某SUV车架多目标拓扑优化设计

为得到同时满足刚度和动态要求的SUV车架,基于SIMP材料插值方法,分别以刚度最大和低阶模态固有频率最大作为优化目标建立拓扑优化模型,利用折中规划法建立多工况下刚度和低阶固有频率多目标优化模型,通过拓扑优化迭代得到新的SUV车架;对新车架进行仿真分析,得到其位移和应力分布及前4阶固有频率.其静态特性满足材料要求且有很大提高,第1阶固有频率提高到30.3 Hz,新车架质量减轻到193.3 kg.计算结果表明该方法能够很好地解决多目标下的结构优化问题。     

A 6-DOF reconfigurable hybrid parallel manipulator

This paper presents a case study on a reconfigurable hybrid parallel robot dubbed ReSl-Bot. It addresses the realm of reconfigurable 6-DOF parallel mechanisms, for sustainable manufacturing. It also features a self-reconfigurable architecture. A systematic analysis involving kinematics, constant orientation workspace, singularity and stiffness is developed in detail. Interesting features are discussed, revealing some unique characteristics of the studied architecture. A multi-objective optimization procedure is also carried out with weighted stiffness, dexterity and workspace volume as the performance indices.     

基于变密度法的飞行器升力面结构多目标拓扑优化设计

为研究权衡结构刚度与低阶振动频率的飞行器升力面最优结构设计,提出两种多目标拓扑优化方案（约束法、结合约束法与评价函数法）.基于变密度方法,在约束法方案中将多目标优化转化为设定参考点位移约束和低阶振动频率约束下,求解结构质量最小化的优化问题.在结合约束法与评价函数法方案中,定义组合柔度指数为评价函数（结构柔度与振动频率的函数）,将多目标优化转化为设定低阶振动频率约束和体积分数约束下,求解结构最小组合柔度指数的优化问题.结果表明两种方案的优化结果具有一定的相似性,各有所长.优化设计不仅减轻了升力面结构重量,而且提高了结构的一、二阶振动频率.     

Design optimization of a runflat structure based on multi-objective genetic algorithm

Runflat structure plays an important role in determining the sustainable mileage after the tire is shot. Lightweight, stiffness and strength are highly relevant to the overall performance of the structure. A parameterized model was built based on the full study of the structure, and a new adaptive meshing method is proposed to ensure the quality of the model. The accuracy of the new model was verified by comparing to the traditional finite element model. The parameter study was carried out to investigate the response of the performance and mass. Multi-objective optimization model was established by applying optimal Latin square design method and response surface model approach. Non-dominated sorting genetic algorithm-II (NSGA-II) was applied to obtain the optimization design. The results indicate that the combination of parameterized model and multi-objective genetic algorithms successfully achieve the goal of multi-objective optimization for mass and displacement while ensuring the stress. Meanwhile, the optimal topology, shape and thickness optimization for the runflat structure have been achieved at the same time.     

飞机多目标优化设计网格的研究与应用

针对飞机多目标拓扑优化提出一种通用的遗传算法计算模型,在此模型基础上,基于对等计算(P2P)技术将分布的计算资源整合为高性能计算环境,以网格服务方式提供统一的资源服务和可视化的用户使用环境,实现多目标优化设计网格,解决飞机设计中遇到的复合材料多目标拓扑优化问题.首先对系统体系结构以及多目标遗传算法做出较详细的描述,然后以优化某型大展弦比机翼为例,给出一组实验数据.结果证明,该系统大大缩短了计算时间,具有良好的并行加速效果.     

