汽车车架结构多目标拓扑优化方法研究

为了研究以静态多工况下刚度和动态振动频率为目标函数的车架拓扑结构,提出了一种结构的多目标拓扑优化研究方法。基于实体各向同性材料惩罚函数的拓扑优化方法,采用折衷规划法定义多目标拓扑优化和多刚度拓扑优化的目标函数,而振动固有频率拓扑优化的目标函数则采用平均频率法定义。通过优化得到了同时满足静态刚度和振动低阶频率要求的汽车车架结构拓扑。该方法避免了单目标拓扑优化无法考虑其他因素的缺点,适合连续体结构的多目标拓扑优化。     

涉及空腔制造的最小长度尺寸限制的清晰结构拓扑优化设计

针对以结构柔顺度最小为目标函数,涉及空腔制造的最小长度尺寸限制的结构拓扑优化设计问题,提出了一种新的拓扑优化求解方法。首先,为了消除现有的结构实体相及空洞相的相同的光滑Heaviside映射导致的强烈对立矛盾,引入光滑Heaviside映射和修改的光滑Heaviside映射分别进行实体相及空洞相的设计变量过滤;而后,构建了合理和协同的涉及实体相和空洞相的几何最小长度尺寸限制的结构拓扑优化模型;利用MMA算法,形成了一种新的涉及实体相和空洞相的几何最小长度尺寸限制的结构拓扑优化算法。给出的算例结果表明,与现有方法比,该方法可解决结构实体相和空洞相的几何最小长度尺寸控制问题。且所提方法可获得清晰0/1分布的优化结构拓扑。     

Novel steel wheel design based on multi-objective topology optimization

This paper aims to propose a multi-objective topology optimization methodology for steel wheel, in which both the compliance and eigenfrequencies are regarded as static and dynamic optimization objectives. Compromise programming method is employed to define the objectives of multi-objective and multi-stiffness topology optimizations, whereas mean-frequency formulation is adopted to settle eigenfrequencies of free vibration optimization. To obtain a clear and useful topology optimization result, cyclical symmetry and manufacturing constraints are set, the influences of which on the outcomes are also discussed. With an appropriate value of the minimum member size, a rough topology optimization of the steel wheel is obtained. The optimization result is modified according to the actual structure and manufacturing process. Moreover, based on this result, eight different steel wheel modes are established to analyze the influence of the manufacturing process and draw beads on the wheel performance through finite element simulation. Simulation results are verified by conducting a stress test of a commercially available wheel. Compared with its initial design, the optimized wheel disc exhibited decreased mass at 0.15 Kg at percentage of 4.57%, manifesting the effectiveness of the proposed method.     

基于可靠性的连续体结构拓扑优化设计

建立水平集函数为设计变量、刚度极小化为目标、具有可靠性约束的连续体结构拓扑优化模型,并提出相应的优化算法.文中提出的基于可靠性的结构拓扑优化算法方法分为两个步骤,结构可靠性分析和结构拓扑优化.可靠性分析采用计算简便、效率高的一次二阶矩法,结构拓扑优化设计则应用稳定高效、最优结构清晰的水平集方法.最后以悬臂梁结构的可靠性拓扑优化为例,表明文中提出的方法既简单又有效.     

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。     

三维线弹性连续体的结构拓扑优化设计

研究了基于水平集模型和SIMP方法的三维线弹性结构的拓扑优化方法，优化模型的目标是结构的柔度最小。引入水平集模型隐含描述具有复杂拓扑关系的三维线弹性结构的几何边界，以材料域的形状为变量进行灵敏度分析，构造水平集方程的速度函数，通过几何边界的演化获得结构的最优形状和拓扑。同时研究了基于SIMP方法的三维连续体结构的拓扑优化设计。对基于水平集模型和SIMP的拓扑优化方法的数值算例进行比较，结果表明，基于水平集的三维结构拓扑优化具有光滑的几何边界，数值算法稳定。     

