基于无网格径向点插值方法的简谐激励下的连续体结构拓扑优化

针对用有限元法进行连续体结构拓扑优化时需不断重构网格来处理网格畸变和网格移动,且存在数值计算不稳定等问题,基于无网格径向点插值方法(Radial Point Interpolation Method,RPIM)对简谐激励下的连续体结构进行拓扑优化.选取节点的相对密度作为设计变量,以结构动柔度最小化为目标函数,基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP)模型建立简谐激励下的优化模型;采用伴随法求解得到目标函数的敏度分析公式;利用优化准则法求解优化模型.经典的二维连续体结构拓扑优化算例证明该方法的可行性和有效性.     

物质点拓扑变量法在柔性机构设计中的应用

为克服柔性机构拓扑优化设计中的各类数值不稳定性问题,提出一种以物质点拓扑变量为设计变量的拓扑优化方法.物质点拓扑变量可视为节点密度概念的进一步拓展,基于修正网格无关性过滤函数提出了新的拓扑变量场插值形函数.基于弹簧模型,建立了柔性机构的多约束拓扑优化模型,推导了常见结构响应量的敏度表达式,采用移动渐进线法进行优化求解.最后通过二维数值算例验证了文中方法的可行性和有效性.     

基于MSC PCL的三心底结构形状优化

将响应面方法和模型参数化相结合,建立以结构重量为目标、结构强度为约束的形状优化模型. 根据结构形状选取独立设计变量,推导结构重量的解析表达式和结构重量对设计变量的一、二阶导数,采用响应面方法拟合结构最大应力的表达式,建立形状优化的二次规划模型. 数值算例表明,该方法具有很强的灵活性,适用范围较广,优化结果具有一定的稳定性和准确性.     

基于Ordered-RAMP模型的热固耦合结构多材料拓扑优化方法

针对传统单材料热固耦合拓扑优化设计难以实现结构材料与性能综合最优的问题,提出一种基于变密度理论有序材料属性有理近似模型的多材料拓扑优化方法.该方法通过搭建比例系数与平移系数,将多种材料属性采用[0,1]连续分布的单设计变量进行描述,并研究和比较与有序固体各向同行惩罚微结构模型的优缺点;其次借助归一化加权方法定义以结构柔度最小化和散热弱度最小化为目标函数的数学模型.结合设计变量敏度分析,详细推导多材料、多目标条件下热固耦合结构拓扑优化的迭代公式.通过数值算例分析对比了不同权系数以及不同材料属性组合对优化结果的影响;结果表明,所提出的优化方法在热固耦合结构多材料多目标拓扑优化设计中具有可行性和有效性.     

基于无网格局部Petrov-Galekin法的板结构拓扑优化

为将无网格法的优势集成到结构拓扑优化中,基于无网格局部Petrov-Galerkin(Meshless Local Petrov-Galerkin,MLPG)法进行板结构的拓扑优化.基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP)的拓扑优化模型和优化准则法建立设计变量的优化修正方案.位移场和相对密度场均采用自然邻接点插值形函数进行离散插值.几种典型的拓扑优化算例证明该数值算法的正确性和有效性.     

图像修补的优化变换方法

采用整体变分(TV)模型修补图像,提出一种图像修补的优化变换方法.引入一个辅助变量,利用优化变换,将TV模型中单变量函数的优化问题转化为等效双变量函数的优化问题,并利用交替迭代最小化算法和Chambolle's投影算法求解模型.实验结果表明,与采用梯度下降法的TV模型算法相比,该方法的图像修补效率和修补效果较优.     

受压杆件的虚拟优化设计

基于ICM(独立、连续、映射)方法解决受压杆件的虚拟优化设计问题.在CAD/CAE软件Patran平台上建立受压杆件的三维模型;建立以结构重量为目标,以屈曲临界力为约束的拓扑优化数学模型;借助泰勒展式、过滤函数及瑞利商将模型作近似处理,避免了灵敏度的计算;将优化模型转化为对偶规划,并利用序列二次规划求解,减少了设计变量的数目,缩小了模型的求解规模.并且找出了拓扑结构中瓶颈的位置,据此可以得到较为理想的受压杆件设计结构.     

