基于ICM方法的多工况位移约束下板壳结构拓扑优化设计

基于ICM方法,建立了多种载荷工况下受位移约束极小化结构重量的拓扑优化近似显式模型,采用精确对偶映射下的序列二次规划算法进行求解,得到了结构的最优拓扑.数值算例表明:ICM方法也可以很好地应用于多工况下板壳结构拓扑优化设计,且收敛快,稳定性好;边界条件和位移约束值都会影响结构的最优拓扑;多工况最优传力路径不是各个单工况最优传力路径的简单叠加.     

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。     

破损-安全拓扑优化的局部破损模式参数影响分析

针对连续体结构，考虑破损-安全拓扑优化中如何处理结构局部破损的关键问题，以位移约束下结构体积极小化拓扑优化问题为例，基于独立连续映射ICM方法，建立了优化模型，给出了求解方法。以单荷载及多荷载工况的数值算例为例，探讨了结构局部破损模式的形状和大小及结构局部破损状况预估分布等对最优结构拓扑的影响。结果表明，（1）相比于不考虑破损-安全的结构拓扑优化，考虑破损-安全得到的最优拓扑具有更多冗余构件及传力路径；（2）不同形状及大小的结构局部破损模式会得到不同的最优结构拓扑；（3）结构局部破损模式布置间距越小，得到的最优拓扑越趋复杂。故在进行考虑破损-安全拓扑优化设计时，宜依据工程问题，合理定义结构局部破损模式的形状和大小及结构局部破损状况的预估分布等，以准确模拟实际结构的局部破损，得到具有适度冗余的最优拓扑。     

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     

位移约束集成化处理的连续体结构拓扑优化

为解决多工况下多位移约束的连续体结构拓扑优化问题,引入了K-S函数对位移约束进行集成化处理.在建立优化模型时,基于莫尔定理按ICM方法导出约束点位移与设计变量之间的近似显函数关系,然后采用Lagrange乘子法进行求解.给出三个算例对该方法进行验证,并与ESO法、BESO法、MD法以及均匀化方法的结果进行比较.结果表明:该方法计算效率较高,并且能够计算出更合理的结构拓扑.     

破损-安全拓扑优化的局部破损模式参数影响分析

针对连续体结构,考虑破损-安全拓扑优化中如何处理结构局部破损的关键问题,以位移约束下结构体积极小化拓扑优化问题为例,基于独立连续映射ICM方法,建立了优化模型,给出了求解方法。以单荷载及多荷载工况的数值算例为例,探讨了结构局部破损模式的形状和大小及结构局部破损状况预估分布等对最优结构拓扑的影响。结果表明,(1)相比于不考虑破损-安全的结构拓扑优化,考虑破损-安全得到的最优拓扑具有更多冗余构件及传力路径;(2)不同形状及大小的结构局部破损模式会得到不同的最优结构拓扑;(3)结构局部破损模式布置间距越小,得到的最优拓扑越趋复杂。故在进行考虑破损-安全拓扑优化设计时,宜依据工程问题,合理定义结构局部破损模式的形状和大小及结构局部破损状况的预估分布等,以准确模拟实际结构的局部破损,得到具有适度冗余的最优拓扑。     

一种变位移约束限的结构拓扑优化方法

针对仅有位移约束和重量最小的结构拓扑优化问题, 基于ICM(独立、连续、映射)方法思路,提出了一种变位移约束限的结构拓扑优化方法. 在每一轮子循环迭代求解开始时,为了控制拓扑设计变量的变化量, 形成和引进了新的位移约束限. 另外,建立了单元删除阈值和几轮迭代循环的单元删除策略. 为了确保优化迭代中结构非奇异和方法具有增添单元的功能,在结构孔洞和边界周围引入了一层人工材料单元,并建立了一套有效结构信息到结构最大设计域信息的映射转换方法. 结合对偶求解方法,形成了一种新的连续体结构的拓扑优化方法. 给出的算例表明该方法没有目标函数的振荡现象,且验证了该方法的正确性和有效性. 关键词:拓扑优化; 位移约束; 连续体结构; ICM方法; 渐进结构优化;      

连续体结构拓扑优化的高精度逼近ICM方法

采用指数类函数为快滤函数的高精度逼近ICM (independent continuous and mapping)方法, 建立了以结构重量为目 标, 应力和位移共同约束下的连续体结构拓扑优化模型. 利用结构畸变比能的方法全局化应 力约束, 单位虚载荷法显式化位移约束, 归一化约束以解决约束限数量级不一致的问题. 针 对不同性态的过滤函数, 给出了指数类快滤函数参数的取值方法. 单工况和多工况的算例表 明了高精度逼近的ICM方法处理多种约束下连续体结构拓扑优化的可行性与有效性.     