隐式功能函数结构体可靠性拓扑优化

考虑工程实际中外载荷、材料属性等的随机不确定性对结构安全性的影响,研究了具有结构位移可靠性约束的拓扑优化设计。建立以柔度最小为目标、以单元相对密度为变量、具有材料体积分数约束和结构位移可靠性约束的拓扑优化数学模型;针对运用有限元数值计算方法时结构功能函数为隐式的情况,运用响应面法近似逼近结构真实的功能函数;利用简便高效的一次二阶矩法计算结构位移可靠度;采用内循环为确定性的拓扑优化、外循环控制结构材料体积分数的策略对连续体结构进行可靠性拓扑优化设计。通过两个算例与确定性拓扑优化结果进行比较,结果表明所提设计方法是高效可行的。     

电动轮自卸车车架结构抗疲劳轻量化设计

针对传统经验式设计的电动轮自卸车车架结构存在刚度不足、焊缝开裂、重量冗余,以及自身固有频率与非簧载质量激励频率接近而可能发生共振等问题,开展车架结构性能多目标优化设计的研究。首先,基于变密度法和SIMP插值模型对原始车架结构进行了考虑疲劳寿命约束的多目标拓扑优化设计,得到了满足静态多工况下柔度最小和多阶低阶固有频率最大的拓扑优化结构。再次,基于Kriging近似模型的抗疲劳轻量化设计,利用非支配排序多目标遗传算法进行全局寻优,优化后的车架结构质量比原始车架结构质量减少4.24%,且车架结构在同样载荷作用下的应力分布更加均匀,车架强度、刚度、动态特性和疲劳寿命等性能均得到改善。     

车身结构NVH特性多目标拓扑优化研究

建立了某车身地板结构动力学有限元模型,通过分析自由模态固有频率和多点激励下频率响应,验证了车身地板数值分析模型的有效性。以地板结构各激励点最大振动速度的平方和最小化作为目标函数,建立了多目标拓扑优化模型。通过解读优化结果,提出了地板结构改进方案。改进后的车身地板结构各阶自由模态固有频率增加达10%以上,各激励点速度响应大大降低,NVH特性明显提高。研究表明,减小振动速度的多目标拓扑优化设计是一种改善车身NVH特性的有效方法。     

Key techniques and applications of adaptive growth method for stiffener layout design of plates and shells

The application of the adaptive growth method is limited because several key techniques during the design process need manual intervention of designers. Key techniques of the method including the ground structure construction and seed selection are studied, so as to make it possible to improve the effectiveness and applicability of the adaptive growth method in stiffener layout design optimization of plates and shells. Three schemes of ground structures, which are comprised by different shell elements and beam elements, are proposed. It is found that the main stiffener layouts resulted from different ground structures are almost the same, but the ground structure comprised by 8-nodes shell elements and both 3-nodes and 2-nodes beam elements can result in clearest stiffener layout, and has good adaptability and low computational cost. An automatic seed selection approach is proposed, which is based on such selection rules that the seeds should be positioned on where the structural strain energy is great for the minimum compliance problem, and satisfy the dispersancy requirement. The adaptive growth method with the suggested key techniques is integrated into an ANSYS-based program, which provides a design tool for the stiffener layout design optimization of plates and shells. Typical design examples, including plate and shell structures to achieve minimum compliance and maximum bulking stability are illustrated. In addition, as a practical mechanical structural design example, the stiffener layout of an inlet structure for a large-scale electrostatic precipitator is also demonstrated. The design results show that the adaptive growth method integrated with the suggested key techniques can effectively and flexibly deal with stiffener layout design problem for plates and shells with complex geometrical shape and loading conditions to achieve various design objectives, thus it provides a new solution method for engineering structural topology design optimization.     

