Multiscale topology optimization for frequency domain response with bi-material interpolation schemes

In areas that require high performance components, such as the automotive, aeronautics and aerospace industries, optimization of the dynamic behavior of structures is sought through different approaches, such as the design of materials specific to the application, for instance through structural topology optimization. The bi-directional evolutionary structural optimization (BESO) method, in particular, has been used for the simultaneous design of hierarchical structures, which means that the structural domain consists not only of the macrostructure but also of the microstructural topology of the materials employed. The purpose of this work is to apply the BESO method to solve two-dimensional multiscale problems in order to minimize the response of structures subjected to forced vibrations in a given frequency range. The homogenization method is applied to integrate the different scales of the problem. In particular, the material interpolation model for two materials is used. The BESO method is applied to different cases of optimization, in macroscale, microscale, and multiscale structural domains. Numerical examples are presented to validate the optimization and demonstrate the potential of this approach. The numerical examples show that the multiscale bi-material topology optimization method implemented here is able to produce structures and microstructures for optimization of the frequency domain response, satisfying prescribed volume constraints.

     

Topology optimization of composite material plate with respect to sound radiation

In this paper, topology optimization of composite material plate with respect to minimization of the sound power radiation has been studied. A new low noise design method based on topology optimization is proposed, which provides great guidance for acoustic designers. The structural vibrations are excited by external harmonic mechanical load with prescribed frequency and amplitude. The sound power is calculated using boundary element method. An extended solid isotropic material with penalization (SIMP) model is introduced for acoustic design sensitivity analysis in topology optimization, where the same penalization is applied for the stiffness and mass of the structural volume elements. Volumetric densities of stiffer material are chosen as design variables. Finally, taking a simple supported thin plate as a simulation example, the sound power radiation from structures subjected to forced vibration can be considerably reduced, leading to a reduction of 20 dB. It is shown that the optimal topology is easy to manufacture at low frequency, while as the loading frequency increases, the optimal topology shows a more and more complicated periodicity which makes it difficult to manufacture.     

振动板速度最小化减振优化设计研究

减振设计是结构设计的重要内容之一，优化设计可在设计阶段通过对设计模型的定量修改获得理想的减振效果。基于有限元直接法计算振动板的频率响应，以板局部厚度为设计变量，计算了振动速度对局部板厚度的灵敏度；以振动板各节点振动速度的平方和最小化为目标，建立了减小振动板振动速度的减振优化数学模型，用可行方向法实现了优化。以一两端固支矩形板的振动为研究算例，对其在1Hz～200Hz的振动实施了优化；优化后振动板各节点在研究频率内的振动速度都得到了降低，降低最大值达0．311m／s。实例结果表明，优化设计通过对结构重量的重新分布可在结构重量相对不变的情况下，在一较宽频段内均得到减振效果。     

一种锥形定位节面变幅杆结构优化设计研究

为提高变幅杆的振动传递及振幅输出特性,基于解析法设计了具有锥形定位节面结构的旋转超声加工变幅杆,通过预应力模态分析与谐响应分析进行了优化设计;通过响应面优化方法建立27个优化设计点,分别以放大系数最大化、最大等效应力最小化与谐振频率最接近理论设计频率为第一、第二与第三优化目标,并提出一种5阶模态频响曲面验证方法,通过(2~6)阶5个模态频响曲面分析结果对优化设计点的最优优化解进行验证。研究表明,基于该研究提出的方法,结构优化设计后的变幅杆能够提高放大系数,降低最大等效应力,并使谐振频率接近理论设计频率,提高超声加工的能量利用率。对旋转超声加工装备的性能研究与开发具有一定的指导意义。     

基于零阶算法的矩形面宽带纵振换能器设计

传统换能器的优化一般采用试算修改的方式进行,这样的方式在待优化参数较多时不仅比较繁琐而且有可能会漏掉各参数组合下较好的设计点,对此提出了利用零阶算法进行换能器多参数联合优化设计的方法。建立了一种带宽评价函数,通过该评价函数和零阶算法尝试了对矩形面纵振换能器带宽的优化设计。经有限元仿真和样机测试表明,两款换能器的性能达到了预期指标要求,实现了宽带工作。得到的两款宽带换能器性能为:1#换能器工作频带为10~21.5 kHz,带内起伏约3 dB,发射电压响应大于134 dB;2#换能器工作频带为7.5~31.5 kHz,带内起伏约6 dB,发射电压响应大于131 dB。该方法可以作为换能器设计的一种新方式。     