结构拓扑优化ICM方法的改善

对结构拓扑优化的ICM(独立、连续、映射)方法进行了深入探讨，通 过选取不同的过滤函数可以不进行每步删除而得到清晰的拓扑图形. 以位移约束为例阐述了 ICM方法建模及求解过程. 对位移约束、频率约束、位移及频率约束、简谐载荷激励下动位 移幅值约束等拓扑优化进行了研究，计算算例表明ICM方法在处理静力问题及动力问题的拓 扑优化都是可行的. 程序算法都在MSC.Nastran及MSC.Patran的二次开发环境下实现，与 原软件有机结合在一起.     

应力约束处理为应变能集成的连续体结构拓扑优化

为克服应力约束下拓扑优化问题约束多、应力敏度计算量大的困难,本文提出了将应力约束处理为应变能集成的结构拓扑优化ICM方法。文中用几个典型算例对该方法进行了检验,结果表明:本方法优化效率较高,而且得到的结构最优拓扑较为合理。     

考虑破损-安全的连续体结构拓扑优化ICM方法

本文瞄准连续体在破损-安全考虑下的结构拓扑优化问题,旨在克服传统模型求解所得最终构型存在的弊病,避免结构因缺乏合理的冗余结构而敏感于局部破坏,实现破损-安全的目标. 首先,梳理了以往虽然用到却并不明晰的4个概念:结构局部破损模式、结构局部破损区域、结构破损状况、结构破损状况的预估分布. 之后,基于独立连续映射(ICM)方法,对该问题建立了力学性能约束下结构体积极小化的模型. 建立目标函数时,利用Minimax的概念将可能出现的结构破损状况对应的所有结构体积目标转化为原结构的唯一结构体积目标,克服了多目标问题的困难. 建立近似约束函数时,将可能出现的所有结构破损状况对应的力学性能的约束皆考虑进去,既能处理载荷单工况也能处理载荷多工况. 最后,以位移约束为例,建立了优化模型并求解. 单工况及多工况位移约束拓扑优化算例验证了算法的有效性. 结果表明:本方法相比于不考虑破损-安全的拓扑优化设计,得到的最优拓扑更复杂,体积比更大即所用材料更多,亦即最优结构具有更多的冗余,此正是考虑破损-安全设计原则的结果. 本文的研究对于航空、航天、其他水、陆等领域运载工具以及其他工程结构在意外破坏、战争创伤或恐怖袭击下的结构设计,乃是非常重要的进展.      

A Nondifferentiable Optimization Algorithm for Structural Problems with Eigenvalue Inequality Constraints*

This paper presents a nondifferentiable optimization algorithm for solution of structural optimal design problems with eigenvalue inequality constraints. The algorithm is shown to be convergent both in the L _∞ and in the sequence space topologies.     

A Comparison of Deterministic,Reliability-Based Topology Optimization under Uncertainties

Reliability and optimization are two key elements for structural design. The reliabilitybased topology optimization(RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topology optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach(the performance measure approach, PMA) and the decoupled approaches(the so-called Hybrid method and the sequential optimization and reliability assessment, SORA). For reliability analysis, the stochastic response surface method(SRSM) was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique.The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the deterministic, RBTOs were compared with one another; and useful conclusions regarding validity,accuracy and efficiency were drawn.     

Design of buckling constrained multiphase material structures using continuum topology optimization

This study contributes to a possibility of evaluating composite structures configuration such as steel and concrete using buckling and volume constraints based on multi-material topology optimization. A Jacobi active-phase algorithm is used to generate multiphase topology optimization. It provides a rational solution appropriated to the topology optimizer, Method of Moving Asymptotes due to the conflict in updating the design variables. A modified material interpolation scheme solving spurious buckling modes problem which occurs in the multi-material topology optimization process is given and discussed. An investigation of buckling constraint parameter is described. It allows a single-objective minimum compliance topology optimization to obtain two objectives of maximizing both structure stiffness and first buckling load factor. The optimal changing topologies of single material structure and multi-material structure corresponding to different buckling constraints are presented. Numerical examples of compression-only structures and compression-tension structures considering structural instability are performed using both single material and multiple materials to verify the efficiency and superiority of the present method.