振动夹具的综合优化设计

夹具设计要求质量轻、刚度大。为了在这两者间取得平衡,文中综合使用拓扑优化和尺寸优化两种方法对夹具进行优化设计以实现设计目标。基于拓扑优化结果设计了夹具的拓扑优化模型。虽然相对于初始模型,该模型的第1阶固有频率降低了36.5%,但其质量降低了66.7%,表明拓扑优化效费比显著。以设计参数的合理设计范围作为约束条件,把使第1阶固有频率最大和夹具质量最轻作为优化目标来实施尺寸优化,得到夹具的详细设计模型。与拓扑优化模型相比,该模型的质量降低了3%,第1阶固有频率提升了6%。之后对振动夹具实施了随机振动试验。受试设备安装点的功率谱密度响应曲线的均方根值最大为输入谱均方根值的1.17倍,说明夹具具有良好的动力学传递特性,夹具的综合优化设计方法有效可行。     

Topology optimization of compressor bracket

Topology optimization is very useful engineering technique especially at the concept design stage. It is common habit to design depending on the designer’s experience at the early stage of product development. Structural analysis methodology of compressor bracket was verified on the static and dynamic loading condition with 2 bracket samples for the topology optimization base model. Topology optimization is able to produce reliable and satisfactory results with the verified structural model. Base bracket model for the topology optimization was modeled considering the interference with the adjacent vehicle parts. Objective function was to minimize combined compliance and the constraint was the first natural frequency over 250 Hz. Multiple load cases such as normal mode calculation and gravity load conditions with 3-axis direction were also applied for the optimization, expecting an even stress distribution and vibration durability performance. Commercial structural optimization code such as optistruct of Altair Engineering was used for the structural topology optimization. Optimization was converged after 14 iterations with the satisfaction of natural frequency constraint. New bracket shape was produced with the CATIA based on the topology optimization result. The new bracket from topology optimization result was compared with the traditional concept model and topology optimization base model under 4 load cases. 14 % 1’st natural frequency of new bracket with only 4 % mass increment increased compared to the concept model. 31 % mass decreased compared to the base model without the increment of stress under gravity load cases. It was analyzed thata new bracket would not fail during a vibration durability test, and these results were verified with a fabricated real sample under the durability condition.     

基于水平集方法的结构可靠性拓扑优化

基于水平集方法,建立以水平集函数为优化变量、结构柔度极小化为目标、具有可靠性约束的结构拓扑优化模型,并提出一种基于可靠性的结构拓扑优化算法。首先,采用计算效率高的一次二阶矩法进行可靠性分析,编制计算可靠性指标的最优化方法。然后,根据结构可靠性指标的几何意义,优化求解符合可靠性约束的随机变量。将修正后的随机变量作为确定性变量进行结构拓扑优化设计,使基于可靠性的结构拓扑优化模型转为常规的结构拓扑优化模型,采用稳定、高效的水平集方法进行结构拓扑优化。最后以悬臂梁结构的可靠性拓扑优化为例,说明文中所提算法的简便性与有效性。     

连续参数型吸振器吸振分析及优化

针对连续参数型动力吸振器与弹性薄板构成的耦合系统,以功率流理论为基础,结合有限元方法,分析了连续参数型动力吸振器变阻尼复合梁的吸振特性。与试验结果进行对比可知,变阻尼层复合梁具有吸振频带宽、吸振效果好的特性。为了提升吸振器的吸振效果,通过ANSYS的优化模块,对连续参数型动力吸振器的吸振性能进行了优化设计,优化后的吸振器在多个频率段内吸振性能得以提升,验证了优化方法的有效性。     

设计相关动压力作用下连续体结构拓扑优化

针对动压力作用下连续体结构拓扑优化问题,文中以结构动柔顺度为目标,以材料体积为约束,建立拓扑优化模型.该优化问题作为一般动力学拓扑优化问题的延伸,其动压力载荷不仅随着时间简谐变化,而且随着结构拓扑和形状的变化而改变力的作用点和方向.文中提出一种基于单元的边界搜索方法,简便而准确地获得优化过程中的压力加载边界.同时采用RAMP(rational approximation of material properties)方法消除局部模态现象.数值算例表明,采用这种新的边界搜索方法,结合RAMP方法处理此类问题是有效的.     

