Topology optimization of internal partitions in a flow-reversing chamber muffler for noise reduction

A topology-optimization-based design method for a flow-reversing chamber muffler is suggested to maximize the transmission loss value at a target frequency considering flow power dissipation. Rigid partitions for high noise reduction should be carefully placed inside the muffler to avoid extreme flow power dissipation due to a 180° change in flow direction from an inlet to an outlet. The optimal flow path for minimum flow power dissipation is well known to change depending on the Reynolds number, which is a function of the inlet flow velocity. To optimize the partition layout with an optimal flow path in an expansion chamber at a given Reynolds number, a flow-reversing chamber muffler design problem is formulated by topology optimization. The formulated topology optimization problem is implemented using the finite element method with a gradient-based optimization algorithm and is solved for various design conditions such as the target frequencies, rigid partition volumes, Reynolds numbers, non-design domain settings, and allowed amounts of flow power dissipation. The effectiveness of our suggested approach is verified by comparing the optimized partition layouts obtained by the suggested method and previous methods.     

A heuristic method for simultaneous tower and pattern-free field optimization on solar power systems

A heuristic method for optimizing a solar power tower system is proposed, in which both heliostat field (heliostat locations and number) and the tower (tower height and receiver size) are simultaneously considered.Maximizing the thermal energy collected per unit cost leads to a difficult optimization problem due to its characteristics: it has a nonconvex black-box objective function with computationally expensive evaluation and nonconvex constraints.The proposed method sequentially optimizes the field layout for a given tower configuration and then, the tower design is optimized for the previously obtained field layout. A greedy-based heuristic algorithm is presented to address the heliostat location problem. This algorithm follows a pattern-free method. The only constraints to be considered are the field region and the nonconvex constraints (which allow heliostats to not collide).The absence of a geometrical pattern to design the field and the simultaneous optimization of the field and the tower designs make this approach different from the existing ones. Our method is compared against other proposals in the literature of heliostat field optimization.     

基于梯度有限元的异质材料实体优化设计

针对具有空间分布梯度的异质材料实体的优化设计,建立了两相材料梯度 有限元的概念,利用拉格朗日单元的形函数对体积分数进行插值,在节点邻域内引入设计变 量自适应下界进行梯度控制,利用移动渐近线算法求解优化设计数学模型以使结构满足特定 的功能和目标,以金属夹钳为算例验证了该方法的可行性和鲁棒性。     

Two-stage size-layout optimization of axially compressed stiffened panels

In this study, a two-stage optimization framework is proposed for cylindrical or flat stiffened panels under uniform or non-uniform axial compression, which are extensively used in the aerospace industry. In the first stage, traditional sizing optimization is performed. Based on the buckling or collapse-like deformed shape evaluated for the optimized design, the panel can be divided in sub-regions each of which shows characteristic deformations along axial and circumferential directions. Layout optimization is then performed using a stiffener spacing distribution function to represent the location of each stiffener. A layout coefficient is assigned to each sub-region and the overall layout of the panel is optimized. Three test problems are solved in order to demonstrate the validity of the proposed optimization framework: remarkably, the load-carrying capacity improves by 17.4 %, 66.2 % and 102.2 % with respect to the initial design.     

Polarisation independent liquid crystal lenses and contact lenses using embossed reactive mesogens

Liquid crystal lenses have promise in optical systems owing to their tunability combined with low electrical power, cost, and weight. A good example of such a system is switchable contact lenses for the correction of age‐related presbyopia. Sufficiently large phase modulation can be done using nematic liquid crystals in a meniscus lens configuration. However, the birefringent materials are inherently polarisation dependent, usually requiring orthogonal polarisations to be focussed separately. A novel method is presented for producing polarisation independent lenses based on reactive mesogens. Results are presented for a 2‐level and 3‐level diffractive Fresnel lenses, and the promise of the technique for use in refractive lenses such as contact lenses is discussed.     

Using Wavefront Tracing for the Visualization and Optimization of Progressive Lenses

Progressive addition lenses are a relatively new approach to compensate for defects of the human visual system. While traditional spectacles use rotationally symmetric lenses, progressive lenses require the specification of free-form surfaces. This poses difficult problems for the optimal design and its visual evaluation.
This paper presents two new techniques for the visualization of optical systems and the optimization of progressive lenses. Both are based on the same wavefront tracing approach to accurately evaluate the refraction properties of complex optical systems.
We use the results of wavefront tracing for continuously re-focusing the eye during rendering. Together with distribution ray tracing, this yields high-quality images that accurately simulate the visual quality of an optical system. The design of progressive lenses is difficult due to the trade-off between the desired properties of the lens and unavoidable optical errors, such as astigmatism and distortions. We use wavefront tracing to derive an accurate error functional describing the desired properties and the optical error across a lens. Minimizing this error yields optimal free-form lens surfaces.
While the basic approach is much more general, in this paper, we describe its application to the particular problem of designing and evaluating progressive lenses and demonstrate the benefits of the new approach with several example images.     

