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.     

Stiffeners layout design of thin-walled structures with constraints on multi-fastener joint loads

The purpose of this paper is to present an extended topology optimization method for the stiffeners layout design of aircraft assembled structures.Multi-fastener joint loads and manufacturing constraints are considered simultaneously.On one hand,the joint loads are calculated and constrained within a limited value to avoid the failure of fasteners.On the other hand,the manufacturing constraints of the material distribution in the machining directions of stiffeners are implemented by an improved piecewise interpolation based on a beveled cut-surface.It is proven that the objective function is strictly continuous and differentiable with respect to the piecewise interpolation.The effects of the extended method with two different constraints are highlighted by typical numerical examples.Compared with the standard topology optimization,the final designs have clearly shown the layout of stiffeners and the joint loads have been perfectly constrained to a satisfying level.     

发动机机匣弧面不规则管路的布局参数多目标优化设计

管路布局优化是降低发动机管路振动应力的重要手段,提出了一种发动机机匣弧面上不规则管路布局参数的多目标优化设计方法。从发动机机匣弧面的U形管路出发,建立了具有复杂布局走向的不规则单管路的参数化建模方法。分析了布局参数对管路的危险固有频率、多点激励响应的灵敏度。综合考虑错频和最大响应等多个目标,采用多目标遗传优化算法,对不规则管路的布局参数实施了优化设计。结果表明:管形布局优化设计效果显著,错开了两个危险固有频率禁带;管路结构在相同激励下最大位移幅值下降约35%,最大应力幅值下降近50%,为发动机管路的振动控制和动力学正向设计提供了参考。      

复合材料加筋板结构优化设计的并行子空间法*

为对复合材料加筋板结构进行布局优化设计,提出并行子空间优化方法。该方法将整个优化问题分为筋条布局优化、筋条尺寸优化和铺层厚度优化三个并行的子空间优化问题,分别以筋条型式、数量、尺寸和铺层厚度为设计变量;每个子问题都独立进行优化计算,优化后将所有结果综合协调,更新设计变量值并重复整个优化过程,直到满足收敛条件。通过三个典型算例验证,结果表明该方法不仅合理而且有很好的优化效果。     

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.     

机翼结构布局优化的并行子空间方法

机翼内部构件的布局优劣在很大程度上影响着机翼结构质量,因此进行布局优化设计尤为重要。采用并行子空间方法求解机翼结构布局优化的问题,将机翼结构布局设计问题分为梁站位优化、桁条优化和厚度优化三个并行的子空间,设计变量在各自的子空间内单独优化;各子空间优化结束后,在系统级中协调三个子空间的设计变量,保持最小质量的子空间的优化变量不变;采用近似一维搜索的方法协调其他子空间的设计变量,然后进行变量迭代直至收敛。结果表明:该方法具有较高的优化效率,能够取得较好的优化结果,具有实际工程应用价值。     

考虑复合材料蒙皮稳定性的飞机翼面结构布局优化设计

 复合材料蒙皮稳定性是飞机翼面结构设计需要考虑的重要方面。由于翼面结构稳定性理论分析的复杂性,工程中,通常采用与理论分析相比拟的简化方法、使用简便可靠的经验公式在设计过程中进行稳定性校核。多墙式结构是当前翼面结构中普遍采用的结构形式,墙的布局和蒙皮的厚度对复合材料蒙皮的临界屈曲载荷有着重要影响。因此,针对多墙式翼面结构,以工程经验公式为基础,以蒙皮单位长度上的的重量为优化目标,以墙的布局参数和蒙皮厚度为设计变量,以临界失稳载荷为约束,建立了一种考虑复合材料蒙皮稳定性的翼面结构布局优化问题的数学模型,导出了目标函数敏度计算的解析式,并提出了优化问题的求解方法。以翼盒结构为例,验证了该方法的有效性。     

Higher-order vibration of thick composite and sandwich plates based on an alternative higher-order model

The transverse stretching vibration of thick sandwich plates, which is attributed to largely different stiffness at the adjacent layers, is a challenging issue, and efficient approach for such issue is less reported in the published literature. Thus, natural frequencies corresponding to stretching vibration modes are generally neglected in engineering design, which might impact structural safety as frequencies of the exciting force are close to transverse stretching vibration frequencies. This paper proposes an alternative higher-order model for dynamic analysis corresponding to the higher-order vibration modes. The proposed model is classified in the displacement-based equivalent single-layer theory, as the number of displacement parameters in the proposed model is independent of the layer number. The continuity of displacements and transverse shear stresses can be fulfilled at the interfaces between the adjacent layers of structures. To demonstrate the capability of the proposed model, typical examples are analyzed by utilizing the proposed model, the three-dimensional finite element method and the chosen higher-order models. By comparing with the exact three-dimensional elasticity solutions, it is found that the proposed model can yield more accurate natural frequencies corresponding to the higher-order displacement modes than the selected models. Moreover, the factors influencing reasonable prediction of the higher-order frequencies are investigated in detail, which can provide a reference for the accurate prediction of the higher-order frequencies.     

