基于反应扩散方程的水平集结构拓扑优化方法与实现

为实现更加先进的拓扑优化算法,研究采用反应扩散方程的水平集结构拓扑优化方法,通过理论推导给出算法中的参数选择建议.该方法允许在拓扑优化过程中生成新的孔洞,初始结构无须包含孔洞,不需要重新初始化步骤,从而可提高算法的收敛性.针对传统拓扑优化中主要采用体积约束、以柔度最小为目标和体积保留率设定存在一定主观性的问题,探究不同体积保留率下的结构应力水平的变化规律,结果显示可以依据结构最大应力水平与体积保留率的变化规律确定最优体积保留率.     

On the optimization problem of fillets and holes in plates with curvature constraints

The focus of this study is two-dimensional optimization problem of fillets and holes in plates considering curvature constraints, defined with the goal of minimizing stress concentration factor. The optimality criteria of uniform energy density are extended to shape optimization with curvature constraint assuming that a good shape design can be obtained when constant energy density along the segment of the designed boundary is achieved, except for the section that has to satisfy the geometry constraint. Feasible solutions are sought out under the assumption that the minimum curvature radius is constant on the last part of the designed boundary, and some interesting features of optimal shape of fillets and holes with prescribed minimum curvature radii are revealed. A finite-element-based method in conjunction with a gradientless algorithm is developed to obtain the optimal shape with curvature constraint. Numerical examples of optimal fillets and holes in flat plates are presented to validate the proposed assumption.     

Artificial neural network based hole image interpretation techniques for integrated topology and shape optimization

Homogenization based and density based topology optimization seeks the best conceptual structural configuration on a predefined design domain with specific boundary and loading conditions. Such structural configuration is most often the minimum-compliance design under a fixed material usage constraint. Shape optimization must be subsequently executed so as to ensure the satisfaction of other practical design constraints such as stress and displacement, and attain the detailed definition of the structure configuration with a smooth circumference and interior hole contours. Complicated procedures involved in connection between topology and shape optimization are major obstacle for most design engineers to overcome. A fully automated configuration optimization system was developed [C.Y. Lin, L.S. Chao, Automated image interpretation for integrated topology and shape optimization, Structural and Multidisciplinary Optimization 20(2) (2000) 125–137] to execute the entire configuration design process automatically with room of improvements in the hole representation templates and hole interpretation reliabilities. In response, this paper proposes two-stage artificial neural networks based hole image interpretation techniques with improved template variety and recognition reliability.     

Optimal topology selection of continuum structures with displacement constraints

This paper deals with the optimal topology selection of continuum structures subject to displacement constraints by using the performance-based design concept. The optimal topology of a continuum structure is generated by gradually eliminating underutilized elements from the discretized design domain. A performance index is developed for monitoring the optimization process and is used as a termination criterion in the optimization algorithm so that the global optimum can be selected from the optimization history. Maximizing the performance index in the design space is proposed as the performance-based optimization criterion. The performance index can be utilized to compare the efficiency of structural topologies produced by different continuum topology optimization methods. Several examples are provided to demonstrate the capabilities of the performance-based optimization approach in selecting the best configuration for the minimum-weight design of continuum structures with maximum stiffness.     

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。     

Combined shape and topology optimization for minimization of maximal von Mises stress

This work shows that a combined shape and topology optimization method can produce optimal 2D designs with minimal stress subject to a volume constraint. The method represents the surface explicitly and discretizes the domain into a simplicial complex which adapts both structural shape and topology. By performing repeated topology and shape optimizations and adaptive mesh updates, we can minimize the maximum von Mises stress using the p-norm stress measure with p-values as high as 30, provided that the stress is calculated with sufficient accuracy.     

Constraint force design method for topology optimization of planar rigid-body mechanisms

This study develops a new design method called the constraint force design method, which allows topology optimization for planar rigid-body mechanisms. In conventional mechanism synthesis methods, the kinematics of a mechanism are analytically derived and the positions and types of joints of a fixed configuration (hereafter the topology) are optimized to obtain an optimal rigid-body mechanism tracking the intended output trajectory. Therefore, in conventional methods, modification of the configuration or topology of joints and links is normally considered impossible. In order to circumvent the fixed topology limitation in optimally designing rigid-body mechanisms, we present the constraint force design method. This method distributes unit masses simulating revolute or prismatic joints depending on the number of assigned degrees of freedom, analyzes the kinetics of unit masses coupled with constraint forces, and designs the existence of these constraint forces to minimize the root-mean-square error of the output paths of synthesized linkages and a target linkage using a genetic algorithm. The applicability and limitations of the newly developed method are discussed in the context of its application to several rigid-body synthesis problems.     