飞机平尾普通肋的优化设计

在飞机平尾普通肋的轻量化设计过程中,采用桁架肋代替传统的腹板肋,并利用HyperWorks的OptiStruct模块对桁架肋进行详细的尺寸优化和形状优化.优化设计时以结构质量最小为目标函数,以肋缘条与斜支柱的截面参数为设计变量,以von Mises应力和临界屈曲因子为约束条件.优化后的桁架肋质量比原腹板肋约减少29%,表明采用该方法对飞机平尾结构进行轻量化设计可行.     

基于Kriging代理模型的加筋柱壳结构优化

基于Kriging代理模型,研究了加筋柱壳型飞行器舱体结构形状和尺寸优化方法.对加筋柱壳结构建立了三维参数化模型,参数化设计变量包括纵向加强筋数量、尺寸和环向加强筋的位置、尺寸,利用试验设计法选取设计变量采样点,使用有限元静力分析和线性屈曲分析得到采样点的应力、变形、屈曲强度因子等响应值,依据设计变量和响应建立Kriging代理模型,使用优化算法对代理模型进行寻优,获得最优设计结果.整个优化过程在Workbench平台中实现,最优结构比初始模型重量减少了11.91％.加筋柱壳结构优化结果分析表明,所使用优化方法优化效果明显、工作流程清晰、优化效率高,具有较大的工程应用价值.     

多变量系统中多参数多目标满意优化研究

本文提出了多变量系统的多参数多目标满意优化方法，将系统性能指标要求的满意设计与控制器参数优化融为一体统一考虑，通过设计性能指标满意度函数和系统综合满意度函数，构造出多变量系统满意优化模型，并用改进遗传算法实现其满意优化．仿真结果显示该方法可获得比传统优化方法更满意的综合性能指标，表明了该方法的有效性和实用性．     

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.     

Design of distributed compliant micromechanisms with an implicit free boundary representation

In this paper, a parameterization approach is presented for structural shape and topology optimization of compliant mechanisms using a moving boundary representation. A level set model is developed to implicitly describe the structural boundary by embedding into a scalar function of higher dimension as zero level set. The compactly supported radial basis function of favorable smoothness and accuracy is used to interpolate the level set function. Thus, the temporal and spatial initial value problem is now converted into a time-separable parameterization problem. Accordingly, the more difficult shape and topology optimization of the Hamilton–Jacobi equation is then transferred into a relatively easy size optimization with the expansion coefficients as design variables. The design boundary is therefore advanced by applying the optimality criteria method to iteratively evaluate the size optimization so as to update the level set function in accordance with expansion coefficients of the interpolation. The optimization problem of the compliant mechanism is established by including both the mechanical efficiency as the objective function and the prescribed material usage as the constraint. The design sensitivity analysis is performed by utilizing the shape derivative. It is noted that the present method is not only capable of simultaneously addressing shape fidelity and topology changes with a smooth structural boundary but also able to avoid some of the unfavorable numerical issues such as the Courant–Friedrich–Levy condition, the velocity extension algorithm, and the reinitialization procedure in the conventional level set method. In particular, the present method can generate new holes inside the material domain, which makes the final design less insensitive to the initial guess. The compliant inverter is applied to demonstrate the availability of the present method in the framework of the implicit free boundary representation.     

最小位移类桁架连续体拓扑设计优化

为将拓扑优化中的柔度最小化问题拓展到一般位移最小化问题,用有限元划分设计域,采用类桁架连续体材料模型,并假设杆件在设计域内连续分布.将杆件在节点位置的密度和方向作为设计变量,将指定位置和方向的位移作为目标函数,采用基于目标函数梯度的优化准则法,通过优化杆件的连续分布场形成拓扑优化的类桁架连续体.该方法可结合结构力学的基本概念,选择部分杆件形成拓扑优化刚架.     

