周期性扩大框架的渐进结构优化方法研究

传统渐进结构优化法(ESO)删除的低效材料,仅是阶段性的低效材料,其中部分材料若不被删除,有可能成为后续优化中的非低效材料。误删材料可能使接下来的优化成为“将错就错”的优化。该文在ESO法基础上提出的“周期性扩大框架的渐进结构优化方法(PEFESO)”,周期性地恢复并检查保留材料周围被删除材料的效率,重新判定该部分材料是否应被恢复到结构中,有效地削弱了ESO法可能误删材料的不良影响。PEFESO法具备一定的全程寻优能力,计算结果优于传统的ESO法,易于在工程中推广使用。     

约束阻尼结构的双向渐进拓扑优化

针对约束层阻尼板的拓扑优化问题,以模态损耗因子最大化为目标函数,约束阻尼材料体积分数为约束条件,建立了约束阻尼板的拓扑优化模型。基于模态应变能方法,推导了目标函数对设计变量的灵敏度。采用双向渐进优化算法(BESO)对约束阻尼材料的布局进行了拓扑优化,获得了约束阻尼材料的最优拓扑构型,并与渐进优化算法(ESO)进行了比较。研究结果表明：双向渐进优化算法相比单向渐进优化算法,获得的模态损耗因子更高,阻尼减振效果更好。     

基于ESO的夹层阻尼圆锯片减振降噪拓扑优化设计

针对夹层阻尼圆锯片的减振降噪拓扑优化设计,基于渐进拓扑ESO（evolutionary structural optimization）算法,寻求阻尼材料最佳布局. 导出了单元删除方法和损耗因子灵敏度计算方法,建立了拓扑优化流程,将损耗因子灵敏度作为衡量单元对结构损耗因子贡献量大小的标准,通过判断阻尼材料各单元对整体结构的减振效果,删除无效单元,得到满足刚度条件下的夹层阻尼圆锯片结构最优配置,使其在减振降噪的同时达到一定的刚度要求. 通过3种圆锯片模型的阻尼损耗因子对比,验证了优化后的圆锯片具有最佳的减振降噪效果．     

适用于支护拓扑优化的双向渐进优化方法

利用近年来发展的渐进结构优化方法(ESO)的概念,发展了适用于支护拓扑优化问题的双向渐进结构优化方法(BESO)。本文方法能在优化过程中控制开孔数,有效地避免了棋盘格式的出现,提出了两个解决振荡问题的技巧。将加固后的岩体看成人工支护材料,可以把加固优化的问题转化为人工支护材料在原岩中的分布的拓扑优化问题。建立了防治底臌帮臌的准则及其敏感度,研究了均匀地基不同地应力条件给定加固量时使得底臌帮臌最小的洞室开挖支护的最优拓扑。最优设计的底臌量明显小于经验设计的底臌量,证明了方法的有效性。     

基于应变能的预应力平面实体结构拓扑优化设计

研究了预应力平面实体钢结构拓扑优化设计问题。建立了以索力值和结构拓扑为设计变量,以结构储存应变能为约束条件,以结构重量最小为目标函数的数学优化模型。在求解方法上,首先以结构储存应变能最小(刚度最大)确定施加在结构上的索力值,然后采用渐进结构优化法(ESO方法)删除低应变能的单元实现结构的拓扑优化并减轻结构重量。算例结果与相应体系受力性能的结论相吻合,表明本文所提出的优化方法是可行的。     

基于ESO法的九宫板阻尼结构的优化设计方法

利用渐进结构拓扑优化方法(Evolution Structural Optimization,ESO),以约束阻尼层质量为约束条件,以最大模态损耗因子为目标函数,编制了ESO法的可执行程序,并基于ABAQUS软件建模,开展了九宫板约束阻尼层的拓扑优化研究。发现随着约束阻尼层的删除率增大,结构模态损耗因子逐渐增至最大值后降低。而随着删除率的增大,结构单位质量阻尼性能逐渐增大,可见优化布局可以提高九宫板结构的抑振性能。为研究优化布局对结构应力分布的影响,模拟了多种振动工况下,优化前后九宫板结构的Mises应力分布云图及其最大应力,结果发现优化布局后九宫板结构Mises应力分布影响很小,且最大Mises应力值得到有效降低。并将该方法应用在一般复杂结构的优化设计,实现了较少阻尼性能损失达到减重的目的,具有重要的工程实用性。     

