基于拓扑优化和形状优化的桨叶结构设计

直升机旋翼桨叶剖面结构设计是研究旋翼动力学设计的基础。提出一种联合拓扑优化和形状优化的 两级优化设计方法,可用于桨叶剖面结构的设计。第一级优化以变密度法(SIMP)作为拓扑优化的材料插值方 法,以桨叶体积最小化为设计目标,约束桨叶节点位移和应力,建立桨叶的拓扑优化求解模型;第二级优化以重 构的桨叶模型为基础开展形状优化,降低局部应力集中以及找到合理的边界节点位置。对优化后的模型进行 有限元分析,结果表明:通过拓扑优化和形状优化的两级优化,能够得到满足强度和稳定性要求的结构布局,为 桨叶结构设计提供指导方案。     

基于Altair OptiStruct的复合材料优化技术

Altair OptiStruct是一个是以有限元法为基础,面向产品设计、分析和优化的有限元和结构优化求解器,拥有全球最先进的优化技术,可提供最全面的优化方法,包括拓扑优化、形貌优化、尺寸优化、形状优化以及自由尺寸和自由形状优化.     

基于ordered-EAMP模型的多材料传热结构拓扑优化

基于多材料变密度拓扑优化方法提出了一种密度指数函数插值的有序多材料性能近似(ordered exponential approximation of material properties,ordered-EAMP)模型,数学性质以及算例表明,与传统的SIMP/RAMP插值相比,该模型具有计算稳定,收敛速度快,优化结构灰度单元少的特点。在优化准则(OC)法求解变密度拓扑优化模型时,构造了一种适用于多材料的密度过滤格式,算例表明:可以有效减少灰度单元,且降低了优化的目标函数值。运用MATLAB-ANSYS联合优化,实现三类热边界条件下复杂热环境的多材料传热结构拓扑优化。相比于高热传导系数的单材料结构,多材料传热拓扑优化结构由于各种热传导系数材料的优化分布,结构的传热势容耗散更小,算例4中对比分析降低了20.3%,传热效率更高。      

流体拓扑优化方法及其在叶轮机械中的应用

相比于结构拓扑优化,流体拓扑优化的发展较为滞后。为了促进流体拓扑优化在叶轮机械领域的应用,根据公开资料中的研究成果,首先介绍了该方法的理论基础,包括优化问题数学模型、流动控制方程及求解方法、灵敏度分析技术、优化不稳定问题的预防措施及几何重构方法。然后总结归纳了流体拓扑优化在叶轮机械气动热力学领域的研究现状,通过对涡轮叶片内部冷却结构、涡轮叶片叶顶结构以及离心压气机弯道设计的描述,指出该方法的技术优势。研究表明,相比于传统形状和尺寸优化方法,拓扑优化具有更高的设计自由度,且突破了结构参数化的限制,有助于挖掘具有优良性能的新型结构。最后,对流体拓扑优化方法在未来叶轮机械设计中的发展进行了展望。     

应力和位移约束下连续体结构的拓扑优化

结构拓扑优化设计是结构初始方案设计的重要方法。同时考虑应力和位移约束,采用遗传算法,用染色体基因映射结构离散化后的单元体,对连续体结构进行拓扑优化。为了消除结构中的铰接和棋盘格现象,在拓扑优化分析中引入了结构约束的概念,并在罚函数方法中引入导向因子,改善优化分析结果。该方法可以为工程结构的初始设计提供多种方案,同时为新结构的设计提供了理论基础。算例分析表明所提出的方法是合理、有效的。     

机翼结构拓扑优化的一种新渐进结构优化方法

基本ESO方法存在着删除准则单一,应用范围局限于简单结构的缺点,本文分析了其用于类似飞机机翼这种复杂结构拓扑优化设计中的不足之处,并进行针对性地改进,提出了一种新的删除准则,构成了一种新的渐进结构优化方法。算例表明,该方法适合于复杂机翼结构的拓扑优化问题,拓展了基本渐进结构优化方法的功能,有着很好的推广应用价值。     

