连续体结构的参数化水平集统一优化

针对传统分步式结构优化设计的不足,提出一种同时进行结构拓扑、形状和尺寸统一优化的设计方法.首先采用水平集函数描述统一的结构优化模型和几何尺寸边界,通过引入紧支径向插值基函数将结构拓扑优化变量、形状优化变量和尺寸优化变量变换为基函数的扩展系数;然后取该扩展系数为设计变量,借助一种参数的变化表达3种优化要素对结构性能的影响,将复杂的多变量优化问题变换为相对简单的参数优化问题,有利于与相对成熟的优化算法相结合提高求解效率;进一步用R函数将其融合为一个整体,构造出统一优化模型,并用最优化准则法进行求解.最后通过数值案例证明了该方法的有效性和精确性.     

A review of optimization of cast parts using topology optimization

In recent years, there has been considerable progress in the optimization of cast parts with respect to strength, stiffness, and frequency. Here, topology optimization has been the most important tool in finding the optimal features of a cast part, such as optimal cross-section or number and arrangement of ribs. An optimization process with integrated topology optimization has been used very successfully at Adam Opel AG in recent years, and many components have been optimized. This two-paper review gives an overview of the application and experience in this area. This is the first part of a two-paper review of optimization of cast parts.Here, we want to focus on the application of the original topology optimization codes, which do not take manufacturing constraints for cast parts into account. Additionally, the role of shape optimization as a fine-tuning tool will be briefly analyzed and discussed.     

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.     

Integrated optimal topology design and shape optimization using neural networks

In this paper, neural network- and feature-based approaches are introduced to overcome current shortcomings in the automated integration of topology design and shape optimization. The topology optimization results are reconstructed in terms of features, which consist of attributes required for automation and integration in subsequent applications. Features are defined as cost-efficient simple shapes for manufacturing. A neural network-based image-processing technique is presented to match the arbitrarily shaped holes inside the structure with predefined features. The effectiveness of the proposed approach in integrating topology design and shape optimization is demonstrated with several experimental examples.     

Adaptive volume constraint algorithm for stress limit-based topology optimization

Homogenization or density-based topology optimization methods work by distributing a fixed amount of material to the most effective areas of the design domain so as to create an optimal structural configuration that meets the minimum compliance criteria. These topology optimization methods generally cannot control the maximum stress levels of the structure; therefore, the smoothened optimum structure is not guaranteed to be ready for immediate use. This can be because it is either unsafe if the maximum stress at this structure exceeds the strength limit, or over designed if the maximum stress is far below the stress limit. Difficult and complex shape optimization must then be done to obtain a minimum-weight structure that meets the maximum stress constraint. This paper proposes an adaptive volume constraint (AVC) algorithm, a heuristic approach, in place of traditional topology optimization methods so that the maximum stress in the optimal structural configuration will be below the predefined stress limit and the smoothened structure will be directly applicable. In order to test the applicability and robustness of the AVC algorithm, topology optimization using both a traditional fixed volume constraint and an AVC are tested on a number of configuration design problems. To further illustrate the usefulness of the AVC algorithm, shape optimizations at the maximum stress constraint are also conducted on the smooth structural models by both optimization approaches on an identical problem set.     

轨道扣件弹性垫板结构优化设计

采用OptiStruct对某型铁路扣件轨下垫板进行拓扑优化和自由形状优化,实现垫板结构轻量化设计.根据优化空间最大化原则,对垂向载荷工况进行拓扑优化、对极限载荷工况进行自由形状优化.使用Abaqus极限载荷扣件系统仿真模型对优化后垫板结构性能进行验证评价.结果表明:优化后的垫板性能基本不变,质量减少约10%,刚度满足设计要求.优化结果可为垫板轻量化设计提供参考.     

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.     

Parallelized structural topology optimization and CFD coupling for design of aircraft wing structures

A set of structural optimization tools are presented for topology optimization of aircraft wing structures coupled with Computational Fluid Dynamics (CFD) analyses. The topology optimization tool used for design is the material distribution technique. Because reducing the weight requires numerous calculations, the CFD and structural optimization codes are parallelized and coupled via a code/mesh coupling scheme. In this study, the algorithms used and the results obtained are presented for topology design of a wing cross-section under a given critical aerodynamic loading and two different spar positions to determine the optimum rib topology.     

Optimal structural design with indirect use of Transferred Forces

An optimal design method based on the concepts of Transferred Forces is introduced. The method uses these forces in an indirect way. The concept of reaction functional based on transferred forces is introduced. The functional approximates the structural behaviour in terms of the properties of a selected region. Using the reaction functionals, a nonlinear programming formulation and a computational method that perform sizing and topology optimization are developed. The procedure does not need structural analyses during optimization iterations. Example problems are solved with the method and the similar solutions are obtained for a refined mesh model and a different starting design. Thus, it is concluded that the new concept presented here is applicable to structural optimization problems. Received June 28, 2000     

PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes

We present an efficient Matlab code for structural topology optimization that includes a general finite element routine based on isoparametric polygonal elements which can be viewed as the extension of linear triangles and bilinear quads. The code also features a modular structure in which the analysis routine and the optimization algorithm are separated from the specific choice of topology optimization formulation. Within this framework, the finite element and sensitivity analysis routines contain no information related to the formulation and thus can be extended, developed and modified independently. We address issues pertaining to the use of unstructured meshes and arbitrary design domains in topology optimization that have received little attention in the literature. Also, as part of our examination of the topology optimization problem, we review the various steps taken in casting the optimal shape problem as a sizing optimization problem. This endeavor allows us to isolate the finite element and geometric analysis parameters and how they are related to the design variables of the discrete optimization problem. The Matlab code is explained in detail and numerical examples are presented to illustrate the capabilities of the code.     