车身结构阻尼材料减振降噪优化设计

本文针对某一乘用车车身结构振动引起的声辐射,建立了车身结构、声学空腔以及声固耦合有限元模型,分析了该乘用车车身的声固耦合特性。通过对车身各板件的贡献度分析,确定了对车内噪声贡献度最大的壁板。针对该壁板的阻尼减振降噪优化设计,建立了拓扑优化模型,采用渐进优化算法（ESO）,计算了阻尼材料的优化布局。研究结果表明：阻尼材料的优化布局使阻尼材料的使用率大大提高,50%的阻尼材料用量能基本达到全覆盖阻尼材料壁板的降噪效果,阻尼结构优化设计对车内噪声控制具有一定的理论指导意义。     

约束层阻尼短圆柱壳拓扑优化分析及实验研究

针对约束层阻尼短圆柱壳拓扑优化问题,采用基于模态应变能法的渐进结构优化算法（ESO）,引入独立网格滤波技术, 通过灵敏度分析,用ANSYS的参数化设计语言APDL编写拓扑优化程序,获得一定约束层阻尼材料用量的约束层阻尼最优拓扑构形,并对约束层阻尼材料的优化布局进行实验验证。研究表明该拓扑优化方法正确,用于短圆柱壳约束层阻尼材料布局优化具有较强的工程实用性。     

圆柱壳体阻尼材料布局拓扑优化研究

采用渐进结构拓扑优化方法,以阻尼结构模态损耗因子最大化为目标,阻尼材料体积分数为约束条件,阻尼胞单元为设计变量,建立了圆柱壳体阻尼材料布局拓扑优化模型,对约束阻尼以及自由阻尼材料布局进行了拓扑优化。研究了阻尼结构模态损耗因子对阻尼胞单元位置的灵敏度,导出灵敏度计算表达式。根据渐进优化算法的优化准则,通过逐步删除利用率低的材料,使目标模态损耗因子达到最大化。给出了数值计算的例子,理论计算结果验证了拓扑优化设计方法的正确性和有效性     

约束阻尼板的渐进法结构减振拓扑动力学优化

旨在为结构减振设计奠定一定基础,研究约束阻尼板减振优化问题。建立约束阻尼板动力学平衡方程,推导模态损耗因子计算模型。构建以模态损耗因子最大为目标,黏弹性材料用量及模态频率变动最小为约束的阻尼板拓扑优化数学模型,推导模态损耗因子灵敏度算式。引入渐进结构优化方法对约束阻尼板动力学优化模型进行求解,采用独立网格滤波技术,解决优化迭代中出现的棋盘格问题。编制阻尼板拓扑优化程序,实现约束阻尼板减振优化。仿真显示,与非优化删除方法相比,采用渐进拓扑动力学优化,更有利于实现黏弹材料优化布局,且模态频率变化比较稳定。对阻尼结构进行谐响应分析,以验证拓扑优化方法有效性,引入模态损耗因子体积密度指标以评价阻尼板减振拓扑优化性能。研究表明,若能实现结构模态损耗因子最大化,约束阻尼板减振效果明显。该方法对于约束阻尼板设计具有较强实用性,拥有较高的稳定性。     

A strength-based multiple cutout optimization in composite plates using fixed grid finite element method

The design of interior cutouts in laminated composite panels is of great importance in aerospace, automobile and structural engineering. Based on the Tsai–Hill failure criterion of the first ply, this paper presents a newly developed Fixed (FG) Grid Evolutionary Structural Optimization (ESO) method to explore shape optimization of multiple cutouts in composite structures. Different design cases with varying number of cutouts, ply orientations and lay-up configurations are taken into account in this study. The examples demonstrate that the optimal boundaries produced by FG ESO are much smoother than those by traditional ESO. The results show the remarkable effects of different opening numbers and various lay-up configurations on resulting optimal shapes. The paper also provides an in-depth observation in the interactive influence of the adjacent cutouts on the optimal shapes.     