基于蚁群算法的机头结构二级布局优化方法

针对民机机头结构布局设计的拓扑变量与尺寸优化变量共存的混合变量设计问题,改进一般的蚁群算法,提出多城市层的蚁群算法转移概率准则,建立基于蚁群算法拓扑优化及准则法尺寸优化设计的二级结构布局优化法,第一级针对离散设计变量,采用蚁群算法确定结构的拓扑布局;第二级针对连续设计变量,基于准则法完成结构在前一级布局下的尺寸优化设计。优化设计结果表明：在满足强度和刚度约束下,相较于初始结构,杆件结构总重量减轻32%,且较常规尺寸优化效果更好。     

基于图形法的仿生拓扑优化方法

针对图形系统自动生成图形拓扑形式的优势,提出了一种以隐式方式表征结构拓扑形式的分步拓扑优化设计方法。该分步优化方法首先以基结构法（ground structure method）的计算结果为基础,并通过均匀化方法得到设计区域内的离散拓扑信息,利用第一步所得的拓扑数据指导分形系统中每一级新增拓扑结构的生长方向,以类似细胞分裂生长的形式完成整体结构拓扑形式生成。最后以参数化建模方式完成模型的结构有限元的批量计算,并结合进化算法,完成对设计模型的优化。其中第一个案例通过本文仿生方法在多目标优化方法下得到了近似Michell结构的最优拓扑结构,第二个方案中机翼蒙皮的屈曲载荷系数提升了10.61%,并且质量降低了10.85%,验证了本文方法在类平面结构拓扑优化方面的可行性。      

基于拓扑与尺寸优化的飞机发动机支撑架轻量化设计

为了提高飞机结构性能,实现为机身结构减重的设计目的,通过拓扑和尺寸优化对飞机发动机支撑架结构进行轻量化设计。在新结构的基础上,以各管件外径为自变量,以结构的最大变形为约束,以体积最小为优化目标,利用遗传算法获得结构的最优尺寸。综合对比优化前和优化后的结构,结果显示通过拓扑与尺寸优化得到的结构有更好的力学性能和更轻的结构重量。     

机翼后缘柔性支撑结构的拓扑优化

针对机翼后缘柔性支撑结构的多目标拓扑优化问题,分析了柔性支撑结构的优化目标及目标函数,并采用位矩阵表示机翼后缘柔性支撑结构,利用非支配排序遗传算法(NSGA-Ⅱ)对该优化问题进行了求解。在优化过程中,引入连通性分析和相似个体过滤,借助ANSYS对可行个体进行有限元分析(FEA),获得了结构质量、变形性能和承载能力等目标值。通过MATLAB对违约个体进行惩罚,实现了位矩阵表示的NSGA-Ⅱ,得到了一组互不支配的机翼后缘柔性支撑优化结构,可根据实际需求选择这些相应的拓扑结构。结果表明,本方法可为机翼后缘柔性支撑结构的拓扑优化提供可行、有效的解。     

面向集中力扩散的回转曲面加筋拓扑优化方法

为了提高航天器回转曲面加筋型连接结构的集中力扩散效率,需要开展回转曲面加筋集中力扩散结构设计。传统放射肋设计方法普遍依赖设计经验、难以满足集中力高效扩散需求。因此,提出一种面向集中力扩散的回转曲面加筋拓扑优化方法。第1步,建立了一种基于各向异性过滤技术的集中力扩散拓扑优化方法,保证拓扑优化结果满足回转曲面加筋制造工艺要求;第2步,提出了一种基于网格变形技术的拓扑优化结果智能重构方法,可高效准确地对回转曲面加筋拓扑优化结果进行模型自动重构。基于所提出方法,以卫星平台对接环这种典型的回转曲面加筋壳为对象开展算例研究,并将优化结果与传统放射肋设计结果进行对比。结果表明,所提出的优化方法可得到加筋构型清晰、满足回转曲面加筋制造工艺要求的优化结果,且具有集中力扩散效率高、网格质量依赖性低、拓扑特征重构高效等优点。     

A review of topology optimization for additive manufacturing: Status and challenges

