双材料自由阻尼层结构拓扑优化设计方法

目的 在不减小板壳结构动刚度的前提下有效提高板壳结构的抗振性能,提出一种板壳阻尼复合结构拓扑优化设计.方法 以结构模态阻尼比为目标函数,以某阶固有频率不小于设定值为约束条件,推导目标函数和约束条件对设计变量的灵敏度表达式,采用SIMP插值函数和移动渐近线法求解优化数学模型.结果 研究表明,文中提出的双材料阻尼层结构相比传统单材料阻尼层结构的振动响应明显减小,同时适当改变设计目标和约束条件,可满足不同的工程应用需要.结论 通过在宏观上对高刚度低阻尼材料和低刚度高阻尼材料的分布进行了设计,优化后的结构兼顾低刚度高阻尼材料的高阻尼特性和高刚度低阻尼材料的高刚度特性,实现了结构高刚度高阻尼的设计.     

考虑瞬态响应的薄板结构阻尼材料层拓扑优化

讨论了敷设阻尼材料的薄板结构考虑瞬态响应时阻尼材料层的最优布局问题。基于SIMP方法构造人工阻尼材料惩罚模型和结构拓扑优化模型,以阻尼材料的相对密度作为设计变量,在给定阻尼材料用量的条件下,最小化结构瞬态位移响应的时间积分。由于结构整体呈现非比例阻尼特性,采用逐步积分法对结构的振动方程进行求解。通过伴随变量法得到目标函数对设计变量的灵敏度表达式,在此基础上采用基于梯度的移动渐近线方法求解。数值算例验证了优化模型与算法的合理性和有效性。     

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber‐reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three‐dimensional solid approach and first‐order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright © 2012 John Wiley & Sons, Ltd.     

声学覆盖层内嵌空腔的一种数值优化方法

给定材料参数的条件下,如何确定最优声腔结构是声学覆盖层设计中的关键问题。针对去耦型声学覆盖层,提出一种轴对称模型与拓扑优化相结合的方法,可以快速寻得最优的声腔结构。文中采用轴对称简化模型来描述周期性覆盖层的声学特性,通过与正方形模型、六边形模型以及实验结果的对比,验证了有限元模型的正确性。采用基于密度的拓扑优化方法,对覆盖层的不同区域进行了优化,以此为基础,获得一种含U型腔的覆盖层结构,在常压和静压下,其隔振性能均优于典型的圆柱空腔覆盖层的隔振性能。     

基于权重比的车架多工况拓扑优化方法研究

在赛车实际行驶过程中车架会受到各种工况的考验,因此在进行车架结构拓扑优化设计时必须同时考虑多个工况下车架的拓扑优化结果.然而,在进行多工况下拓扑结构设计时往往会遇到如何分配各个工况权重比的问题,各工况权重比的分配直接影响车架最终的拓扑结构.针对此问题进行研究,通过构造代理模型并利用遗传算法寻找最佳权重比.首先,采用折衷规划法建立同时考虑多个工况下车架刚度的拓扑优化综合目标函数模型;接着,采用最优拉丁超立方试验设计方法采样,构造径向基函数代理模型,并在代理模型的基础上利用NSGA-II进行求解,得到各个工况最佳权重比;最后,将获得的各个工况最佳权重比代入综合目标模型中进行拓扑计算,获得同时考虑各工况下车架刚度的拓扑结构.将该方法与获得权重比常用的层次分析法(AHP)和正交试验法(OED)进行比较,该方法较其他两种方法得到的综合目标值是最优的,车架所有工况的加权柔度是最低的.结果表明,所提出的方法很好地解决了多工况下拓扑优化权重比分配的问题,并且较其他方法具有明显的优越性.     