Deposition path planning-integrated structural topology optimization for 3D additive manufacturing subject to self-support constraint

This paper presents a novel level set-based topology optimization implementation, which addresses two main problems of design-for-additive manufacturing (AM): the material anisotropy and the self-support manufacturability constraint. AM material anisotropy is widely recognized and taking it into account while performing structural topology optimization could more realistically evaluate the structural performance. Therefore, both build direction and in-plane raster directions are considered by the topology optimization algorithm, especially for the latter, which is calculated through deposition path planning. The self-support manufacturability constraint is addressed through a novel multi-level set modeling. The related optimization problem formulation and solution process are demonstrated in detail. It is proved by several numerical examples that the manufacturability constraints are always strictly satisfied. Marginally, the recently popular structural skeleton-based deposition paths are also employed to assist the structural topology optimization, and its characteristics are discussed.     

Optimal topology design of structures under dynamic loads

When elastic structures are subjected to dynamic loads, a propagation problem is considered to predict structural transient response. To achieve better dynamic performance, it is important to establish an optimum structural design method. Previous work focused on minimizing the structural weight subject to dynamic constraints on displacement, stress, frequency, and member size. Even though these methods made it possible to obtain the optimal size and shape of a structure, it is necessary to obtain an optimal topology for a truly optimal design. In this paper, the homogenization design method is utilized to generate the optimal topology for structures and an explicit direct integration scheme is employed to solve the linear transient problems. The optimization problem is formulated to find the best configuration of structures that minimizes the dynamic compliance within a specified time interval. Examples demonstrate that the homogenization design method can be extended to the optimal topology design method of structures under impact loads.Presented at WCSMO-2, held in Zakopane, Poland, 1997     

Constrained adaptive topology optimization for vibrating shell structures

This paper describes an algorithm for structural topology optimization entitled Constrained Adaptive Topology Optimization or CATO which is applied here to produce the optimum design of shell structures under free vibration conditions. The algorithm, based on an artificial material model and an updating scheme, combines ideas from the more mathematically rigorous homogenization (h) methods and the more intuitive evolutionary (e) methods. Thus, CATO can be seen as a hybrid h/e method. The optimization problem is defined as maximizing or minimizing a chosen frequency with a constraint on the structural volume/mass by redistributing the material through the structure. The efficiency of the proposed algorithm is illustrated through several numerical examples. Received February 17, 2000     

柔性结构形态重构的感知网络优化配置研究

以航天结构健康监测为研究背景,针对柔性板状结构形态重构的感知网络进行优化配置研究.在基于应变模态的结构形态重构算法中,以应变位移转换矩阵的条件数作为传感器优化配置的优化准则,以结构形态重构误差作为优化效果评价指标,采用一种改进的模拟退火算法对传感器优化配置进行了研究.针对传感器优化配置中的传感器数量、位置、方向以及多个目标的综合进行了传感器配置优化设计,仿真结果显示通过传感器配置的优化设计,可以有效地提高柔性结构的形态重构效果.最后,通过实验验证了传感器优化配置的有效性,为结构形态重构的感知网络优化配置提供了一定的理论依据.     

基于拓扑优化的四旋翼无人机结构设计

为实现某四旋翼无人机的轻量化结构设计,采用Inspire进行拓扑优化设计,并对获得的拓扑优化结构进行静力分析和动力学分析。分析结果表明,通过拓扑优化方法获得的无人机结构应力分布合理,结构位移小且频率较高,满足静态和动态结构设计要求。研究结果可为实现低成本、轻量化的四旋翼无人机结构设计提供一条新的途径。     

列车车辆设备安装的过渡件结构优化和应用

对某型号列车车辆下部设备安装的过渡件进行结构分析,发现结构强度冗余较大.为提高材料使用率,减小列车整车整备质量,开展结构轻量化设计研究并提出改进措施.对常用底架设备安装方式进行有限元分析,利用OptiStruct对过渡件进行拓扑优化.根据材料工艺成型特点和结构安全要求对结构进行重新设计,并对新结构进行形状优化,获得最佳优化效果的结构设计方案.     