部件级多组件结构系统的整体式拓扑布局优化

基于多组件结构系统整体式拓扑布局优化设计方法,研究了同时含有部件布局、组件布局、主结构框架构型和部件结构构型4类设计变量的复杂系统协同优化设计问题,是整体式拓扑布局优化设计面向复杂飞行器结构系统设计的拓展。采用多点约束(MPC)模拟组件、部件及支撑结构之间的刚性连接,采用有限包络圆方法(FCM)解决组件之间、组件与设计域边界之间的几何干涉问题。通过整体式拓扑布局的刚度优化设计,部件和组件均可以获得优化的布局位置,同时主结构框架构型和部件结构构型获得优化的结构样式,充分体现了整体式拓扑布局优化设计方法应用于复杂结构系统设计的能力。     

工程化复合材料结构优化设计方法

复合材料结构的可设计性带来大量设计变量,单靠传统方法难以实现结构优化,复合材料结构优化的铺层优化设计也是关键问题之一。从工程实际出发,探讨具有工程操作性的复合材料结构优化设计方法,形成 从结构布置优化到初始尺寸优化,再到详细铺层优化的三级优化设计方法,并在设计过程中加入符合复合材料 工艺要求的制造性约束;以某飞机复合材料垂尾翼盒结构设计为例,采用该方法对其进行优化设计。结果表明:本文提出的三级优化设计方法是适用于航空复合材料结构优化设计的一种通用方法,可降低结构质量、缩短研制周期。     

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。     

伴随压力分布反设计方法在大型客机气动优化中的初步探索

从工程应用角度出发,对离散伴随压力分布反设计优化方法在宽体客机机翼设计中的应用进行了研究。提出了三维构型伴随压力分布反设计与伴随优化相结合的优化设计思路,促进了离散伴随气动优化设计方法的工程化。首先,针对CRM机翼构型进行了三维压力分布反设计,验证了离散伴随压力分布反设计在三维问题中的准确性和高效性。其次,应用提出的新的优化设计思路,在某宽体全机构型两点气动优化结果的基础上,引入压力分布反设计约束方法,改进了机翼压力分布和低马赫数的阻力蠕增特性,并取得了不错的减阻及阻力发散特性提升效果,提升了优化构型的工程适用性。     

随机振动响应下的组件结构布局优化设计

 从工程应用需求出发,研究了随机振动载荷作用下的组件结构布局优化问题。提出采用有限包络圆族描述组件外形轮廓的近似方法,有效解决了设计过程中预防组件干涉的问题;建立了随机振动响应分析有限元模型,并对模型进行了实验验证与结果分析。在此基础上,以随机振动载荷下特定点自由度响应均方根（RMS）值之和最小为目标函数建立了组件布局通用优化设计模型,研究了单一组件与4组件问题的布局优化问题,并分别采用梯度优化算法和遗传算法进行优化求解比较研究。结果表明,所提出的设计方法能够有效地实现随机振动响应下的组件结构布局优化设计,两种优化算法均能显著降低结构关键部位的动力学响应。     

某型飞机翼盒结构多约束优化设计

将翼盒尺寸设计中多学科设计要求,包括应力、稳定性、气动弹性、变形和制造等要求转化为优化设计过程中和结构尺寸相关联的约束条件,从而将翼盒尺寸多学科优化设计(MDO)问题转化为多约束优化设计(MCO)问题。基于Hyperworks优化设计平台,建立了某型飞机翼盒有限元模型并利用TCL\TK语言将多学科约束嵌入到翼盒尺寸优化设计过程中,定义了多约束优化设计模型。优化设计结果减重7.4%,有效指导了翼盒结构详细设计。     

Optimization and analysis of composite sandwich box beam for solar drones

Solar drones have garnered considerably research attention in recent years due to their continuous cruising capability, and the feasibility of design schemes is sensitive to the weight of structure. Sandwich box beam composed of carbon fiber and polymethacrylimide (PMI) foam is conducive to realize the lightweight of structure. In this study, a two-stage optimization design methodology for sandwich box beam is proposed. This methodology is primarily based on a low-order analytical method for evaluating stress/deflection and the linear buckling analysis method combined with experimental correction factor for predicting the buckling eigenvalues. Subsequently, a case study was conducted using an 18-m wingspan solar drone, where the results of mechanical test verified the optimization results. For validating the use of sandwich box beam in solar drones of other scales, additional analysis was conducted based on three aspects: (A) effects of stiffness and stability constraints on the design of sandwich box beam; (B) crucial role of the weight of foam inter layer and application scope of sandwich box beam; (C) best method to improve the buckling eigenvalue of sandwich box beam. Overall, the methodology and general rules presented in this paper can support the design of light wing beam for solar drones.     