零泊松比超材料设计的多评价点功能基元拓扑优化方法

提出基于多评价点约束的零泊松比超材料功能基元拓扑优化设计方法。在同一功能基元拓扑基结构中,通过建立对于多个评价点的正、负泊松比约束,实现胞元零泊松比效应。分别采用最小质量和最大柔度目标函数拓扑优化模型优化设计出与半内六角蜂窝相似的零泊松比功能基元最优拓扑构型。提取功能基元最优构型并周期性序构了零泊松比超材料试件,通过有限元方法验证了该功能基元的零泊松比效应,并分析超材料试件的静、动力学特性。计算结果表明,最大柔度目标函数设计的功能基元构型的泊松比更接近于零,且具有更好的承载与隔振性能。设计了零泊松比超材料环肋双层圆柱壳结构,进行外壳静压和内部设备激振下壳体水下辐射噪声分析。研究表明,零泊松比超材料环肋可将外壳压缩变形转换为内外壳间环肋旋转,实现耐压壳内壳的保形,且具有较好的降噪性能。      

动载荷激励下板壳结构加筋自适应成长方法

自适应成长法是基于自然界分支系统形态形成机理的一种高效结构拓扑优化设计方法。通过引入等效静态载荷法理论,运用自适应成长法解决板壳加筋结构在承受动载荷激励下的动态响应拓扑优化设计问题。根据板壳结构所受的动载荷边界条件,构建以动柔度为目标的优化数学模型,推导迭代公式,使板壳结构的加强筋从"种子"开始,沿着使结构最佳力学性能方向成长,从而形成最优加强筋分布形态。研究在简谐载荷和冲击载荷作用下的板壳结构加强筋设计例,并与静态载荷作用下的设计结果进行比较。研究结果表明,板壳结构在动态载荷作用下,其主加强筋布局形态和在静态载荷作用下相同,但在靠近载荷作用点附近出现与主加强筋平行的截面积较小的加强筋,以增加抵抗动态载荷的作用;而冲击载荷作用下的加强筋与一般简谐载荷作用下的加强筋相比,多出一层较复杂的框型筋板抵抗瞬时冲击力。     

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．     

激光增材制造无人机框梁结构拓扑优化设计及刚度分析

目的 以选区激光熔化成形(SLM)无人机接头框梁结构为研究对象,研究不同工况条件下零件的变形分布情况,对原零件进行拓扑结构优化,并对优化后的零件进行二次静力学验证。方法 以AlSi10Mg铝合金粉末为原材料,利用Ansys Workbench软件的Mechanical模块对SLM成形接头零件4种工况下的静力学刚度行为进行有限元仿真。采用变密度法进行拓扑优化,以刚度最大化为目标、保留质量40%为响应约束进行结构优化,根据拓扑优化密度云图设计孔洞位置及尺寸,对模型进行重构,并在Ansys Workbench软件中进行二次静力学刚度仿真。结果 在4种工况条件下,接头零件弯曲时最大位移位置在上耳片边缘,除工况A外,其余工况均呈现沿z轴正向变形的趋势。在工况B下,总变形最大为0.289 mm,优化后为0.626 mm。优化后的零件使上、下耳片变形程度差异显著减小,最大变形差由0.128 mm减至0 mm。结论 不同位置接头零件的变形演变规律不同,几乎不存在扭转变形,主要是框梁结构的竖直弯曲变形,经拓扑结构优化后零件变形总体趋势并未改变,但整体结构的稳定性和一致性得到了显著提高。     

Truss topology optimization with static and dynamic constraints using modified subpopulation teaching–learning-based optimization

In this study, an improved version of the teaching–learning-based optimization (TLBO) algorithm is proposed for truss topology optimization (TTO), with static and dynamic constraints on planar and space trusses. The basic TLBO algorithm is improved to enhance its exploration and exploitation abilities by considering various factors such as the number of teachers, adaptive teaching, tutorial learning and self-motivated learning. The TTO problems are considered with multiple load conditions and subjected to constraints for natural frequencies, element stresses, nodal displacements, Euler buckling criteria and kinematic stability conditions. TTO is achieved with the removal of superfluous elements and nodes from the ground structure, and results in a mass saving. In this method, difficulties arise owing to singular solution and unnecessary analysis; therefore, the finite element model is reformed to resolve these issues. A single-stage optimization approach is used, in which size and topology optimization are considered simultaneously. The results obtained are compared with the best solutions obtained by the algorithm. The results reveal that the modified subpopulation teaching–learning-based optimization (MS-TLBO) algorithm is more effective than other state-of-the-art algorithms.     

