拓扑优化中去除数值不稳定性的算法研究

分析了拓扑优化计算中常出现的多孔材料、棋盘格、网格依赖性、局部极值等数值不稳定现象;分析了克服数值不稳定性现象的各种数值方法,及其各自的特点;提出了一种基于卷积因子前处理和小波分析后处理的综合过滤算法,能够有效消除拓扑优化中的数值不稳定现象。     

Manufacturing- and machining-based topology optimization

Topology optimization is used in the initial stage of the product manufacturing process. However, the non-manufacturable or non-machineable results of topology optimization have become an obstacle to process manufacturing. This paper proposes a modified topology optimization method by adding manufacturing and machining constraints to the topology optimization formulation. A hybrid topology optimization algorithm (combining the method of moving asymptotes and wavelets) is applied to solve this optimization problem. With this approach, the design space can be reduced and an engineering-accepted and manufacturable topology result can be guaranteed.     

多相材料的连续体结构拓扑优化设计

采用改进的过滤技术进行多相材料的连续体结构拓扑优化设计。以应变能最小化作为目标函数,结构体积作为约束,建立多相材料的连续体结构拓扑优化模型,将移动近似算法用于拓扑优化问题求解,采用改进的过滤求解技术对目标函数灵敏度及单元设计变量进行过滤,避免迭代过程中出现数值不稳定现象。数值算例结果表明,采用改进的过滤技术的多相材料连续体结构拓扑优化设计方法是有效的,能够获得清晰的结构拓扑图。     

周期性功能梯度结构稳态热传导拓扑优化设计

提出了一种考虑周期性约束的功能梯度结构稳态热传导拓扑优化设计方法。建立了基于变密度理论的固体各向同性微结构惩罚（SIMP）模型的周期性功能梯度拓扑优化模型。以整体结构散热弱度最小化为目标函数、体积分数为约束条件进行宏观拓扑优化,提取了最优构型中各预设梯度层的体积分数;通过重新分配单元散热弱度,实现了梯度层周期性约束设置。借助基于偏微分方程的灵敏度过滤方法消除数值不稳定问题,并采用移动渐近线法对设计变量进行了迭代更新。通过2D和3D数值算例分析了全局周期以及周期性分层梯度设置下,不同离散单元和子区域个数对宏观结构和微观构型的影响规律。研究结果表明：所提方法能够实现周期性约束下功能梯度结构的拓扑优化设计,不同子区域个数条件下均能获得清晰的周期性功能梯度结构且所获得的结构具有良好的散热性能。     

NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION

0 INTRODUCTIONTwo types of algorithms are currently widely used instructure optimization. The first one is the optimization criteria(OC) method. The OC method can be understood directly, but it isdifficult to deduce different types of optimization criteri…     

基于人工材料密度的新型拓扑优化理论和算法研究

对基于人工材料密度的拓扑优化理论作了深入分析;推导出了一种基于人工材料密度的拓扑优化准则算法,将该算法应用于拓扑优化的计算中,并给出了基于人工材料密度的拓扑优化迭代分析流程;提出了一种卷积因子方法,用于消除拓扑优化计算结果中易出现的棋盘格式和多孔材料现象;通过数值计算验证了理论和算法的有效性;分析讨论了不同优化参数对拓扑优化计算结果的影响。     

含自重载荷的功能梯度材料结构时域动力学拓扑优化设计

提出了一种含自重载荷的功能梯度材料(FGM)结构时域动力学拓扑优化设计方法。在固体各向同性材料惩罚(SIMP)框架下,提出了一种针对FGM-SIMP的结构自重载荷分布策略。以FGM结构动柔度最小为优化目标、以结构体积为约束,建立了动力学结构优化列式。基于伴随法,在时域内进行了灵敏度推导,并用移动渐近线方法进行求解。通过二维和三维典型数值算例系统研究了含自重载荷下FGM结构的拓扑优化设计问题,并深入探讨了自重载荷和材料梯度分布方向对结构优化结果的影响,发现自重载荷和材料梯度分布方向对FGM结构的优化构型和动刚度具有很大影响。最后,以均一材料(FGM的特例)为例,通过数值仿真和实验测试方法验证了所提方法的有效性,并证实了所提方法可有效提高结构的固有频率和结构动刚度。     

Topology optimum design of unimorph piezoelectric cantilevered Mindlin plates as a vibrating electric harvester

An FEM-based topology optimization approach is proposed to calculate the topologies of a substrate plate and a piezoelectric layer used for vibrating unimorph cantilevered plate-like electricity generators (energy harvesters). The Mindlin plate theory was combined with a topology optimization algorithm to consider the shear effect. Each optimum topology for a plate and a piezoelectric layer is computed and combined by reflecting the natural frequencies of the substrate plate, electromechanical couplings of piezoelectric materials, tip masses and method of moving asymptotes. The piezoelectric coefficients such as elasticity, piezoelectric coupling and capacitance are interpolated by element density variables. The cantilevered plate generators with optimal topologies were designed for three piezoelectric materials such as PZT, PMN-PT and PMN-PT single crystal fiber MFC, and their voltage outputs were compared using a developed FEM-based optimization code to investigate the suitable material for harvesters.     

