量,借助泰勒展式、过滤函数将目标函数作二阶近似展开;借助瑞利商、泰勒展式、过滤函数将屈曲约束化为近似显函数;将应力这种局部性约束采用全局化策略进行处理,即借助第四强度理论、过滤函数将应力局部性约束转化为应变能约束,大大减少了灵敏度分析的计算量;将优化模型转化为对偶规划,减少了设计变量的数目,并利用序列二次规划求解,缩小了模型的求解规模。数值算例表明:该方法可以有效地解决屈曲与应力约束共同作用的连续体拓扑优化问题,能够得到合理的拓扑结构,并有较高的计算效率。     

采用相似变换解决含压杆稳定约束的桁架满应力设计

基于满应力设计思想,考虑桁架杆件在压力作用下的局部稳定约束,采用相似变换的方法,找出了惯性矩I与截面面积A的关系,根据压杆的临界应力分别导出大、中、小柔度的迭代公式,设计出压杆的截面积,解决了同时满足应力约束和局部稳定约束的桁架结构截面优化问题。在MSC/NASTRAN上利用PCL语言开发出了含局部稳定约束的桁架优化的更合理、更精确的优化软件。     

一类非理想杆端约束下的转角位移方程

将结构的结点视为理想和非理想结点,建立了一类非理想杆端约束——弹性结点的基本概念,给出了杆端均为非理想和一端为理想约束、另一端为非理想约束情况下的转角位移方程。通过比较表明,该方程更具一般性,两端理想约束下的转角位移方程可视为其特例。举例说明了该方程的应用及结构内力随杆端约束的变化情况。     

AutoCAD中基于超图约束驱动参数化设计的实现

使用超图表示约束模型,采用基于超图约束驱动的几何推理约束满足法进行参数化设计,几何实体的计算基于特征点。作者结合在AutoCAD上开发参数化设计模块的实践,得出该方法能处理多实体约束关系(如面积约束),提高求解效率,降低时间复杂度。     

AutoCAD 中基于超图约束驱动参数化设计的实现

 使用超图表示约束模型,采用基于超图约束驱动的几何推理约束满足法进行参数化设计,几何实体的计算基于特征点。作者结合在ＡｕｔｏＣＡＤ上开发参数化设计模块的实践,得出该方法能处理多实体约束关系（如面积约束）,提高求解效率,降低时间复杂度。     

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.     

Continuum structural topological optimizations with stress constraints based on an active constraint technique

Stress‐related problems have not been given the same attention as the minimum compliance topological optimization problem in the literature. Continuum structural topological optimization with stress constraints is of wide engineering application prospect, in which there still are many problems to solve, such as the stress concentration, an equivalent approximate optimization model and etc. A new and effective topological optimization method of continuum structures with the stress constraints and the objective function being the structural volume has been presented in this paper. To solve the stress concentration issue, an approximate stress gradient evaluation for any element is introduced, and a total aggregation normalized stress gradient constraint is constructed for the optimized structure under the r?th load case. To obtain stable convergent series solutions and enhance the control on the stress level, two p‐norm global stress constraint functions with different indexes are adopted, and some weighting p‐norm global stress constraint functions are introduced for any load case. And an equivalent topological optimization model with reduced stress constraints is constructed,being incorporated with the rational approximation for material properties, an active constraint technique, a trust region scheme, and an effective local stress approach like the qp approach to resolve the stress singularity phenomenon. Hence, a set of stress quadratic explicit approximations are constructed, based on stress sensitivities and the method of moving asymptotes. A set of algorithm for the one level optimization problem with artificial variables and many possible non‐active design variables is proposed by adopting an inequality constrained nonlinear programming method with simple trust regions, based on the primal‐dual theory, in which the non‐smooth expressions of the design variable solutions are reformulated as smoothing functions of the Lagrange multipliers by using a novel smoothing function. Finally, a two‐level optimization design scheme with active constraint technique, i.e. varied constraint limits, is proposed to deal with the aggregation constraints that always are of loose constraint (non active constraint) features in the conventional structural optimization method. A novel structural topological optimization method with stress constraints and its algorithm are formed, and examples are provided to demonstrate that the proposed method is feasible and very effective. © 2016 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.     