Effects of boundary conditions on buckling and postbuckling responses of composite laminate with various shaped cutouts

The objective of the present work is to study the effects of flexural boundary conditions on buckling and postbuckling behavior of axially compressed quasi-isotropic laminate, (+45/−45/0/90)_2s with various shaped cutouts (i.e., circular, square, diamond, elliptical–vertical and elliptical–horizontal) of various sizes using the finite element method. The FEM formulation is based on first order shear deformation theory and von Karman’s assumptions are used to incorporate geometric nonlinearity. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that the laminates clamped and simply supported on all edges have the highest and lowest buckling and postbuckling strength, respectively, irrespective of cutouts shape and size. It is also noted that a fully clamped laminate with large size elliptical–vertical cutout can take higher compressive buckling load than the laminate without cutout for same boundary condition.     

Knowledge‐based algorithms in fixed‐grid GA shape optimization

Shape optimization through a genetic algorithm (GA) using discrete boundary steps and the fixed‐grid (FG) finite‐element analysis (FEA) concept was recently introduced by the authors. In this paper, algorithms based on knowledge specific to the FG method with the GA‐based shape optimization (FGGA) method are introduced that greatly increase its computational efficiency. These knowledge‐based algorithms exploit the information inherent in the system at any given instance in the evolution such as string structure and fitness gradient to self‐adapt the string length, population size and step magnitude. Other non‐adaptive algorithms such as string grouping and deterministic local searches are also introduced to reduce the number of FEA calls. These algorithms were applied to two examples and their effects quantified. The examples show that these algorithms are highly effective in reducing the number of FEA calls required hence significantly improving the computational efficiency of the FGGA shape optimization method. Copyright © 2003 John Wiley & Sons, Ltd.     

Structural optimization using the boundary element method and topological derivative applied to a suspension trailing arm

This work investigates the optimization of elasticity problems using the boundary element method (BEM) as a numerical solver. A topological shape sensitivity approach is used to select the points showing the lowest sensitivities. As the iterative process evolves, the original domain has portions of material progressively removed in the less efficient areas until a given stop criterion is achieved. Two benchmark tests are investigated to demonstrate the influence of the boundary conditions on the final topology. Following this, a suspension trailing arm is optimized and a new design is proposed as an alternative to commercially available methods. A postprocedure of smoothing using Bézier curves was employed for the final topology of the trailing arm. This process allowed the external irregular shapes to be overcome. The BEM coupled with the topological derivative was shown to be an alternative to traditional optimization techniques using the finite element method. The present methodology was shown to be efficient for delivering optimal topologies with few iterations. All routines used were written in open code.     

A new efficient convergence criterion for reducing computational expense in topology optimization: reducible design variable method

A new efficient convergence criterion, named the reducible design variable method (RDVM), is proposed to save computational expense in topology optimization. There are two types of computational costs: one is to calculate the governing equations, and the other is to update the design variables. In conventional topology optimization, the number of design variables is usually fixed during the optimization procedure. Thus, the computational expense linearly increases with respect to the iteration number. Some design variables, however, quickly converge and some other design variables slowly converge. The idea of the proposed method is to adaptively reduce the number of design variables on the basis of the history of each design variable during optimization. Using the RDVM, those design variables that quickly converge are not considered as design variables for the next iterations. This means that the number of design variables can be reduced to save the computational costs of updating design variables. Then, the iteration will repeat until the number of design variables becomes 0. In addition, the proposed method can lead to faster convergence of the optimization procedure, which indeed is a more significant time saving. It is also revealed that the RDVM gives identical optimal solutions as those by conventional methods. We confirmed the numerical efficiency and solution effectiveness of the RDVM with respect to two types of optimization: static linear elastic minimization, and linear vibration problems with the first eigenvalue as the objective function for maximization. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimum weight design of fiber composite plates in flexure based on a two level strategy