Power flow response based dynamic topology optimization of bi-material plate Structures

Work on dynamic topology optimization of engineering structures for vibration suppression has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, minimization of the dynamic compliance subject to forced vibration, and minimization of the structural frequency response. A dynamic topology optimization method of bi-material plate structures is presented based on power flow analysis. Topology optimization problems formulated directly with the design objective of minimizing the power flow response are dealt with. In comparison to the displacement or velocity response, the power flow response takes not only the amplitude of force and velocity into account, but also the phase relationship of the two vector quantities. The complex expression of power flow response is derived based on time-harmonic external mechanical loading and Rayleigh damping. The mathematical formulation of topology optimization is established based on power flow response and bi-material solid isotropic material with penalization(SIMP) model. Computational optimization procedure is developed by using adjoint design sensitivity analysis and the method of moving asymptotes(MMA). Several numerical examples are presented for bi-material plate structures with different loading frequencies, which verify the feasibility and effectiveness of this method. Additionally, optimum results between topological design of minimum power flow response and minimum dynamic compliance are compared, showing that the present method has strong adaptability for structural dynamic topology optimization problems. The proposed research provides a more accurate and effective approach for dynamic topology optimization of vibrating structures.     

面向制造的连续体结构拓扑优化设计方法研究

为了更好地解决结构拓扑优化的工程实用化问题,研究了一种面向制造的连续体结构拓扑优化设计的方法,即面向制造的分级拓扑优化方法。该方法可使优化结果同时满足设计性能和制造性能的要求。为消除数值不稳定,研究了密度和敏度混合高斯函数过滤算法,该算法能有效解决棋盘格式及网格依赖等数值不稳定问题,并能获得良好的优化结果。利用研究的分级拓扑优化方法和有关算法,对经典算例进行计算,所得结果验证了该方法的可行性和有效性。     

结构拓扑优化设计的研究现状及其应用

介绍了结构拓扑设计的发展过程和主要的数学模型;分析了目前存在的拓扑数值稳定性问题和这些问题的常用处理技术;描述了优化准则法、序列线性规划法和移动渐进线法三种常用的优化算法;举例说明了拓扑设计在静态结构、动态特性和柔性机构设计中的应用;根据国内外目前在结构拓扑设计领域的研究现状和笔者的科研经验,总结了拓扑设计今后研究的重点内容和发展方向。     

基于混合元胞自动机的柔顺机构多目标拓扑优化方法

采用无梯度优化方法——混合元胞自动机方法进行体积约束下柔顺机构多目标拓扑优化设计。以应变能最小化和互应变能最大化为目标,以结构体积为约束,采用标准化方法定义多目标拓扑优化的目标函数,消除不同性质目标函数在数量级上的差异。将混合元胞自动机方法用于多目标优化问题的求解,以比例控制作为局部控制规律。数值算例结果表明,该方法用于柔顺机构多目标拓扑优化设计是有效的,优化迭代次数较少,且结构不易出现单节点铰链现象。     

用拓扑优化方法进行微型柔性机构的设计研究

研究了微型柔性机构拓扑优化设计中的几个关键问题，提出了一种基于优化准则法和移动渐进优化算法的综合求解策略，在柔性机构设计中采用了非线性求解技术和伴随矩阵敏度分析技术，并将这些关键技术在算法上进行了实现，设计出了几种典型的微型柔性机构器件。     

基于最大应力约束的柔顺机构拓扑优化设计

采用拓扑优化方法获得柔顺机构构型容易出现类铰链结构,导致应力集中、疲劳可靠性差。为了抑制类铰链结构,提出了一种基于最大应力约束的柔顺机构拓扑优化设计方法。采用改进的固体各向同性材料惩罚模型（Solid isotropic material with penalization,SIMP）,以柔顺机构的互应变能最大化作为目标函数,采用P范数方法对所有单元的局部应力凝聚化成一个全局化应力约束,利用自适应约束缩放法使得P范数应力更加接近最大应力,以机构的最大应力和体积作为约束,建立柔顺机构最大应力约束拓扑优化模型,采用全局收敛移动渐近线算法求解柔顺机构最大应力约束拓扑优化问题。结果表明,采用P范数方法进行柔顺机构最大应力约束拓扑优化设计,能够有效抑制类铰链结构。随着应力约束极限值减少,获得机构构型由集中式柔顺机构逐渐转变为分布式柔顺机构,应力分布更加均匀,但机构的互应变能逐渐减小。     