An approximation-concepts approach to shape optimal design

In the past, much of the work done in structural optimization consisted in resizing the members of fixed configuration models. In that case, a powerful design procedure has now emerged, which is based on the coordinate use of explicit high-quality approximations of the behavior constraints and dual methods of mathematical programming.There is, however, a large class of problems for which the main degrees of freedom for the designer correspond to the shape of the structure itself.The main objectives of this paper are to recall briefly a convenient geometric representation, in which the boundaries of the structure are represented by Bezier or B-spline curves, and then to discuss the choice of optimization algorithm. It is shown that cost-efficient methods for structural sizing may be advantageously extended to shape optimal design problems. Different approximation schemes are tested and a new general optimization algorithm is presented that combines mixed approximations and dual methods. Many large-scale applications are treated to demonstrate the generality and the efficiency of the new formulation. Finally, considerations are given about an integrated approach including CAD computer codes and finite element optimization software.     

Target-matching test problem for multiobjective topology optimization using genetic algorithms

This paper describes the multiobjective topology optimization of continuum structures solved as a discrete optimization problem using a multiobjective genetic algorithm (GA) with proficient constraint handling. Crucial to the effectiveness of the methodology is the use of a morphological geometry representation that defines valid structural geometries that are inherently free from checkerboard patterns, disconnected segments, or poor connectivity. A graph- theoretic chromosome encoding, together with compatible reproduction operators, helps facilitate the transmission of topological/shape characteristics across generations in the evolutionary process. A multicriterion target-matching problem developed here is a novel test problem, where a predefined target geometry is the known optimum solution, and the good results obtained in solving this problem provide a convincing demonstration and a quantitative measure of how close to the true optimum the solutions achieved by GA methods can be. The methodology is then used to successfully design a path-generating compliant mechanism by solving a multicriterion structural topology optimization problem.     

Ant colony approaches for multiobjective structural optimization problems with a cardinality constraint

Two Ant Colony Optimization algorithms are proposed to tackle multiobjective structural optimization problems with an additional constraint. A cardinality constraint is introduced in order to limit the number of distinct values of the design variables appearing in any candidate solution. Such constraint is directly enforced when an ant builds a candidate solution, while the other mechanical constraints are handled by means of an adaptive penalty method (APM). The test-problems are composed by structural optimization problems with discrete design variables, and the objectives are to minimize both the structure’s weight and its maximum nodal displacement. The Pareto sets generated in the computational experiments are evaluated by means of performance metrics, and the obtained designs are also compared with solutions available from single-objective studies in the literature.     

Combined size and shape optimization of structures with a new meta-heuristic algorithm

In this study, a new meta-heuristic algorithm called teaching-learning-based optimization (TLBO) is used for the size and shape optimization of structures. The TLBO algorithm is based on the effect of the influence of a teacher on the output of learners in a class. The cross-sectional areas of the bar element and the nodal coordinates of the structural system are the design variables for size and shape optimization, respectively. Displacement, allowable stress and the Euler buckling stress are taken as the constraint for the problem considered. Some truss structures are designed by using this new algorithm to show the efficiency of the TLBO algorithm. The results obtained from this study are compared with those reported in the literature. It is concluded that the TLBO algorithm presented in this study can be effectively used in combined size and shape optimization of the structures.     

Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization

In topology optimization of a continuum, it is important to consider stress-related objective or constraints, from both theoretical and application perspectives. It is known that the problem is challenging. Although remarkable achievements have been made with the SIMP (Solid Isotropic Material with Penalization) framework, a number of critical issues are yet to be fully resolved. In the paper, we present an approach of a shape equilibrium constraint strategy with the level-set/X-FEM framework. We formulate the topology optimization problem under (spatially-distributed) stress constraints into a shape equilibrium problem of active stress constraint. This formulation allows us to effectively handle the stress constraint, and the intrinsic non-differentiability introduced by local stress constraints is removed. The optimization problem is made into one of continuous shape-sensitivity and it is solved by evolving a coherent interface of the shape equilibrium concurrently with shape variation in the structural boundary during a level-set evolution process. Several numerical examples in two dimensions are provided as a benchmark test of the proposed shape equilibrium constraint strategy for minimum-weight and fully-stressed designs and for designs with stress constraint satisfaction.