Topology optimization was developed as an advanced structural design methodology to generate innovative lightweight and high-performance configurations that are difficult to obtain with conventional ideas. Additive manufacturing is an advanced manufacturing technique building as-designed structures via layer-by-layer joining material, providing an alternative pattern for complex components. The integration of topology optimization and additive manufacturing can make the most of their advantages and potentials, and has wide application prospects in modern manufacturing. This article reviews the main content and applications of the research on the integration of topology optimization and additive manufacturing in recent years, including multi-scale or hierarchical structural optimization design and topology optimization considering additive manufacturing constraints. Meanwhile, some challenges of structural design approaches for additive manufacturing are discussed, such as the performance characterization and scale effects of additively manufactured lattice structures, the anisotropy and fatigue performance of additively manufactured material, and additively manufactured functionally graded material issues, etc. It is shown that in the research of topology optimization for additive manufacturing, the integration of material, structure, process and performance is important to pursue high-performance, multi-functional and lightweight production. This article provides a reference for further related research and aerospace applications.     

Multi-scale design and optimization for solid-lattice hybrid structures and their application to aerospace vehicle components

By integrating topology optimization and lattice-based optimization, a novel multi-scale design method is proposed to create solid-lattice hybrid structures and thus to improve the mechanical performance as well as reduce the structural weight. To achieve this purpose, a two-step procedure is developed to design and optimize the innovative structures. Initially, the classical topology optimization is utilized to find the optimal material layout and primary load carrying paths. Afterwards, the solid-lattice hybrid structures are reconstructed using the finite element mesh based modeling method. And lattice-based optimization is performed to obtain the optimal cross-section area of the lattice structures. Finally, two typical aerospace structures are optimized to demonstrate the effectiveness of the proposed optimization framework. The numerical results are quite encouraging since the solid-lattice hybrid structures obtained by the presented approach show remarkably improved performance when compared with traditional designs.     

多孔材料夹层结构声辐射特性的两尺度拓扑优化设计

基于均匀化计算理论结合结构构型设计和材料构型设计,建立以声辐射功率为目标的两尺度材料/结构协同优化模型,针对夹层结构声学设计问题,开展了声辐射特性拓扑优化研究。分别给出了声辐射功率对宏观和微观设计变量的灵敏度,结合移动渐近线法(MMA)实现了材料/结构两尺度设计。结果表明,声辐射功率两尺度优化改变了夹层结构各阶主振型的形状和顺序,同时也改变了被激发的振型。此外,算例研究了激励频率和约束对优化结果的影响以及声辐射功率目标优化的特殊现象。     

惯导系统结构拓扑优化方法研究

针对惯导系统结构拓扑优化问题,提出了一种考虑多工况组合和等效边界处理的优化方法.以惯导系统结构件为研究对象,梳理了不同结构件的载荷工况;以刚度最大为 目标函数,以体积分数、结构频率和最大变形等作为约束条件,研究了变密度拓扑优化方法;以某惯导系统的盖板、惯性台体和外壳体3个结构件为例,进行了优化方法验证.结果表明,与传统设计相比,在满足系统刚度、频率及动态特性的前提下,优化后的3个结构件质量分别减小18.3％、22.6％和18.0％,整体质量减小18.7％,实现了惯导系统结构的轻量化设计.     

多组件结构系统布局拓扑优化中处理组件干涉约束的惩罚函数方法

包含大量组件的多组件结构系统布局拓扑优化设计中存在大量的组件干涉约束,研究了包含大量组件的结构系统整体式拓扑布局优化设计问题,基于有限包络圆方法（FCM）提出了处理组件干涉约束的惩罚函数方法,构造了包含结构刚度和组件之间几何干涉函数的内外混合惩罚函数,应用基于梯度的优化算法对包含数十个组件上百个干涉约束的多组件结构系统进行刚度优化设计,得到了清晰的支撑结构构型和无干涉的组件布局位置,充分体现了提出的混合惩罚函数方法在解决多组件结构系统布局拓扑优化设计中组件干涉问题上的有效性和适用性。     