基于变频率区间约束的结构材料优化设计

针对频率约束的结构材料优化问题,基于结构拓扑优化思想,提出变频率区间约束的结构材料优化方法。借鉴均匀化及ICM(独立、连续、映射)方法,以微观单元拓扑变量倒数为设计变量,导出宏观单元等效质量矩阵及导数,进而获得频率一阶近似展开式。结合变频率区间约束思想,获得以结构质量为目标函数、频率为约束条件的连续体微结构拓扑优化近似模型;采用对偶方法求解。通过算例验证该方法的有效性及可行性,表明考虑质量矩阵变化影响所得优化结果更合理。     

硅片机器人大臂结构多目标拓扑优化设计

目的为了改善硅片机器人结构的静、动力学性能,实现结构的轻量化设计。方法引入多目标优化理论,并结合层次分析法,实现硅片机器人大臂的结构优化设计。依据设计方案分析大臂的受力情况,采用固体各向同性材料惩罚模型分别构建多目标优化数值模型,并运用优化准则法进行优化求解。引入数理统计中的层次分析法确定各子目标函数的权重比,依据折衷规划组合方法构造关于静刚度和一阶固有频率的总目标函数。结果优化结果可知,大臂的柔度从26.890 mm/N降到13.221 mm/N,一阶固有频率从556.86 Hz增加到629.90 Hz,结构质量从1.48 kg减少到0.583 kg。结论多目标优化结果表明,基于多目标优化理论对硅片机器人大臂结构的改进设计,不仅有效地提高了其静刚度特性,一阶固有频率的提高说明大臂结构能抑制振动能力的提升,还实现了大臂结构轻量化设计。层次分析法的引入为多目标优化问题中各子目标函数的重要性提供了客观的理论依据。     

Design of ultrasonic array elements for acoustic power considerations

In sound-transmitting applications such as therapeutic ultrasound, the acoustic power at a particular operating frequency is a critical figure of merit for transducer/array design. A design methodology for enhancing the acoustic power radiated from fluid-loaded piezoelectric array elements at a fixed frequency is developed in this paper. A gradient-based optimization algorithm is integrated within the finite element framework to guide the determination of the two design variables, the piezoelectric element thickness and the matching layer thickness, to optimize the acoustic power output. A method for avoiding explicit remeshing in the optimization iteration is presented. Optimized designs are determined numerically, and the effectiveness of the design method is confirmed by experimental measurements. The validated numerical analysis also shows that conventional design strategies using one-dimensional transducer analysis and rule-of-thumb matching layer or protection layer sizing rules may not give the best design for array elements in acoustic power applications     

约束阻尼结构的改进准则法拓扑减振动力学优化

旨在为减振设计提供理论基础,研究约束阻尼结构拓扑动力学优化。以阻尼材料用量、振动特征方程、模态频率为约束,以多模态损耗因子倒数的加权和最小为目标,建立了约束阻尼结构拓扑优化模型,引入MAC因子控制结构的振型跃阶。在引入质量阵惩罚因子基础上推导出优化目标灵敏度。考虑到优化目标函数的非凸性,采用常规准则法(OC)寻优可能会使拓扑变量出现负值或陷入局部优化,故引入数学规划移动渐近技术对OC法进行改进,从而将全体拓扑变量纳入改进算法的优化迭代全过程。编程实现了约束阻尼板改进OC法拓扑动力学优化并对改进法性能进行了仿真。结果显示,改进算法可得到更合理的约束阻尼层构形,可使结构取得更佳减振效果。研究表明,改进算法迭代稳定性更好、寻优效率更高、更具全域最优性。     

Topology design of reactive mufflers for enhancing their acoustic attenuation performance and flow characteristics simultaneously

When seeking to enhance the acoustic attenuation performance of a reactive muffler, it is necessary to ensure that the flow resistance does not increase significantly. To date, there have been very few attempts to simultaneously optimize the transmission loss and pressure drop of a muffler. In this study, a multiobjective topology optimization problem is formulated to maximize the transmission loss at a target frequency and minimize the pressure drop simultaneously. The objective function in the formulation is given as the sum of weighted transmission loss and weighted pressure drop. The effect of the weighting factors on the optimal topologies of a muffler is investigated. Furthermore, the physical interpretation of partition layouts of optimized mufflers is discussed. The proposed muffler design method involving multiobjective topology optimization is compared with the previous muffler design method that involves single‐objective topology optimization to maximize only the transmission loss. The most important advantage of this study is shown by considering numerical results; the proposed muffler design method is applicable to nonconcentric expansion chamber mufflers, unlike the previous muffler design method. Copyright © 2012 John Wiley & Sons, Ltd.     