燃油管路系统振动特性有限元技术研究

航空发动机燃油管主要用于提供燃油,属于复杂3维管路系统.为了更好地分析管路系统的振动特性,以双路总管燃油管路系统为例,结合其管路繁多、连接结构多样、支撑结构特殊、管内充液等特点,系统研究了各部件的有限元模拟方法.考虑到支撑刚度对管路系统振动特性有较大影响,采用有限元静力分析对其进行了求解.结合以上不同部件的分析方法,建立起系统的振动有限元模型.对该管路系统进行模态分析,得到系统固有频率变化规律及具有分簇特点的振动模态;对系统进行共振评估,认为副燃油分管最有可能发生共振,提出了振动优化的合理建议.     

简谐力激励下多组件结构系统的整体优化设计

多组件结构系统整体优化设计通过协同优化支撑结构拓扑构型和组件布局来使结构系统的位移响应最小。本文提出通过模态加速度法（MAM）求解多组件结构系统的位移响应,并以位移响应值最小作为优化目标;引入多点约束（MPC）方法模拟组件与设计域间的铆钉或螺栓连接形式;采用有限包络圆法（FCM）来避免组件之间及组件与设计域边界产生干涉。建立了多组件结构系统整体优化问题的数学模型,并对动响应目标函数关于设计变量的灵敏度进行了推导。最后,通过几个算例验证了整体优化方法在简谐力激励下求解问题的可行性及其在实际问题中的有效性。     

薄壁结构的加筋布局优化设计

采用拓扑优化方法研究了薄壁结构的加筋布局优化问题.考虑到航空航天领域薄壁加筋结构的大量使用与结构形式的复杂性,提出了一种适用于有限元自由网格剖分的加筋设计新方法--几何背景网格法.该方法一方面通过定义几何背景网格的大小,实现了加筋设计域内任意离散网格沿加筋高度方向的布局参数化定义;另一方面,通过背景网格曲线坐标系下的定义,实现了三维曲面薄壁壳结构的加筋布局设计.采用该方法分别对平面结构与曲面薄壁结构进行了以结构刚度最大为目标的加筋优化设计.数值结果表明,所提出的方法能有效获得合理的加筋布局.     

考虑阻尼性能的复合结构多尺度拓扑优化设计

最优阻尼复合结构应该是阻尼材料自身的材料性能和阻尼材料在板壳结构上的分布形态均是最优的。针对板壳阻尼复合结构的多尺度设计问题,建立了基于非比例阻尼模型的复合结构多尺度拓扑优化方法,实现了阻尼材料在宏微观两尺度上的协同设计,同时获得最优的阻尼材料宏观分布形态和微观构型。以结构模态阻尼比为目标,分别研究了复合结构的单目标和多目标多尺度设计问题。结果表明,在单目标设计中,当最大化结构的某一阶模态阻尼比时,优化后结构的该阶模态阻尼比最大,同时结构在该阶处的频率响应最小;在多目标设计中,以结构前3阶模态阻尼比之和为目标,虽然在每一阶处的性能劣于单目标设计结果,但是结构前3阶模态阻尼比的总体性能更优。同时,从微结构的构型可得,最优的微结构构型中低刚度高阻尼材料的分布相互连接,其损失模量（微结构复弹性矩阵的虚部）和阻尼因子（微结构复弹性矩阵的虚部与实部之比）都相对较高,且呈现负泊松比现象。优化后复合结构的动力学性能显著提高。     

基于自适应随机抽样敏度分析的双向渐进结构优化方法

为了解决周期循环结构拓扑优化难题,在传统的双向渐进结构优化方法(BESO)的基础上,引入了一种自适应参数策略和随机抽样的方法,提出了基于自适应随机抽样敏度分析的双向渐进结构优化方法,该方法同样适用于非周期结构.以该方法为基础,对Michell桁架结构进行了拓扑优化设计,得到了与理论解一致的结构,并且相对初始结构质量减少了71.5%,说明了所提方法的正确性.基于此方法对多辐板风扇盘进行了结构拓扑优化设计,得到了三辐板风扇盘结构,相比同等设计条件下的参考风扇盘质量减少了17.12%,进一步说明了此方法具有处理复杂周期循环结构拓扑优化设计问题的能力,另外此方法克服了传统双向渐进结构优化方法中容易产生的振荡问题.