基于OptiStruct的麦弗逊悬架下控制臂优化

针对麦弗逊悬架下控制臂的优化问题,为减轻其质量、增强其刚度,基于拓扑优化理论和有限元法,用OptiStruct对某铸造麦弗逊悬架下控制臂进行拓扑优化.在规定的体积内获得最佳的材料分布,使刚度最大.优化后重建CAD模型,并与原件的刚度和模态进行比较,结果表明该优化能减轻控制臂质量、增强下控制臂刚度。     

Topology optimization of a swing arm type actuator using the response surface method

In the frame of topology optimization, the multi-objective ability has to be considered since structural design is usually required to satisfy more than one requirement. A modified topology optimization method based on the response surface method (RSM) is proposed to generate a structure of a small form factor (SFF) swing arm type actuator satisfying maximum compliance and maximum stiffness at the same time using the multi-objective optimization approach. The multi-objective function is defined to maximize the compliance in the direction of focusing as well as the eigen-frequency of the structure. The design of experiments (DOE) is performed to select sensitive variables. Based on DOE results, the response surface functions are formulated to construct the multi-objective function. The weight factors between conflicting objective functions are determined by the Pareto optimum method. By applying the optimal combination of design variables to the design domain, the optimized topology can be obtained.This work was supported by Korea Research Foundation (KRF) Grant KRF-2004-042-D00004.     

Lightweight flatbed trailer design by using topology and thickness optimization

A new design for a lightweight flatbed trailer with high bending stiffness and torsional frequency is presented. The design procedure consists of two main steps: topology optimization and thickness optimization. During topology optimization, a creative frame layout different from existing ladder-type frames can be obtained by searching the best layout out of all possible layouts of a simplified design domain model. After approximating the result of topology optimization as a thin-walled structure, the approximated thicknesses of the plates are optimized to minimize the mass of a trailer. The bending stiffness and torsional frequency obtained by topology optimization are set as design constraints for thickness optimization. Due to the closed cross-section, the optimized trailer can efficiently increase the stiffness-to-mass ratio to a large extent. Discrete thicknesses are employed as design variables for thickness optimization so that the thicknesses of the plates of a trailer can be included in those of commercially available high-strength steel products. The final model has a 29% reduction in total mass, a 21% decrease in mean compliance with a uniform bending load, and a 169% increase in torsional frequency.     

空间桁架结构优化设计

为获得空间桁架结构的合理构型,以某空间设备支撑结构为例,分析结构材料在设计空间的分布形式和桁架结构的传力路径。在已知载荷约束和设计空间大小的条件下,基于连续体拓扑优化方法,以静态多工况刚度和动态固有频率为多目标函数进行优化分析。依据设计要求确定计算模型的结点数和结点位置,获得满足要求的空间桁架结构并进行优化设计。优化结果比原模型质量减少36.7%,一阶模态提高3.6%。     

Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material

The present paper studies multi-objective design of lightweight thermoelastic structure composed of homogeneous porous material. The concurrent optimization model is applied to design the topologies of light weight structures and of the material microstructure. The multi-objective optimization formulation attempts to find minimum structural compliance under only mechanical loads and minimum thermal expansion of the surfaces we are interested in under only thermo loads. The proposed optimization model is applied to a sandwich elliptically curved shell structure, an axisymmetric structure and a 3D structure. The advantage of the concurrent optimization model to single scale topology optimization model in improving the multi-objective performances of the thermoelastic structures is investigated. The influences of available material volume fraction and weighting coefficients are also discussed. Numerical examples demonstrate that the porous material is conducive to enhance the multi-objective performance of the thermoelastic structures in some cases, especially when lightweight structure is emphasized. An “optimal” material volume fraction is observed in some numerical examples.     

基于多目标优化技术的发动机罩加强筋布局设计研究

为了加强发动机罩壳的静态刚度特性和抑制振动能力,实现罩壳结构的轻量化,引入基于水平集法的拓扑优化技术和多目标理论,完成发动机罩加强筋布局的多目标优化设计。采用折衷规划法构建关于静刚度和一阶固有频率的多目标优化模型,运用水平集法求出罩壳加强筋的最佳分布形式。结果表明,该方法能大大地提高静动态结构性能,最大应力的下降说明罩壳应力集中现象得到有效的改善,缓解罩壳的疲劳现象。此外,基于层次分析法确定权重因子,避免了多目标优化模型构建中的主观能动性。采用平均频率法对动态目标函数的处理,有效地消除了动态优化过程中的收敛性。     