An integrated approach to topology,sizing, and shape optimization

Topology optimization has become very popular in industrial applications, and most FEM codes have implemented certain capabilities of topology optimization. However, most codes do not allow simultaneous treatment of sizing and shape optimization during the topology optimization phase. This poses a limitation on the design space and therefore prevents finding possible better designs since the interaction of sizing and shape variables with topology modification is excluded. In this paper, an integrated approach is developed to provide the user with the freedom of combining sizing, shape, and topology optimization in a single process.     

A level set method for structural shape and topology optimization using radial basis functions

This paper presents an alternative level set method for shape and topology optimization of continuum structures. An implicit free boundary representation model is established by embedding structural boundary into the zero level set of a higher-dimensional level set function. An explicit parameterization scheme for the level set surface is proposed by using radial basis functions with compact support. In doing so, the originally more difficult shape and topology optimization, driven by the temporal and spatial Hamilton–Jacobi partial differential equation (PDE), is transformed into a relatively easier size optimization of the expansion coefficients of the basis functions. The design optimization is converted to an iterative numerical process that combines the parameterization with a derivation of the shape sensitivity of the design functions, so as to allow using mathematical programming algorithms to solve the level set-based design problem and avoid directly solving the Hamilton–Jacobi PDE. Furthermore, a numerically more stable and efficient volume integration scheme is proposed to implement calculations of the shape derivatives, leading to the creation of new holes which are generated initially along the boundary and then propagated to the interior of the design domain. Two widely studied examples are used to demonstrate the effectiveness of the proposed optimization method.     

A study on X-FEM in continuum structural optimization using a level set model

In this paper, we implement the extended finite element method (X-FEM) combined with the level set method to solve structural shape and topology optimization problems. Numerical comparisons with the conventional finite element method in a fixed grid show that the X-FEM leads to more accurate results without increasing the mesh density and the degrees of freedom. Furthermore, the mesh in X-FEM is independent of the physical boundary of the design, so there is no need for remeshing during the optimization process. Numerical examples of mean compliance minimization in 2D are studied in regard to efficiency, convergence and accuracy. The results suggest that combining the X-FEM for structural analysis with the level set based boundary representation is a promising approach for continuum structural optimization.     

基于无网格局部Petrov-Galekin法的板结构拓扑优化

为将无网格法的优势集成到结构拓扑优化中,基于无网格局部Petrov-Galerkin(Meshless Local Petrov-Galerkin,MLPG)法进行板结构的拓扑优化.基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP...     

Topology optimization of dynamic stress response reliability of continuum structures involving multi-phase materials

This paper proposes a methodology for maximizing dynamic stress response reliability of continuum structures involving multi-phase materials by using a bi-directional evolutionary structural optimization (BESO) method. The topology optimization model is built based on a material interpolation scheme with multiple materials. The objective function is to maximize the dynamic stress response reliability index subject to volume constraints on multi-phase materials. To solve the defined topology optimization problems, the sensitivity of the dynamic stress response reliability index with respect to the design variables is derived for iteratively updating the structural topology. Subsequently, an optimization procedure based on the BESO method is developed. Finally, a series of numerical examples of both 2D and 3D structures are presented to demonstrate the effectiveness of the proposed approach.

     

Eulerian shape design sensitivity analysis and optimization with a fixed grid

Conventional shape optimization based on the finite element method uses Lagrangian representation in which the finite element mesh moves according to shape change, while modern topology optimization uses Eulerian representation. In this paper, an approach to shape optimization using Eulerian representation such that the mesh distortion problem in the conventional approach can be resolved is proposed. A continuum geometric model is defined on the fixed grid of finite elements. An active set of finite elements that defines the discrete domain is determined using a procedure similar to topology optimization, in which each element has a unique shape density. The shape design parameter that is defined on the geometric model is transformed into the corresponding shape density variation of the boundary elements. Using this transformation, it has been shown that the shape design problem can be treated as a parameter design problem, which is a much easier method than the former. A detailed derivation of how the shape design velocity field can be converted into the shape density variation is presented along with sensitivity calculation. Very efficient sensitivity coefficients are calculated by integrating only those elements that belong to the structural boundary. The accuracy of the sensitivity information is compared with that derived by the finite difference method with excellent agreement. Two design optimization problems are presented to show the feasibility of the proposed design approach.