SAFE-FAIL LINE METHOD—AN ALGORITHM TO REDUCE THE CALCULATION OF COMPLEX CONSTRAINTS IN DESIGN OPTIMIZATION

A rather simple but quite effective algorithm is proposed for reducing the number of calculations of complex constraint functions in optimization problems. A type of monotonicity is used to set up a direct relationship between the design variables and the critical constraints. It can frequently be predicted whether or not the constraints are satisfied at a design point just by checking the variation in the design variables. It can be established in advance that a given constraint function varies with respect to a design variable in one of four ways, and rules can be defined, based on the previous history of function values, whether or not a constraint function need be evaluated. Trial calculations of a sample of problems suggest typical savings of 40-50%. The procedure is illustrated by stress constraints; but the same method can be used in other types.     

A sequential approximation method using neural networks for engineering design optimization problems

There are three characteristics in engineering design optimization problems: (1) the design variables are often discrete physical quantities; (2) the constraint functions often cannot be expressed analytically in terms of design variables; (3) in many engineering design applications, critical constraints are often ‘pass–fail’, ‘0–1’ type binary constraints. This paper presents a sequential approximation method specifically for engineering optimization problems with the three characteristics. In this method a back-propagation neural network is trained to simulate a rough map of the feasible domain formed by the constraints using a few representative training data. A training data point consists of a discrete design point and whether this design point is feasible or infeasible. Function values of the constraints are not required. A search algorithm then searches for the optimal point in the feasible domain simulated by the neural network. This new design point is checked against the true constraints to see whether it is feasible, and is then added to the training set. The neural network is trained again with this added information, in the hope that the network will better simulate the boundary of the feasible domain of the true optimization problem. Then a further search is made for the optimal point in this new approximated feasible domain. This process continues in an iterative manner until the approximate model locates the same optimal point in consecutive iterations. A restart strategy is also employed so that the method may have a better chance to reach a global optimum. Design examples with large discrete design spaces and implicit constraints are solved to demonstrate the practicality of this method.     

面向思维约束的产品造型概念设计

目的针对概念设计思维的发散特性,基于约束理论的思想流程,在产品造型概念设计过程中引入思维约束理论,解决方案设计繁琐及控制难度较大的问题。方法对思维约束在产品造型概念设计中的可行性进行分析,从用户的角度归纳个体差异化、群体公共化和功能技术化3类导向模式。然后详细论述思维约束在产品造型概念设计中的系统性、理念导向性、层次性和时序性,形成约束体系。结论面向思维约束的产品造型概念设计方法,由产品情景构建、产品概念定位约束形成概念约束环节,通过约束环节中约束要素的解构,进行造型方案设计。以案例应用进行验证,理论在降低造型概念设计思维流程的复杂性方面具有可用性,为产品造型概念设计提供参考。     

基于FRG的约束模型管理

为实现设计环境的自然化和智能化，本文将特征模型分为模型描述和模型数据两个层次，模型描述是基于约束的，故称为约束模型，并定义为满足一定约束关系集的特征集合。     

Structural shape and topology optimization of cast parts using level set method

This paper presents a level set‐based shape and topology optimization method for conceptual design of cast parts. In order to be successfully manufactured by the casting process, the geometry of cast parts should satisfy certain moldability conditions, which poses additional constraints in the shape and topology optimization of cast parts. Instead of using the originally point‐wise constraint statement, we propose a casting constraint in the form of domain integration over a narrowband near the material boundaries. This constraint is expressed in terms of the gradient of the level set function defining the structural shape and topology. Its explicit and analytical form facilitates the sensitivity analysis and numerical implementation. As compared with the standard implementation of the level set method based on the steepest descent algorithm, the proposed method uses velocity field design variables and combines the level set method with the gradient‐based mathematical programming algorithm on the basis of the derived sensitivity scheme of the objective function and the constraints. This approach is able to simultaneously account for the casting constraint and the conventional material volume constraint in a convenient way. In this method, the optimization process can be started from an arbitrary initial design, without the need for an initial design satisfying the cast constraint. Numerical examples in both 2D and 3D design domain are given to demonstrate the validity and effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

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。     

离散变量结构优化设计的最优综合效能法

针对结构优化问题的位移约束,引入关键约束的界约参数,提出了结构位移统一约束的缩减形式,从而简化了结构优化模型。根据离散变量结构优化问题的特点,提出了效能系数的概念,它衡量设计变量在离散邻域范围内变化对目标函数与约束函数值的影响,并研究了基于效能系数取值分类的四种主要调整方式。根据结构应力和位移约束的影响区域属性,以综合效能最大化为引导,提出了求解离散变量结构优化问题的最优综合效能法。算例结果显示该算法具有良好的优化效率,可求得问题的最优解或获得历史上的最优记录。