Shell topology optimization using the layered artificial material model

A general methodology for topology optimization using the finite element method is described for shell structures. Four‐ and nine‐node Reissner–Mindlin shell elements with drilling degrees of freedom are used for the finite element response analysis. The artificial material model is used in the topology optimization and in particular, an isotropic multi‐layer shell model is introduced to allow the formation of holes or stiffening zones. In addition, a single design variable resizing algorithm is implemented based on the existing criterion which is found to be adequate for the artificial material model. Several benchmark tests are presented to show the overall performance of the proposed methodology. The strain energy variation together with the variation of the layout of the structure is monitored. Some detailed examples are provided with comparisons of the use of the four‐ and nine‐node elements and studies of critical solution parameters. Copyright 2000 John Wiley & Sons, Ltd.     

Nonlinear response topology optimization using equivalent static loads—case studies

Nonlinear structural optimization is fairly expensive and difficult, because a large number of nonlinear analyses is required due to the large number of design variables involved in topology optimization. In element density based topology optimization, the low density elements create mesh distortion and the updating of finite element material with low density elements has a severe effect on the optimization results in the next cycles. In order to overcome these difficulties, the equivalent static loads method for nonlinear response structural optimization (ESLSO) primarily used for size and shape optimization has been applied to topology optimization. The nonlinear analysis is performed with the given loading conditions to calculate equivalent static loads (ESLs) and these ESLs are used to perform linear response optimization. In this paper, the authors have presented the results of five case studies with material, geometric and contact nonlinearities showing good agreement and providing justification of the proposed method.     

Topology optimization using a continuous density field and adaptive mesh refinement

A new method of topology optimization is introduced in which a continuous material field is combined with adaptive mesh refinement. Using a continuous material field with different analysis and design meshes allows the method to produce optimal designs that are free of numerical artifacts like checkerboard patterns and material islands. Adaptive mesh refinement is then applied to both meshes to precisely locate the optimal boundary of the final structure. A Helmholtz‐type density filter is used to prevent the appearance of small topological features as the mesh refinement proceeds. Results are presented for several test problems, including problems with geometrically complex domain boundaries.     

Optimization of a passive structure for active vibration isolation: an interval-computation- and constraint-propagation-based approach

This article is concerned with the optimization of the mechanical structure of a one-degree-of-freedom vibration isolator. An efficient optimization algorithm based on an interval-computation method is used. The authors’ general objective is to include and develop an optimization step in the pre-design process of a smart structure. In this article, the idea of this pre-design is to obtain, very quickly and very simply, the global structural geometry of the passive isolation device. For this purpose, a simplified mathematical model is built, which describes the main natural mode shapes of the suspension device. The method is applicable to large-scale dynamic systems for a first optimization process step because it's clearly an effective time-saving optimization approach. The results obtained are quite sufficient for a first pre-design step. For a real case scenario, the optimized structure is applied to a numerical active vibration control process.     

A new method to generate the ground structure in truss topology optimization

The aim of this article is to provide an effective method to generate the ground structure in truss topology optimization. The core of this method is to place nodal points for the ground structure at the intersection of the first and third principal stress trajectories, which are obtained by solving the equivalent static problem in the design domain with a homogeneous isotropic material property. It is applicable to generate the ground structure for arbitrary regular and irregular geometric design domains. The proposed method is tested on some benchmark examples in truss topology optimization. The optimization model is a standard linear programming problem based on plastic design and solved by the interior point algorithm. Compared with other methods, the proposed method may use a well-defined ground structure with fewer nodes and bars, resulting in faster solution convergence, which shows it to be efficient.     