Conceptual and detailed design of an automotive engine cradle by using topology,shape, and size optimization

An automotive engine cradle supports many crucial components and systems, such as an engine, transmission, and suspension. Important performance measures for the design of an engine cradle include stiffness, natural frequency, and durability, while minimizing weight is of primary concern. This paper presents an effective and efficient methodology for engine cradle design from conceptual design to detailed design using design optimization. First, topology optimization was applied on a solid model which only contains the possible engine cradle design space, and an optimum conceptual design was determined which minimizes weight while satisfying all stiffness constraints. Based on topology optimization results, a design review was conducted, and a revised model was created which addresses all structural and manufacturability concerns. Shape and size optimization was then performed in the detailed design stage to further minimize the mass while meeting the stiffness and natural frequency targets. Lastly, the final design was validated for durability. The initial design domain had the mass of 82.6 kg; topology optimization in conceptual design reduced the mass to 26.7 kg; and the detailed design task involving shape and size optimization further reduced the mass to 21.4 kg.     

On simultaneous shape and material layout optimization of shell structures

This work presents a computational method for integrated shape and topology optimization of shell structures. Most research in the last decades considered both optimization techniques separately, seeking an initial optimal topology and refining the shape of the solution later. The method implemented in this work uses a combined approach, were the shape of the shell structure and material distribution are optimized simultaneously. This formulation involves a variable ground structure for topology optimization, since the shape of the shell mid-plane is modified in the course of the process. It was considered a simple type of design problem, where the optimization goal is to minimize the compliance with respect to the variables that control the shape, material fraction and orientation, subjected to a constraint on the total volume of material. The topology design problem has been formulated introducing a second rank layered microestructure, where material properties are computed by a “smear-out” procedure. The method has been implemented into a general optimization software called ODESSY, developed at the Institute of Mechanical Engineering in Aalborg. The computational model was tested in several numerical applications to illustrate and validate the approach.     

基于最优激励位姿序列的机械臂负载估计

重力补偿方法广泛地应用于由连杆与旋转机构组成的机器人系统中,更换机器人末端执行器造成了补偿模型的不确定性．针对该问题,提出了一种利用机器人关节力矩与位置信息的负载参数离线辨识方法．基于机器人静力学方法提出了2种负载参数的计算模型,并通过采集机器人在多个静态位姿条件下的关节力矩与位置信息获得负载参数的最小二乘解．进一步,本文针对机器人的辨识位姿选取问题展开研究,提出了同时保证辨识精度与辨识简便性的多目标优化问题,使用多目标粒子群优化方法获得最优辨识位姿．根据辨识后的负载参数,给出了机械臂各关节负载的重力补偿量计算方法．实验结果表明所提方法具有较高的辨识精度,负载质量的辨识误差最小值达到0.007 06 kg,最大值达到0.151 kg,负载质心位置的辨识误差最小值达到0.025 4 m,最大值达到0.122 m,验证了上述方法的可行性与有效性．     

Topology optimization framework for structures subjected to stationary stochastic dynamic loads

The field of topology optimization has progressed substantially in recent years, with applications varying in terms of the type of structures, boundary conditions, loadings, and materials. Nevertheless, topology optimization of stochastically excited structures has received relatively little attention. Most current approaches replace the dynamic loads with either equivalent static or harmonic loads. In this study, a direct approach to problem is pursued, where the excitation is modeled as a stationary zero-mean filtered white noise. The excitation model is combined with the structural model to form an augmented representation, and the stationary covariances of the structural responses of interest are obtained by solving a Lyapunov equation. An objective function of the optimization scheme is then defined in terms of these stationary covariances. A fast large-scale solver of the Lyapunov equation is implemented for sparse matrices, and an efficient adjoint method is proposed to obtain the sensitivities of the objective function. The proposed topology optimization framework is illustrated for four examples: (i) minimization of the displacement of a mass at the free end of a cantilever beam subjected to a stochastic dynamic base excitation, (ii) minimization of tip displacement of a cantilever beam subjected to a stochastic dynamic tip load, (iii) minimization of tip displacement and acceleration of a cantilever beam subjected to a stochastic dynamic tip load, and (iv) minimization of a plate subjected to multiple stochastic dynamic loads. The results presented herein demonstrate the efficacy of the proposed approach for efficient multi-objective topology optimization of stochastically excited structures, as well as multiple input-multiple output systems.