连续体结构拓扑优化改进的敏度修正方法研究

为了消除拓扑优化中的棋盘格现象,在对常用敏度过滤方法的研究基础上,提出了一种新型敏度修正方法来解决数值不稳定性的问题。该方法通过设置中心单元过滤权重对拓扑优化结果进行控制。利用经典的柔度最小化数值算例研究了新型敏度修正方法对拓扑优化结果的影响,数值分析结果表明,该方法能达到消除棋盘格、网格依赖性现象以及避免边界过度磨平的目的。     

考虑碳排放与收益的随机并行拆卸线平衡优化

针对废旧产品回收过程中,需有选择对综合收益高的零部件进行拆卸的问题。选择最小工作站数,平滑度,碳排放量,拆卸收益作为优化目标,并对相应目标进行量化分析,提出一种随机并行拆卸线平衡优化方法。在构建随机并行拆卸线基本解集的基础上,为避免Pareto解集逐渐趋同的问题,提出一种基于环形拓扑结构的花授粉算法(Ring topology flower pollination algorithm, Ring-FPA),实现了对Pareto解集的决策处理,获得考虑碳排放与收益的随机并行拆卸线平衡最优解。以手机和笔记本电脑并行拆卸线平衡优化为例,选择NSGA-Ⅱ、FPA,以及AFSA算法进行对比,对所提方法的可行性和有效性进行了验证。     

A novel particle swarm optimization approach for product design and manufacturing

This paper presents a novel optimization approach that is a new hybrid optimization approach based on the particle swarm optimization algorithm and receptor editing property of immune system. The aim of the present research is to develop a new optimization approach and then to apply it in the solution of optimization problems in both the design and manufacturing areas. A single-objective test problem, tension spring problem, pressure vessel design optimization problem taken from the literature and two case studies for multi-pass turning operations are solved by the proposed new hybrid approach to evaluate performance of the approach. The results obtained by the proposed approach for the case studies are compared with a hybrid genetic algorithm, scatter search algorithm, genetic algorithm, and integration of simulated annealing and Hooke-Jeeves pattern search.     

Multiobjective trajectory optimization of intelligent electro-hydraulic shovel

Multiobjective trajectory planning is still face challenges due to certain practical requirements and multiple contradicting objectives optimized simultaneously. In this paper, a multiobjective trajectory optimization approach that sets energy consumption, execution time, and excavation volume as the objective functions is presented for the electro-hydraulic shovel (EHS). The proposed cubic polynomial S-curve is employed to plan the crowd and hoist speed of EHS. Then, a novel hybrid constrained multiobjective evolutionary algorithm based on decomposition is proposed to deal with this constrained multiobjective optimization problem. The normalization of objectives is introduced to minimize the unfavorable effect of orders of magnitude. A novel hybrid constraint handling approach based on ε-constraint and the adaptive penalty function method is utilized to discover infeasible solution information and improve population diversity. Finally, the entropy weight technique for order preference by similarity to an ideal solution method is used to select the most satisfied solution from the Pareto optimal set. The performance of the proposed strategy is validated and analyzed by a series of simulation and experimental studies. Results show that the proposed approach can provide the high-quality Pareto optimal solutions and outperforms other trajectory optimization schemes investigated in this article.     

Isogeometric topology optimization based on energy penalization for symmetric structure

We present an energy penalization method for isogeometric topology optimization using moving morphable components (ITO–MMC), propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint. The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads. Topology optimization problems of asymmetric, bilateral symmetric, and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach. Compared with the conventional ITO–MMC, the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6% to 44.5% for the optimization of the asymmetric structure. For the ITO–MMC under a bilateral symmetric constraint, the proposed method can reduce the objective value by 5.6% and obtain a final optimized topology that has a clear boundary with decreased iterations. For the ITO–MMC under a periodic symmetric constraint, the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.     

Optimization of multi-pass turning operations using hybrid teaching learning-based approach

This paper presents a novel hybrid optimization approach based on teaching–learning based optimization (TLBO) algorithm and Taguchi’s method. The purpose of the present research is to develop a new optimization approach to solve optimization problems in the manufacturing area. This research is the first application of the TLBO to the optimization of turning operations in the literature The proposed hybrid approach is applied to two case studies for multi-pass turning operations to show its effectiveness in machining operations. The results obtained by the proposed approach for the case studies are compared with those of particle swarm optimization algorithm, hybrid genetic algorithm, scatter search algorithm, genetic algorithm and integration of simulated annealing, and Hooke–Jeeves patter search.