Multiobjective layout optimization of robotic cellular manufacturing systems

This paper proposes a multiobjective layout optimization method for the conceptual design of robot cellular manufacturing systems. Robot cellular manufacturing systems utilize one or more flexible robots which can carry out a large number of operations, and can conduct flexible assemble processes. The layout design stage of such manufacturing systems is especially important since fundamental performances of the manufacturing system under consideration are determined at this stage. In this paper, the design criteria for robot cellular manufacturing system layout designs are clarified, and objective functions are formulated. Next, layout design candidates are represented using a sequence-pair scheme to avoid interference between assembly system components, and the use of dummy components is proposed to represent layout areas where components are sparse. A multiobjective genetic algorithm is then used to obtain Pareto optimal solutions for the layout optimization problems. Finally, several numerical examples are provided to illustrate the effectiveness and usefulness of the proposed method.     

Integration of design and manufacturing for structural shape optimization

This paper presents an integrated design and manufacturing approach that supports shape optimization of structural components. The approach starts from a primitive concept stage, where boundary and loading conditions of the structural component are given to the designer. Topology optimization is conducted for an initial structural layout. The discretized structural layout is smoothed using parametric B-Spline surfaces. The B-Spline surfaces are imported into a CAD system to construct parametric solid models for shape optimization. Virtual manufacturing (VM) techniques are employed to ensure that the optimized shape can be manufactured at a reasonable cost. The solid freeform fabrication (SFF) system fabricates physical prototypes of the structure for design verification. Finally, a computer numerical control (CNC) machine is employed to fabricate functional parts as well as mold or die for mass production of the structural component. The main contribution of the paper is incorporating manufacturing into the design process, where manufacturing cost is considered for design. In addition, the overall design process starts from a primitive stage and ends with functional parts. A 3D tracked vehicle roadarm is employed throughout this paper to illustrate the overall design process and various techniques involved.     

基于电路控制的梯度折射率曲面声学透镜研究

针对现有声学透镜结构确定后功能单一的问题,提出一种利用可调谐材料实现梯度折射率曲面声学透镜的新技术;不同于以往声学透镜依靠几何阵列结构渐变的方式,该曲面声学透镜通过电路系统建立温度与材料声学折射率的映射关系,调控梯度折射率的精确分布;曲面声学透镜在不同梯度温度控制下可实现多种声学功能器件,如隐身斗篷、吕内堡透镜和鱼眼透镜等,具有调试简单,便于操作等特点;基于透镜材料声学特性可调谐和热电路温度控制技术,实现了一个功能可切换的梯度折射率曲面声学透镜器件,研究结果可为设计新型多功能声波导控制器件提供理论与技术支持.     

Multi-objective layout optimization of a satellite module using the Wang-Landau sampling method with local search

The layout design of satellite modules is considered to be NP-hard. It is not only a complex coupled system design problem but also a special multi-objective optimization problem. The greatest challenge in solving this problem is that the function to be optimized is characterized by a multitude of local minima separated by high-energy barriers. The Wang-Landau (WL) sampling method, which is an improved Monte Carlo method, has been successfully applied to solve many optimization problems. In this paper we use the WL sampling method to optimize the layout of a satellite module. To accelerate the search for a global optimal layout, local search (LS) based on the gradient method is executed once the Monte-Carlo sweep produces a new layout. By combining the WL sampling algorithm, the LS method, and heuristic layout update strategies, a hybrid method called WL-LS is proposed to obtain a final layout scheme. Furthermore, to improve significantly the efficiency of the algorithm, we propose an accurate and fast computational method for the overlapping depth between two objects (such as two rectangular objects, two circular objects, or a rectangular object and a circular object) embedding each other. The rectangular objects are placed orthogonally. We test two instances using first 51 and then 53 objects. For both instances, the proposed WL-LS algorithm outperforms methods in the literature. Numerical results show that the WL-LS algorithm is an effective method for layout optimization of satellite modules.     

Digital redesign of uncertain interval systems based on extremal gain/phase margins via a hybrid particle swarm optimizer

In this paper, a hybrid optimizer incorporating particle swarm optimization (PSO) and an enhanced NM simplex search method is proposed to derive an optimal digital controller for uncertain interval systems based on resemblance of extremal gain/phase margins (GM/PM). By combining the uncertain plant and controller, extremal GM/PM of the redesigned digital system and its continuous counterpart can be obtained as the basis for comparison. The design problem is then formulated as an optimization problem of an aggregated error function in terms of deviation on extremal GM/PM between the redesigned digital system having an interval plant and its continuous counterpart, and subsequently optimized by the proposed optimizer to obtain an optimal set of parameters for the digital controller. Thanks to the performance of the proposed hybrid optimizer, frequency-response performances of the redesigned digital system using the digital controller evolutionarily derived by the proposed approach bare a far better resemblance to its continuous-time counter part in comparison to those obtained using existing open-loop discretization methods.     