     

Topological design considering flexibility under periodic loads

Topology optimization has been extensively considered to design the structural configuration for the stiffness maximization and the eigenfrequency maximization. In this paper, we construct a topology optimization method implementing flexibility with the time-periodic loading condition. First, the flexibility in the dynamic periodic loading is formulated using the mutual energy concept. Second, the multi-optimization problem is formulated using a new multi-objective function in order to obtain an optimal solution incorporating both flexibility and stiffness. Next, the topology optimization procedure is developed using the homogenization design method. Finally, some examples are provided to confirm the optimal design method presented here. Received January 18, 1999     

Multi-objective optimization by genetic algorithm of structural systems subject to random vibrations

This paper deals with a multi-objective optimization criterion for linear viscous-elastic device utilised for decreasing vibrations induced in mechanical and structural systems by random loads. The proposed criterion for the optimum design is the minimization of a vector objective function. The multi-objective optimization is carried out by means of a stochastic approach. The design variables are the device frequency and the damping ratio. As cases of study, two different problems are analysed: the base isolation of a rigid mass and the tuned mass damper positioned on a multi degree of freedom structural system subject to a base acceleration. The non-dominated sorting genetic algorithm in its second version (NSGA-II) is adopted to obtain the Pareto sets and the corresponding optima for different characterizations of the system and input.     

Evolutionary topology optimization of continuum structures with an additional displacement constraint

Evolutionary structural optimization (ESO) and its later version Bi-directional ESO (BESO) have been successfully applied to optimum material distribution problems for continuum structures. However, the existing ESO/BESO methods are limited to the topology optimization of an objective function such as mean compliance with a single constraint e.g. structural volume. The present work extends the BESO method to the stiffness optimization with a material volume constraint and a local displacement constraint. As a result, one will obtain a structure with the highest stiffness for a given volume while the displacement of a certain node does not exceed a prescribed limit. Several examples are presented to demonstrate the effectiveness of the proposed method.     

Application of topology optimization to design an electric bicycle main frame

Electric bicycle main frame is the most principal structure, connecting and supporting other various components, while bearing a variety of forces and moments. In this paper the topology optimization technology is applied to generate robust electric bicycle main frame by optimizing the material distribution subject to the constraints and dynamic loads. Geometric, mechanical and finite element models, as well as a flexible coupling dynamic model are constructed. Validity and accuracy of these models are investigated through real-life testing. By applying typical road excitation, dynamic loads of all key points are extracted. A set of forces data is extracted every 0.5?s during the whole simulation, including peak values of these forces. In order to obtain appropriate topology optimization results, the values of two crucial parameters, volume fraction and minimum member size, are discussed respectively. Then the topology optimization of multi-load case is implemented with the objective of minimizing the set of weighted compliances resulting from individual load cases. Results illustrate that element density distribution of the model is optimized with manufacturing constraints of minimum member size control and extrusion constraint. Consequently, the better frame form design of the electric bicycle is obtained. Modal analysis for the original and refined models is performed respectively to evaluate the structure stiffness. The results indicate that this optimization program is effective enough to develop a new electric bicycle frame as a reference for manufacturers.     

An integrated approach for shape and topology optimization of shell structures

In this paper an automated approach for simultaneous shape and topology optimization of shell structures is presented. Most research in the last decades considered these optimization techniques separately, seeking an initial optimal material layout and refining the shape of the solution later. The method developed in this work combines both optimization techniques, where the shape of the shell structure and material distribution are optimized simultaneously, with the aim of finding the optimum design that maximizes the stiffness of the shell. This formulation involves a variable ground structure for topology optimization, since the shape of the shell is modified in the course of the process. The method has been implemented into a computational model and the feasibility of the approach is demonstrated using several examples.