Layout design of thin-walled structures with lattices and stiffeners using multi-material topology optimization

In this paper, the thin-walled structures with lattices and stiffeners manufactured by additive manufacturing are investigated. A design method based on the multi-material topology optimization is proposed for the simultaneous layout optimization of the lattices and stiffeners in thin-walled structures. First, the representative lattice units of the selected lattices are equivalent to the virtual homogeneous materials whose effective elastic matrixes are achieved by the energy-based homogenization method. Meanwhile, the stiffeners are modelled using the solid material. Subsequently, the multi-material topology optimization formulation is established for both the virtual homogeneous materials and solid material to minimize the structural compliance under mass constraint. Thus, the optimal layout of both the lattices and stiffeners could be simultaneously attained by the optimization procedure. Two applications, the aircraft panel structure and the equipment mounting plate, are dealt with to demonstrate the detailed design procedure and reveal the effect of the proposed method. According to numerical comparisons and experimental results, the thin-walled structures with lattices and stiffeners have significant advantages over the traditional stiffened thin-walled structures and lattice sandwich structures in terms of static, dynamic and anti-instability performance.     

An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing

Combination of topology optimization and additive manufacturing technologies provides an effective approach for the development of light-weight and high-performance structures. A heavy-loaded aerospace bracket is designed by topology optimization and manufactured by additive manufacturing technology in this work. Considering both mechanical forces and temperature loads, a formulation of thermo-elastic topology optimization is firstly proposed and the sensitivity analysis is derived in detail. Then the procedure of numerical optimization design is presented and the final design is additively manufactured using Selective Laser Melting (SLM). The mass of the aerospace bracket is reduced by over 18%, benefiting from topology and size optimization, and the three constraints are satisfied as well in the final design. This work indicates that the integration of thermo-elastic topology optimization and additive manufacturing technologies can be a rather powerful tool kit for the design of structures under thermal-mechanical loading.     

A new procedure for aerodynamic missile designs using topological optimization approach of continuum structures

This paper presents a multi-objective programming scheme for the conceptual design of aerodynamic missile's structure using topological optimization approaches, in which both the compliance and eigenfrequency are regarded as static and dynamic optimization objectives, respectively. During the conceptual design of the aerodynamic missile with multiple loadings, both the multilevel sequential programming approach and the compromising programming method are coupled together to settle the associated difficulties when the whole structure of the missile body is considered as a pre-defined design domain. The compromise programming method is first applied to describe the statically loaded multi-stiffness topology optimization, and the dynamic formulation is used to establish the subsequent optimization problem mainly concerned with free vibration. The main advantage of the proposed scheme is the flexibility of dealing with optimal topology designs for the whole structures of aerodynamic missiles with complicated loading cases. Solid isotropic material with penalization (SIMP) is used as the interpolation scheme to indicate the dependence of material modulus upon regularized element densities. The sequential convex programming approach is applied to solve the optimization problem. An engineering application is used to demonstrate the characteristics of the presented methodologies based on the commercial software package of Hyperworks.OptiStruct at Altair®.     

面向增材制造的拓扑优化技术发展现状与未来

增材制造技术通过材料逐层打印制备结构,为复杂构件制造提供了新的成形方式。拓扑优化因不依赖于初始构型的选择,可设计出传统理念难以获得的创新构型,已成为航空航天和高端装备领域高性能、轻量化结构设计的重要手段。拓扑优化与增材制造有机融合,充分发挥各自优势和潜力,在现代制造业中展现出广阔应用前景。回顾了近年来关于增材制造与拓扑优化技术融合研究的主要内容和应用成果,包括以材料结构一体化为核心的多尺度/多层级结构优化设计、以设计制造一体化为核心的考虑增材制造工艺约束的优化方法等。同时,也分析了未来研究工作中存在的问题与挑战,如点阵结构性能表征及其尺度关联效应、增材制造材料成形各向异性、功能梯度材料与结构、增材制造材料与结构疲劳特性等对设计方法和成形工艺带来的挑战,为未来相关研究工作和航空航天应用提供参考。