This paper offers a method for weight optimization of multilayer fiber composite plates under the action of lateral loadings. The objective is to design a fiber composite plate of minimum thickness which can sustain multiple static loadings applied normal to its surface without exhibiting failure based on Tsai-Hill criterion in any of its layers. In this investigation, fiber orientation angles are treated as discrete variables, which can vary only by pre-assigned increments, while thicknesses of layers are treated as continuous variables. The optimization procedure is based on a two stage strategy; in the first of which only the fiber orientation angles for the layers are treated as variables, and in the second, only the layer thicknesses. A powerful criterion based on a load factor has been defined to find the best angle for a new layer in the first stage, and the method of center points has been used for thickness optimization in the second stage. After any angle and thickness optimization has been done, a new layer is added to the thickness and the procedure is repeated for other new layers. The end of the two stage procedure is signaled whenever the thickness of the new layer in the optimization process approaches zero; meaning that no new layers would improve the set of layers already found. In this way at the end of the optimization procedure the plate thickness would be made of a minimum number of layers whose fibers are optimally oriented, and whose thicknesses are minimal. A poor choice of layers in the stack produce near zero thickness for the respective layer, and are thus deleted from the set. A repeat process is performed after each cycle, to modify layer angles in order to compensate for errors due to approximations involved. The priorities exercised in the choice of new layers for inclusion in the set and exclusion of all the un-necessary ones, allow an optimal state of stacking sequence to be achieved. Several examples are given to demonstrate the operation of the algorithm.     

A projection-based method for topology optimization of structures with graded surfaces

Graded surfaces widely exist in natural structures and inspire engineers to apply functionally graded (FG) materials to cover structural surfaces for performance improvement, protection, or other special functionalities. However, how to design such structures with FG surfaces by topology optimization is a quite challenging problem due to the difficulty for determining material properties of structural surfaces with prescribed variation rule. This paper presents a novel projection-based method for topology optimization of this class of FG structures. Firstly, a projection process is proposed for ensuring the material properties of the surfaces vary with a prescribed function. A criterion of determining the values of parameters in projection process is given by a strict theoretical derivation, and then, a new interpolation function is established, which is capable of simultaneously obtaining clear substrate topologies and realizable FG surfaces. Though such structures are actually multimaterial gradient structures, only the design variables of single-material topology optimization problem are needed. In the current research, the classical compliance minimization problem with a mass constraint is considered and the robust formulation is used to control the length scale of substrates. Several 2D and 3D numerical examples illustrate the validity and applicability of the proposed method.     

Structural shape optimization using equivalent static loads transformed from dynamic loads

In structural optimization, static loads are generally utilized although real external forces are dynamic. Dynamic loads have been considered only in small‐scale problems. Recently, an algorithm for dynamic response optimization using transformation of dynamic loads into equivalent static loads has been proposed. The transformation is conducted to match the displacement fields from dynamic and static analyses. This algorithm can be applied to large‐scale problems. However, the application has been limited to size optimization. The present study applies the algorithm to shape optimization. Because the number of degrees of freedom of finite element models is usually very large in shape optimization, it is difficult to conduct dynamic response optimization with conventional methods that directly treat dynamic response in the time domain. The optimization process is carried out by interfacing an optimization system and an analysis system for structural dynamics. Various examples are solved to verify the algorithm. The results are compared to the results from static loads. It is found that the algorithm using static loads transformed from dynamic loads based on displacement is valid for very large‐scale shape optimization problems. Copyright © 2005 John Wiley & Sons, Ltd.