Effect of loading and lamination parameters on the optimum design of laminated plates

This paper illustrates the effect of loading conditions and lamination parameters on the optimum design of the laminated composite plates. Optimum design procedure based on the flexibility criterion is presented in this paper. The objective is to determine the optimum thickness of the laminate layers and its optimum orientations without exhibiting any failure. The finite element method based on Mindlin plate theory is used in conjunction with an optimization method in order to determine the optimum design. Newmark implicit time integration scheme is used to discretize the time domain and calculate the transient response of the laminated plate. Exterior penalty method is exploited as a constrained minimization technique. For this purpose, four numerical examples are presented to figure out the effects of dynamic loading profile, boundary conditions, number of layers, and degree of orthotropy on the optimum weight design.     

基于面光滑有限元的复杂三维结构拓扑优化

为了增强拓扑优化计算对任意复杂模型的适应性,改进基于线性四面体有限元的拓扑优化结果,引入了一种新型高精度的基于面光滑有限元模型(FS-FEM)来进行拓扑优化,通过每次迭代时提供很好的梯度解及位移解,从而达到改善拓扑优化结果的目的。在基于面光滑有限元模型的拓扑优化中,以柔度最小作为目标函数,建立了基于固体各向同性材料惩罚插值(SIMP)的拓扑优化数学模型,该数学模型通过最优准则进行求解。多个不同载荷的拓扑优化数值算例说明,采用基于面光滑有限元进行拓扑优化,结果都能够单调收敛,且采用该方法建立的拓扑优化模型能抑制棋盘格现象。与商业软件OptiStruct的计算比较表明,该方法相比有限元方法能得到更合理的拓扑结构。     

基于模态控制的结构/控制一体化优化设计

先分析了结构主动控制的模态控制。从结构与控制器一体化优化设计的角度出发 ,提出了以结构的质量和控制能量最小化为优化目标、以基频和结构的动响应为约束的联合优化设计模型。并对该优化设计模型进行了一定的简化处理 ,采用改进的拓扑组方法进行结构的集成拓扑优化设计。数值算例的结果表明 ,结构 /控制一体化优化设计是可行且有效的。     

机载SAR天线座连接支架的拓扑优化设计

拓扑优化方法在雷达天线座的减重设计中具有突出优势,特别适合于大型精密雷达和机载雷达天线座的结构优化设计。文中建立了连接支架的拓扑优化模型,以单元密度为设计变量,体积分数上限为约束条件,加权应变能最小化为优化目标,对机载SAR天线座连接支架进行了拓扑优化设计。考虑到结构美观和制造性,添加了对称平面约束和拔模约束。结果表明:拓扑优化结果符合仿生学原理,在减轻质量的同时,也提高了结构性能。     

多载荷工况下无网格Galerkin法的拓扑优化

连续体结构拓扑优化位于产品的概念设计阶段,能够为产品结构的创新提供可能。基于此,提出以节点相对密度作为设计变量,以多载荷工况下结构柔度的加权平均值为目标函数,建立多载荷工况下基于无网格迦辽金法的连续体结构拓扑优化模型,利用Lagrange乘子法来施加本质边界条件,推导出相应的灵敏度计算公式。结合固体各向同性惩罚插值模型编写程序完成两个多工况的拓扑优化算例,并对单、多工况的优化结果进行了比较。所得结果表明,多工况的优化结果并不是单工况结果的简单迭加。同时利用节点密度的最大优势是影响域中的密度与位移具有相同的逼近策略,从而使所建立的模型能有效地提高密度场的连续性,并从模型上抑制了棋盘格现象,该方法的可行性得到验证。