Microspeaker Diaphragm Optimization for Widening the Operating Frequency Band and Increasing Sound Pressure Level

We report on the optimization of a microspeaker diaphragm for widening the working frequency band between its first and second eigenfrequencies and increasing its sound pressure level (SPL). A metallic diaphragm produces a larger magnetic force and thus a higher sound pressure level; therefore a Ni-coating on a common poly ethylene naphthalene (PEN) diaphragm is appropriate. For the best diaphragm design, it is important to simultaneously optimize the diaphragm shape and the Ni-coating distribution on the top of the diaphragm. Since complete Ni-coating increases SPL but also reduces the frequency band, special attention must be paid to the Ni-coating. We solved the optimization problem by a two-step approach: standard shape optimization of a PEN diaphragm for widening the frequency band, followed by distribution optimization of the Ni material on the diaphragm. To facilitate the Ni distribution optimization, we formulated the problem as a special topology design optimization. Since the optimization requires a coupled analysis involving the electromagnetic field, mechanical vibration and sound radiation, the multiphysical system behavior should be properly modeled. After presenting the fundamental multiphysical equations, we provide shape and topology optimization procedures to find an optimal microspeaker diaphragm. We verified the validity of an optimized diaphragm configuration optimized by our method from a physical viewpoint.     

基于最小响应偏离度的振动夹具优化设计

为了解决夹具传递给试件的振动量级的输入严重不均匀和偏离参考谱加速度均方根值的现象,依据电动振动台多点控制原理和夹具频响函数特性,建立夹具优化计算模型。以某试件夹具设计为实例,依据Nastran软件计算夹具频响函数值,根据所建优化计算模型,求出夹具最优设计参数。优化结果表明,优化后夹具传力点处的响应均方偏离度及加速度均方根值的变动范围均小于传统方法设计的夹具所求值;同时,优化后的夹具振动试验测试结果表明,传力点处实测加速度均方根值的变动范围与夹具设计阶段优化后的计算值变动范围基本一致,这就证明该优化方法是可行的和实用的,可以为振动试验实施和夹具设计提供实践和理论指导。     

基于铺层设计特征的碳纤维增强复合材料悬架控制臂结构优化

基于铺层设计特征,提出一种使用碳纤维复合材料对承载结构件进行结构优化设计的方法和流程.该方法综合考虑结构几何特征、材料铺层方式、铺层厚度及铺层角度在设计环节中的序列关系,通过几何设计空间构建、离散变量多目标优化、基于工艺可行性的最优决策等方法实现结构设计.以碳纤维增强复合材料悬架控制臂的轻量化设计为例:首先,以钢质控制臂结构为参考建立复合材料控制臂的几何设计空间;然后,以复合材料铺层便利性为原则对其进行结构设计,采用准各向同性铺层对控制臂的铺层厚度进行设计;进而,以提高控制臂刚度和1阶固有频率为目标,使用优化算法对铺层角度进行多目标优化设计;最后,以工艺可行性为约束对优化结果进行筛选并最终完成结构设计.结果表明,所设计复合材料结构具有更大的刚度和1阶固有频率,并且与钢质结构相比减重47.9%.所提出的方法能够较好地兼顾结构特征和复合材料设计要求之间的关系,为复合材料结构优化设计理论与方法的发展提供有益参考.     

随机参数平面连续体结构的频率拓扑优化设计

摘 要 研究几何和物理参数均为随机变量的平面连续体结构在结构基频约束下的拓扑优化设计问题。以结构总质量均值极小化为目标函数,以结构的形状拓扑信息为设计变量,以结构基频概率可靠性指标为约束条件,构建了随机结构拓扑优化设计数学模型。利用代数综合法,导出了随机参数结构动力响应的均值和均方差的计算表达式。采用渐进结构优化的求解策略与方法,通过两个算例验证了文中模型及求解方法的合理性和可行性。     

Structure optimization of connection frames based on frequency sensitivity in macro-micro motion platforms

High-performance connection frames are of great significance for ultra-high acceleration and ultra-precision positioning in macro-micro motion platforms. This paper first takes the connection frame as a research object,builds a finite element model(FEM) of the natural frequency of the frame, and then verifies the correctness of this model. The frequency sensitivity method is then used to perturb the structural parameters of the FEM of the connection frame, and the sensitivities of the first-order natural frequency and mass of the corresponding structural parameters are obtained by calculation and analysis. The design variables are also determined. The natural frequency is used as the optimization objective, and the design parameters and mass of the connection frame are constrained. The structural parameters of the connecting frame are obtained through optimization, and the model is built and verified by experiments. The results show that the first-order natural frequency of the connecting frame is effectively improved by the frequency sensitivity method, avoids resonance between the connecting frame and the voice coil motor, and realizes the lightweight design of the connection frame. This research provides a reliable basis for the stable operation and ultra-precision positioning of ultra-high acceleration macro-motion platforms.     