约束阻尼结构的改进准则法拓扑减振动力学优化

旨在为减振设计提供理论基础,研究约束阻尼结构拓扑动力学优化。以阻尼材料用量、振动特征方程、模态频率为约束,以多模态损耗因子倒数的加权和最小为目标,建立了约束阻尼结构拓扑优化模型,引入MAC因子控制结构的振型跃阶。在引入质量阵惩罚因子基础上推导出优化目标灵敏度。考虑到优化目标函数的非凸性,采用常规准则法(OC)寻优可能会使拓扑变量出现负值或陷入局部优化,故引入数学规划移动渐近技术对OC法进行改进,从而将全体拓扑变量纳入改进算法的优化迭代全过程。编程实现了约束阻尼板改进OC法拓扑动力学优化并对改进法性能进行了仿真。结果显示,改进算法可得到更合理的约束阻尼层构形,可使结构取得更佳减振效果。研究表明,改进算法迭代稳定性更好、寻优效率更高、更具全域最优性。     

Static and free vibration analysis of sandwich cylindrical shell based on theory of elasticity and using DQM

In this paper, static and free vibration analysis of a sandwich cylindrical shell is performed using theory of elasticity formulation. The core layer is made of functionally graded material with material properties varying along the thickness direction according to a simple power law. For the case of simply supported boundary conditions, equations of motion and equilibrium equations are solved analytically by applying a state-space technique along the radial direction and Fourier series expansion along the axial and circumferential direction. When boundary conditions are not simply supported, a semi-analytically solution is performed by using the differential quadrature method along the axial direction. The present approach is validated by comparing the obtained numerical results with those published in the available literature. Moreover, effects of boundary conditions, graded direction, mid-radius to thickness and length to mid-radius ratios on bending and vibration behavior are considered.     

混沌免疫遗传算法在汽车悬置系统设计中的应用

传统的悬置系统参数优化方法容易使优化结果陷入局部最优,遗传算法因其易于早熟收敛而限制了实际优化效果,为此提出使用混沌免疫遗传算法对汽车动力总成悬置系统参数进行优化设计。优化设计中,以动力总成悬置系统六自由度能量解耦为目标函数,以悬置刚度和安装角度为优化变量,并考虑悬置系统的模态频率匹配、能量解耦率、悬置静态剪切和压缩变形等约束条件。优化结果表明,基于设计的寻优方法,改善动力总成悬置系统与整车匹配程度,提高动力总成悬置系统的隔振性能。     

基于密度-敏度层次更新策略的三维连续体结构拓扑优化

针对三维连续体结构静力学拓扑优化中灰度单元过多的问题,以结构的柔度最小为目标函数,运用基于SIMP插值方法建立的静力学拓扑优化数学模型,提出一种密度-敏度层次更新策略.以数控插齿机床身为例,运用该更新策略,采用MATLAB编程进行三维拓扑优化.优化结果中灰度单元明显减少,说明了密度-敏度层次更新策略的合理性.     

Identification of the dynamical properties of structures using free vibration data and distributed genetic algorithms

The dynamical properties of structures, such as natural frequencies, damping ratios and mode shapes, can be obtained by several identification methods. Some are based on the direct signal processing in a time domain; others transform response data to the frequency domain. The development of these techniques is useful in the production of more accurate structural models; they can be also used to test the level of damage in structures (or verify their strength to support new load actions) by using experimental data. There are situations where frequency domain algorithms and conventional system identification techniques fail, do not allow adequate solution of the identification problems or become trapped in a local optimum. It is in these cases where evolutionary optimization techniques are important tools for evaluating the dynamical properties of structural systems in practical applications. This article presents a methodology to determine the dynamic properties of structures knowing their response in terms of displacement, velocities or accelerations in the time domain when they are subjected to a free vibration excitation. In order to do that, a specialized evolutionary algorithm capable of adapting its parameters to the different types of registers obtained from the dynamic time response of a structure is implemented in a robust way, making this approach useful in practical situations. A distributed real genetic algorithm (DRGA) based on an island model of different subpopulations is used to adjust a simulated response signal of a building to the real response signal. Initially, computer-generated synthetic response signals are used but, in future, the approach will be validated with signals obtained from free vibration experimental tests and will be extended to other types of dynamical excitation signals. Finally, the method will be tested with data obtained from earthquake events.