带静不平衡约束的矩形装填问题的启发式算法

卫星舱布局问题不仅是一个复杂的耦合系统设计问题,也是一个特殊的优化问题,具有NP难度性。解决这类问题最大的挑战在于需要优化的目标函数具有大量的被高能势垒分隔开的局部极小值点。Wang-Landau（WL）抽样算法是一种改进的蒙特卡罗方法,已经被成功地运用蛋白质结构预测等优化问题。本文以卫星舱布局优化问题为背景,首次将WL抽样算法引入矩形装填问题的求解。针对矩形装填物的特点,提出了启发式格局更新策略,以引导抽样算法在解空间中进行有效行走。为了加速搜索全局最优解,每次蒙特卡罗扫描生成新的布局时,便执行梯度法进行局部搜索。通过将局部搜索机制、启发式格局更新策略与WL抽样算法相结合,提出了一种用于解决带静不平衡约束的任意矩形装填问题的启发式布局算法。在布局优化过程中,通过在挤压弹性势能的基础上增加静不平衡量惩罚项并采用质心平移的方法,使布局系统的静不平衡量达到约束要求。另外,为了改进算法的搜索效率,提出了改进的有限圆族法用于装填物之间的干涉性判断和干涉量计算。通过对文献中两组共10个有代表性的算例进行实算,计算结果表明,所提出的装填算法是一种求解带静不平衡性能约束的任意矩形装填问题的有效算法。     

EvoArch: An evolutionary algorithm for architectural layout design

The architectural layout design problem, which is concerned with the finding of the best adjacencies between functional spaces among many possible ones under given constraints, can be formulated as a combinatorial optimization problem and can be solved with an Evolutionary Algorithm (EA). We present functional spaces and their adjacencies in form of graphs and propose an EA called EvoArch that works with a graph-encoding scheme. EvoArch encodes topological configuration in the adjacency matrices of the graphs that they represent and its reproduction operators operate on these adjacency matrices. In order to explore the large search space of graph topologies, these reproduction operators are designed to be unbiased so that all nodes in a graph have equal chances of being selected to be swapped or mutated. To evaluate the fitness of a graph, EvoArch makes use of a fitness function that takes into consideration preferences for adjacencies between different functional spaces, budget and other design constraints. By means of different experiments, we show that EvoArch can be a very useful tool for architectural layout design tasks.     

The optimum shape of cooling towers

Numerous computer optimization techniques have been developed and applied primarily to the design of structures composed of discrete elements. Continuous surface structures have been optimized primarily by methods based upon the differential or integral calculus (e.g. the calculus of variations). However, the determination of the optimal shape of continuous surface structures can also be approached by algebraic methods more suitable for digital computation. If the coordinates of the middle surface of a shell are expressed by a finite polynomial series, an optimization problem in a finite set of discrete variables results. In the present work, this method is applied to a particular example of a shell of revolution: a natural draft cooling tower. A simple preliminary design model is formulated in order to evaluate the potential savings due to numerical optimization, and the resulting nonlinear programming problem is solved by iterated linear programming. The results indicate that the method is feasible and that significant savings might be attainable by computerized shape optimization.     

A level-set-based topology and shape optimization method for continuum structure under geometric constraints

Recent advances in level-set-based shape and topology optimization rely on free-form implicit representations to support boundary deformations and topological changes. In practice, a continuum structure is usually designed to meet parametric shape optimization, which is formulated directly in terms of meaningful geometric design variables, but usually does not support free-form boundary and topological changes. In order to solve the disadvantage of traditional step-type structural optimization, a unified optimization method which can fulfill the structural topology, shape, and sizing optimization at the same time is presented. The unified structural optimization model is described by a parameterized level set function that applies compactly supported radial basis functions (CS-RBFs) with favorable smoothness and accuracy for interpolation. The expansion coefficients of the interpolation function are treated as the design variables, which reflect the structural performance impacts of the topology, shape, and geometric constraints. Accordingly, the original topological shape optimization problem under geometric constraint is fully transformed into a simple parameter optimization problem; in other words, the optimization contains the expansion coefficients of the interpolation function in terms of limited design variables. This parameterization transforms the difficult shape and topology optimization problems with geometric constraints into a relatively straightforward parameterized problem to which many gradient-based optimization techniques can be applied. More specifically, the extended finite element method (XFEM) is adopted to improve the accuracy of boundary resolution. At last, combined with the optimality criteria method, several numerical examples are presented to demonstrate the applicability and potential of the presented method.     