Multi-objective optimization of a stirling-type pulse tube refrigerator

A genetic algorithm (GA) optimization method which is coupled to a one-dimensional finite volume method is proposed and implemented as a computer program for the modeling and optimization of a stirling-type pulse tube refrigerator (PTR). The multi-objective optimization procedure is applied to provide the optimization design parameters which are charge pressure, operating frequency, and temperature of after-cooler as well as swept volume of compressor. The procedure is selected to obtain the maximum coefficient of performance (COP) and the minimum cooling temperature (T_cold) as two objective functions. In order to validate the simulation code, the results were compared with the results of other models and experiments. The results showed a reasonably well agreement between simulation output and experimental data. The results of optimal designs are a set of multiple optimum solutions, called Pareto optimal solutions. Moreover, the closed form relations between two objectives are derived for Pareto optimal solutions of pulse tube refrigerator. Finally, a sensitivity analysis of the variation of each design parameter on both objective functions was carried out as well and the results are presented. As a result, the COP is more sensitive than T_cold in the optimum design points. The frequency of refrigerator is the most sensitive factor which affects the COP even with little changes.     

约束阻尼板结构振动声辐射优化

根据经典薄板理论,建立约束阻尼板有限元模型,将其视作镶嵌于无限大刚性障板,利用Rayleigh积分法推导结构的辐射声功率及灵敏度表达式。以一阶峰值频率或频带激励下的声功率最小化为目标,约束阻尼材料体积分数为约束条件,建立拓扑优化模型,采用渐进优化算法,编制了优化计算程序,获得了约束阻尼材料的最优拓扑构型,并与全覆盖板及基板的辐射声功率进行了对比。研究表明：以声功率最小化为目标,对约束阻尼材料布局进行拓扑优化,能有效抑制结构的振动声辐射,为结构低噪声设计提供了重要的理论参考和技术手段。     

考虑惯性参数测量误差的动力总成悬置系统优化方法

汽车动力总成的惯性参数（转动惯量和惯性积）通常采用实验方法进行测量,测量误差一般不超过3 %。动力总成悬置系统的固有特性与动力总成惯性参数、悬置刚度、位置、角度密切相关,从而悬置系统的固有频率和解耦率的理论设计值与其真实值之间必然存在一定程度偏差。采用均匀分布随机变量描述惯性参数,以悬置刚度为优化设计变量,提出稳健优化模型对某轿车悬置系统固有特性进行稳健优化。优化结果表明,与确定性优化方法相比,稳健优化方法可以较大幅度地提高频率、解耦率、频率间隔的稳健性。     

基于复合优化方法立式数控加工中心的多目标优化设计

为实现加工中心动静态性能不低于优化前性能,达到整机重量最轻的要求,本文提出了一种复合优化方法来研究多变量、多约束和多目标的数控加工中心优化设计。采用有限元分析和实验模态测试方法分析各大件动态性能,并验证了有限元模型的精确性。然后以该有限元模型为基础进行静态分析,得出各大件的最大变形及应力等。以柔度为目标,采用变密度法拓扑优化设计立柱结构的外形框架;以固有频率为目标,基于元结构的可适应性动态优化方法设计加工中心的筋板结构;以固有频率和质量为目标,基于响应面法的尺寸优化确定各结构的最优尺寸。最后将优化后的各大件进行整机装配,分析校核整机动静态性能。分析结果表明,优化后的整机在保证加工中心动静态性能的条件下,整机质量从12749kg减少到12127kg,减重达到4.9%,达到了整机的优化设计要求,说明该方法具有较高的精度和较强的工程实用性。     

汽车仪表板异响仿真优化及试验研究

为在产品开发前期识别出某SUV仪表板的异响风险,利用仿真方法对其进行典型路谱下的频率响应分析,采用E-line法计算仪表板总成相邻部件之间的相对位移,结合部件间的间隙尺寸信息识别潜在的敲击异响风险点,并且计算风险率。总结导致相对位移较大的原因,结合工程经验及设计要求考虑方案的可实施性,提出控制异响的优化方案。仿真计算结果表明改进方案有良好的抑制敲击异响的效果。在样车调教阶段,进行整车四立柱异响主观评价试验,验证了仿真分析方法的有效性。