Topology optimization of joint load control with geometrical nonlinearity

This paper presents an extended topology optimization approach considering joint load constraints with geo-metrical nonlinearity in design of assembled structures. The geometrical nonlinearity is firstly included to reflect the structural response and the joint load distribution under large deformation. To avoid a failure of fastener joints, topology optimization is then carried out to minimize the structural end compliance in the equilibrium state while controlling joint loads intensities over fasteners. During nonlinear analysis and optimization, a novel implementation of adjoint vector sensitivity analysis along with super element condensation is introduced to address numerical instability issues. The degrees of freedom of weak regions are condensed so that their influences are excluded from the iterative Newton-Raphson (NR) solution. Numerical examples are presented to validate the efficiency and robustness of the proposed method. The effects of joint load constraints and geometrical nonlinearity are highlighted by comparing numerical optimization results.     

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.     

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。     

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。     

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。     

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.     

稳态热传导下基于多相材料的一体化设计

提出一种基于多相多孔材料的一体化模型。模型以结构散热弱度最小为目标,以结构体积比与材料微结构质量为约束。引入独立的宏观设计变量和微观相设计变量,通过单元相密度建立两类变量间的联系;基于对等混合材料插值模型建立单元相密度与热传导系数间的惩罚关系;推导得到目标函数灵敏度表达式。求解偏微分方程实现单元散热弱度过滤,消除棋盘格及网格依赖性现象。通过二维数值算例讨论并分析了材料特性、热载荷、体积比约束以及质量约束对一体化优化结果的影响。数值实验结果表明,该建模方法在多相材料/结构一体化稳态热传导优化设计中具有可行性和有效性。     

Precise output loads control of load-diffusion components with topology optimization

The purpose of this paper is to present a novel topology optimization approach to control precisely the output loads under static loads and harmonic excitations. We introduce the Artificial Bar Element (ABE) at the designated output positions, where the output loads are equivalently measured and constrained with the nodal displacements of ABE. Optimization model is then formulated considering the output load constraints as well as the minimization of strain energy and dynamic displacement responses respectively under the static and dynamic conditions. The influences of the ABEs stiffness, different material usages of the design domain, widths of the output loads constraint intervals and variation ratios of output loads are discussed in detail. The proposed method is verified with several numerical examples with clear and reasonable load transfer paths.     

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.     

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。     

Geometry and size optimization of stiffener layout for three-dimensional box structures with maximization of natural frequencies

Based on the growth mechanism of natural biological branching systems and inspiration from the morphology of plant root tips, a bionic design method called Improved Adaptive Growth Method (IAGM) has been proposed in the authors’ previous research and successfully applied to the reinforcement optimization of three-dimensional box structures with respect to natural frequencies. However, as a kind of ground structure methods, the final layout patterns of stiffeners obtained by using the IAGM are highly subjected to their ground structures, which restricts the optimization effect and freedom to further improve the dynamic performance of structures. To solve this problem, a novel post-processing geometry and size optimization approach is proposed in this article. This method takes the former layout optimization result as start, and iteratively finds the optimal layout angles, locations, and lengths of stiffeners with a few design variables by optimizing the positions of some specific node lines called active node lines. At the same time, thicknesses of stiffeners are also optimized to further improve natural frequencies of three-dimensional box structures. Using this method, stiffeners can be successfully separated from their ground structures and further effectively improve natural frequencies of three-dimensional box structures with less material consumption. Typical numerical examples are illustrated to validate the effectiveness and advantages of the suggested method.     

用参数最优化方法计算最优飞行轨迹

介绍了如何应用参数最优化方法将具有状态变量不等式约束和控制变量不等式约束以及终端等式约束的最优控制问题转化为静态非线性规划问题,并提出了将求解静态约束最优化问题的系贯加权因子法,即ＳＷＩＦＴ(ＳｅｑｕｅｎｔｉａｌＷｅｉｇｈｔ－ＩｎｃｒｅａｓｉｎｇＦａｃｔｏｒＴｅｃｈｎｉｑｕｅ)法推广为求解动态约束最优化问题的增广ＳＷＩＦＴ法。最后用计算美国航天飞机的返回最优轨迹说明了该法的可行性。     

拓扑优化方法在飞机结构件概念设计中的应用

为了能够有效地降低飞机结构承力件的重量,针对飞机骨架,以加强框和普通框以及翼梁的概念设计为研究内容,通过对"敏度阈值"概念的分析,指出其不足,提出了"改进的敏度阈值"概念,并与"约束补偿"策略结合而形成新的拓扑优化算法,用于上述结构件的材料布局优化设计.多个算例中的拓扑优化结果均显示其结构型式十分新颖,值得深入地探讨.     

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。     

飞机骨架结构方案的优化设计

为了能够有效地降低飞机结构承力件的重量,针对飞机骨架,以加强框和普通框以及翼梁的概念设计为研究内容,通过对“敏度阈值“概念的分析,指出其不足,提出了“改进的敏度阈值“概念,并与“约束补偿“策略结合而形成新的拓扑优化算法,用于上述结构件的材料布局优化设计.多个算例中的拓扑优化结果均显示其结构型式十分新颖,值得深入地探讨.由此可以得出3点结论:(1)采用CAD/CAE和拓扑优化相结合用于飞机结构件的初始方案设计是可行的;(2)作者提出的“改进的敏度阈值“拓扑优化算法是有效的;(3)构建一种具有良好操作性的、有别于经验设计的飞机结构件概念设计新方法.     

Shape preserving topology optimization for structural radar cross section control

The purpose of this paper is to present a shape preserving topology optimization method to prevent the adverse effects of the mechanical deformation on the Radar Cross Section(RCS).The optimization will suppress the variation of RCS on the perfect conductor surface by structural design. On the one hand, the physical optics method is utilized to calculate the structural RCS,which is based on the surface displacement field obtained from the finite element analysis of the structure. The correspondi...     

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.     

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。     

考虑多点保形的结构拓扑优化设计方法

为了抑制飞行器结构局部区域内多个控制点的翘曲变形,提出考虑结构保形的拓扑优化设计新方法。基于由局部区域内保形控制点生成的人工附加弱单元(AWE),定义AWE的变形能约束函数,从而引入了对结构局部区域的多点保形约束,定量衡量并抑制了该区域内结构的弹性翘曲变形程度。进一步讨论并分析了保形约束与整体刚度之间的消长关系以及优化过程中可能存在的传力路径畸变现象。拓扑优化数值算例的设计结果对比表明,保形拓扑优化方法相比现有拓扑优化方法,能够有效抑制多点间的相对位移和翘曲变形,实现保形设计效果。     

不同约束条件下跨声速涡轮叶栅伴随气动优化设计

发展了一种简化的基于无反射边界理论的伴随方程进出口边界条件确定方法,研究了考虑不同约束的叶片气动外形优化设计。研究结果表明:采用流动强耦合的简化伴随方程进出口边界条件确定方法,能够确定精度较高的伴随灵敏度,在不同类型的伴随气动优化设计中均具有较好适用性。无约束的出口质量熵优化后,出口质量熵降低0.253%,流道面积和出口气流角变化较大。分别考虑出口气流角气动约束、流道面积几何约束和同时考虑上述两种约束的影响,优化后出口质量熵分别降低0.176%、0.227%和0.164%,优化后叶片气动性能显著提升,且满足约束条件。改变叶型曲率能有效减弱激波强度,吸力面前段曲率降低时,流动减速、出口气流角增大,吸力面前段曲率变化较小时,出口气流角约束较好。