A consistent formulation for imposing packaging constraints in shape optimization using Vertex Morphing parametrization

This paper aims at imposing no-penetration condition over arbitrary surfaces which act as bounding surfaces, also known as packaging constraints, on the design surface of shape optimization problem. We use Vertex Morphing technique for the shape parametrization. Vertex Morphing is a consistent surface control approach for node-based shape optimization. The suitability of this technique has been assessed and demonstrated for a wide range of engineering applications without geometric shape constraints. In this contribution, a consistent formulation is presented for the implementation of numerous point-wise geometric constraints in four main steps. First, a potential contact between optimization surface points and the bounding surface is identified via the so-called gap function. Second, the shape gradients of objective functions and active constraints are mapped onto the Vertex Morphing’s control space, where the optimization problem is formulated. Third, the linear least squares method is used to project the steepest-descent search direction onto the subspace tangent to the mapped active constraints. Finally, the feasible design update is mapped onto the geometry space. To verify the perfect consistency between the geometry space (where the constraints are formulated) and the control space (where the optimization problem is solved) two applications of CFD shape optimization in the automotive industry are presented.     

Topology optimization for the design of flow fields in a redox flow battery

This paper presents topology optimization for the design of flow fields in vanadium redox flow batteries (VRFBs), which are large-scale storage systems for renewable energy resources such as solar and wind power. It is widely known that, in recent VRFB systems, one of the key factors in boosting charging or discharging efficiency is the design of the flow field around carbon fiber electrodes and in flow channels. In this study, topology optimization is applied in order to achieve optimized flow field designs. The optimization problem is formulated as a maximization problem for the generation rate of the vanadium species governed by a simplified electrochemical reaction model. A typical porous model is incorporated into the optimization problem for expressing the carbon fiber electrode; furthermore, a mass transfer coefficient that depends on local velocity is introduced. We investigate the dependencies of the optimized configuration with respect to the porosity of the porous electrode and the pressure loss. Results indicate that patterns of interdigitated flow fields are valid designs for VRFBs.     

Factors that affect planning in a knowledge-based system for mechanical engineering design optimization with application to the design of mechanical power transmissions

Intelligent computer-aided design (CAD) emulates the human activity of design so that production planning, decision making, and inventive design can be performed by computers.Based on the history of human experience in engineering design, a formalized and systematic approach to design should include procedures from (1) conceptual design, (2) layout design, and (3) numerical optimization. The highest level within such a system should be responsible for specifying and symbolically optimizing skeleton structures of generic (nonspecific) elements within the design process that are eventually to be specified uniquely (pinned down) and ultimately optimized numerically. Planning plays a key role in such a system.Planning has been utilized as a tool for process organization within the knowledge domains of chemical engineering, electrical engineering, manufacturing, as well as for general problem formulation and solution. State estimation, subtask scheduling, and constraint propagation have been found to be factors of prime importance in this type of problem.Problems associated with the implementation of a planning strategy within a knowledge-based system for mechanical engineering design optimization are discussed. A hypothesis for planning is put forth and examined within the context of a model of the mechanical design optimization process. An example that demonstrates the applicability of this approach to mechanical power transmission design is considered.     

Computer-aided design optimization of polyphase induction motors

The design of squirrel-cage induction motors is formulated as a nonlinear programming problem, to predict a computer-aided optimum design. The cost of active materials is taken as an objective function. A constrained optimization method called the Complex Method is used to predict optimum design while meeting the specification requirements, formulated as constraints. The flow-chart diagram and design procedure is given.     

A non-parametric free-form optimization method for shell structures

This paper presents a numerical shape optimization method for the optimum free-form design of shell structures. It is assumed that the shell is varied in the out-of-plane direction to the surface to determine the optimal free-form. A compliance minimization problem subject to a volume constraint is treated here as an example of free-form design problem of shell structures. This problem is formulated as a distributed-parameter, or non-parametric, shape optimization problem. The shape gradient function and the optimality conditions are theoretically derived using the material derivative formulae, the Lagrange multiplier method and the adjoint variable method. The negative shape gradient function is applied to the shell surface as a fictitious distributed traction force to vary the shell. Mathematically, this method is a gradient method with a Laplacian smoother in the Hilbert space. Therefore, this shape variation makes it possible both to reduce the objective functional and to maintain the mesh regularity simultaneously. With this method, the optimal smooth curvature distribution of a shell structure can be determined without shape parameterization. The calculated results show the effectiveness of the proposed method for the optimum free-form design of shell structures.