     

单侧接触约束下桁架拓扑优化的若干结果

对考虑应力和无摩擦单侧接触位移约束的桁架拓扑优化问题进行了研究,采用解析方法,通过对典型算例不同初始接触间隙下的拓扑优化解的讨论,发现这一优化问题中存在解不唯一现象,研究也表明,接触状态对结构拓扑有一定影响,不同初始接触间隙可能导致不同的拓扑结构,对利用数值方法该问题进行了研究,为克服结构拓扑优化中奇异最优解问题,采用ε松弛方法建立桁架拓扑优化模型列式,并利用双层优化方法求解本拓扑优化问题,第一层,通过求解与原接触问题等价的二次规划问题来进行结构接触分析;第二层,利用第一层得到的位移及应力,采用ε-松弛方法进行结构拓扑优化。     

桁架结构拓扑优化设计可行域研究

本文提出了桁架结构拓扑优化设计的k维可行子域、相邻可行子域、k维连通可行子域、k维奇异可行子域的定义，在这些定义的基础上，采用集合描述的方法，对Rozvany关于结构拓扑优化设计奇异最优解的定义进行了重新描述。基于以上定义，本文研究了桁架结构拓扑优化设计的可行域，证明了对于截面尺寸下限为零，且无尺寸上限的桁架结构受应力约束的拓扑优化设计问题，其设计空间不同拓扑的可行子域总是连通的，同时也给出了对于具有尺寸下限约束、具有局部稳定性约束的桁架结构拓扑优化设计的可行子域不连通的实例。     

SOME RESULTS ON OPTIMAL TOPOLOGY DESIGN OF TRUSS WITH UNILATERAL CONTACT CONSTRAINTS

The optimal topology design of truss structures concerning stress and frictionless unilateral contact displacement constraints is investigated. The existence of ununique optimal solution under contact gaps is found. This shows that the contact conditions have an effect on structural topology, and different initial contact gaps may lead to different structural topologies. To avoid the singular optima in structural topology optimization in multiple loading cases, an ε-relaxed method is adopted to establish the relaxing topology optimization formulations. The problem is solved by means of a two-level optimization method. In the first sublevel, the solution of the frictionless unilateral contact problem is obtained by solving an equivalent quadratic programming. In the second sublevel, topology optimization of truss is carried out by an ε-relaxed method. The validity of the method proposed is verified by computational results. Supported by the Postdoctoral Science and Research Foundation of Shanghai, China.     

Topology design and optimization of nonlinear periodic materials

This paper explores optimal topologies yielding large band gap shifts in one- and two-dimensional nonlinear periodic materials. The presence of a nonlinearity in a periodic material system results in amplitude-dependent dispersion behavior, leading to novel wave-based devices such as tunable filters, resonators, and waveguides. The performance of these devices over a broad frequency range requires large, tunable band gaps, motivating the present study. Consideration of a one-dimensional bilayer system composed of alternating linear and nonlinear layers shows that optimal designs consist of thin, compliant nonlinear layers. This is at first surprising considering the source of the shift originates from only the nonlinear layer; however, thin layers lead to localized stresses that activate the nonlinear character of the system. This trend persists in two-dimensional materials where optimization studies are performed on plane-stress models discretized using bilinear Lagrange elements. A fast algorithm is introduced for computing the dispersion shifts, enabling efficient parametric analyses of two-dimensional inclusion systems. Analogous to the one-dimensional system, it is shown that thin ligaments of nonlinear material lead to large dispersion shifts and group velocity variations. Optimal topologies of the two-dimensional system are also explored using genetic algorithms aimed at producing large increases in complete band gap width and shift, or group velocity variation, without presupposing the topology. The optimal topologies that result resemble the two-dimensional inclusion systems, but with small corner features that tend to enhance the production of dispersion shift further. Finally, the study concludes with a discussion on Bloch wave modes and their important role in the production of amplitude-dependent dispersion behavior. The results of the study provide insight and guidance on selecting topologies and materials which can yield large amplitude-dependent band gap shifts and group velocity variations, thus enabling sensitive nonlinear devices.