A performance index for topology and shape optimization of plate bending problems with displacement constraints

This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending. Received November 27, 1998?Revised version received June 6, 1999     

ε-relaxed approach in structural topology optimization

This paper presents a so-called -relaxed approach for structural topology optimization problems of discrete structures. The distinctive feature of this new approach is that unlike the typical treatment of topology optimization problems based on the ground structure approach, we eliminate the singular optima from the problem formulation and thus unify the sizing and topology optimization within the same framework. As a result, numerical methods developed for sizing optimization problems can be applied directly to the solution of topology optimization problems without any further treatment. The application of the proposed approach and its effectiveness are illustrated with several numerical examples.     

Sufficiency of a finite exponent in SIMP (power law) methods

A common way to perform discrete optimization in shape or topology optimization is to use a method called the artificial power law or SIMP. The focus of this paper is to show that this method gives a discrete solution under some conditions. Examples from topology optimization are included for illustrative purposes. Received December 22, 1999     

Topology optimization of beam cross-section considering warping deformation

The beam cross-section optimization problems have been very important as beams are widely used as efficient load-carrying structural components. Most of the earlier investigations focus on the dimension and shape optimization or on the topology optimization along the axial direction. An important problem in beam section design is to find the location and direction of stiffeners, for the introduction of a stiffener in a closed beam section may result in a topologically different configuration from the original; the existing section shape optimization theory cannot be used. The purpose of this paper is to formulate a section topology optimization technique based on an anisotropic beam theory considering warping of sections and coupling among deformations. The formulation and corresponding solving method for the topology optimization of beam cross-sections are proposed. In formulating the topology optimization problem, the minimum averaged compliance of the beam is taken as objective, and the material density of every element is used as design variable. The schemes to determine the rigidity matrix of the cross-sections and the sensitivity analysis are presented. Several kinds of topologies of the cross-section under different load conditions are given, and the effect of load condition on the optimum topology is analyzed.     

Automotive door design with the ULSAB concept. using structural optimization

Weight reduction for an automobile body is sought to achieve fuel efficiency and energy conservation. Recently, the UltraLight Steel Auto Body (ULSAB) concept is suggested using a few methods. ULSAB pursues a lightweight automotive with steel structure. Tailor welded blank (TWB) is one of the ULSAB methods and TWB can be utilized for an automobile door. Optimization technology is applied to the inner panel of a door which is made by TWB. A design process is appropriately defined for the inner panel. The design starts from an existing component. At first, the inner reinforcements are removed to use TWB technology. In the conceptual design stage, topology optimization is conducted to find the distribution of the variable thickness. The number of parts and the welding lines are determined from the topology design. In the detailed design process, size optimization is carried out to find thickness while the stiffness constraints are satisfied. Size optimization is performed based on the welding lines determined from topology optimization. The final parting lines are tuned by shape optimization. The results from size optimization are considered constant in shape optimization. A commercial optimization software GENESIS is utilized for the optimization processes. Received November 10, 2000     

基于ANSYS Workbench的T形结构优化设计

针对T形结构传统设计周期长、材料利用率低、设计成本高等问题,使用SolidWorks建立数字模型,将其转换成ANSYS Workbench可读的格式文件,进行拓扑优化设计。对T形结构在载荷作用下进行最优化设计,建立以单元材料密度为设计变量,以结构最小柔顺度为目标函数,以质量减少百分比为约束函数的数学模型。采用ANSYS Workbench的Topology Optimization模块进行拓扑优化设计,对比优化前、后结构的应力和变形,可知运用拓扑优化技术实现T形结构的轻量化设计合理有效。     

Hybrid multi-objective shape design optimization using Taguchi’s method and genetic algorithm

This research is based on a new hybrid approach, which deals with the improvement of shape optimization process. The objective is to contribute to the development of more efficient shape optimization approaches in an integrated optimal topology and shape optimization area with the help of genetic algorithms and robustness issues. An improved genetic algorithm is introduced to solve multi-objective shape design optimization problems. The specific issue of this research is to overcome the limitations caused by larger population of solutions in the pure multi-objective genetic algorithm. The combination of genetic algorithm with robust parameter design through a smaller population of individuals results in a solution that leads to better parameter values for design optimization problems. The effectiveness of the proposed hybrid approach is illustrated and evaluated with test problems taken from literature. It is also shown that the proposed approach can be used as first stage in other multi-objective genetic algorithms to enhance the performance of genetic algorithms. Finally, the shape optimization of a vehicle component is presented to illustrate how the present approach can be applied for solving multi-objective shape design optimization problems.     

A gradient-based,parameter-free approach to shape optimization

In shape optimization, the independent node movement approach, wherein finite element node coordinates are used directly as design variables, allows the most freedom for shape change and avoids the time-consuming parameterization preprocess. However, this approach lacks a length scale control that is necessary to ensure a well-posed shape optimization problem and avoid numerical instability. Motivated by the success of filtering techniques that impose minimum length scales in topology optimization, we propose a scheme with consistent filtering to introduce a length scale and thereby ensure smoothness in shape optimization while preserving the advantages of the independent node movement approach.     

转向架齿轮箱吊杆的优化设计

针对某转向架齿轮箱吊杆开发设计过程中吊杆原始结构工作安全因数过大的问题,为进行轻量化设计,基于OptiStruct采用拓扑优化结合自由形状优化的方法对吊杆进行优化设计.优化后吊杆的质量减轻约38.3%,其工作安全因数和刚度满足要求.