结构拓扑优化中变量连接算法研究与软件实现Research and software implementation of variable connection algorithm for structural topology optimization

结构拓扑优化的变量连接,是通过对设计变量之间添加约束关系,从而得到特定的拓扑优化构型,使得优化结果能够满足工程上的特殊要求和工艺制造技术的限制。针对拓扑优化中的几类过滤形式及灵敏度分析,给出了考虑变量连接的计算公式;基于自主研发的SiPESC软件集成化平台,在SiPESC ．TOPO拓扑优化模块上进行二次开发,构建了拓扑优化的变量连接算法框架,其核心思想是基于面向对象设计方法和软件设计模式,实现算法与数据分离。详细阐述了变量连接的作用方式,以及软件框架通用接口设计方案,并通过数值算例验证了其在静力问题、动力问题和热传导问题上的可行性。     

A method for the determination of the contact area between a tyre and the ground

In this study, a detailed investigation for determining the contact area of types interacting with deformable soil is presented. A mathematical model has been developed using a rectangular coordinate system to determine the coordinates of points in the contact region. A computer program was used to evaluate the coordinates of the contact region. The model was experimentally verified by specially fabricated instrumentation.     

Crack identification method in beam-like structures using changes in experimentally measured frequencies and Particle Swarm Optimization

In this paper, a technique is presented for the detection and localization of an open crack in beam-like structures using experimentally measured natural frequencies and the Particle Swarm Optimization (PSO) method. The technique considers the variation in local flexibility near the crack. The natural frequencies of a cracked beam are determined experimentally and numerically using the Finite Element Method (FEM). The optimization algorithm is programmed in MATLAB. The algorithm is used to estimate the location and severity of a crack by minimizing the differences between measured and calculated frequencies. The method is verified using experimentally measured data on a cantilever steel beam. The Fourier transform is adopted to improve the frequency resolution. The results demonstrate the good accuracy of the proposed technique.     

二级多点近似方法在整星结构优化设计中的应用

以整星结构为研究对象,针对含有离散变量的混合变量优化问题,应用二级多点近似方法给出从卫星拓扑布局设计到尺寸的一体化优化求解过程。首先,对整星结构进行仿真和振动试验,设计满足总体指标要求且已得到在轨验证。其次,建立以极小化卫星质量为目标的多工况优化模型后利用分段多点逼近函数建立了显式近似问题。最后,采用遗传算法和变尺度法分别对离散/连续两类变量寻优,并以拓扑构型一致性和目标函数的下降程度作为收敛的判定依据。结果显示,在满足频率和静力的约束下,卫星质量降低了7.9%,且结构分析迭代次数仅为50~60次,从而验证了该方法在求解整星结构多变量多工况下的一体化设计问题时具有很高的计算效率和准确性。     

Working processes of cyclic-action machinery for soil deformation—Part IV

The analysis deals with a system consisting of a main unit-moving with uniform velocity and generating the necessary tractive force- and a centrifugal vibrator, connected to the main unit by means of a spring and oscillating together with the tool as a single subsystem. The working process is described through piecewise-linear approximation of the frontal resistance force of the soil, as a function of the tool displacement. By this means interrelationship is established between the system parameters (with the possibility of their effective control) and the mechanical characteristics of the soil. It is shown that the process is feasible for a definitive set of the parameters, a change in one of them affecting the others.Special attention is devoted to the tractive force, whose role consists mainly in permitting uptake of the unloading energy and braking of the vibrator-tool subsystem during its backward motion. The latter is accompanied by compression of the spring, which, on being released, restores to the tool the energy expended during loading. The maximum tractive force in a cycle may be varied effectively over a fairly wide range through variation of the system parameters, each of which may be considered as definitive. A methodology for their determination is presented.Analytical relationships are derived for minimizing the energy requirement of the process, so as to optimize its parameters.     

A parametric study for improving the centrifugal pump impeller for use in viscous fluid pumping

Essentially, performance of centrifugal pumps is affected when pumping viscous fluids. In this paper a new idea is proposed to overcome the undesirable effects of viscosity on the pump performance parameters. This idea based on this matter that one specific impeller can be designed, made and installed on the pump for pumping of one fluid with specific viscosity. Therefore a specific pump can be used for pumping of different fluids with different viscosity, by replacement of pump impeller. Replacement of the impeller is more cost effective in comparison to the replacement of the whole of the pump. Passage width and outlet angle of impeller are considered as design variables and the effects of such variables investigated using experimentally validated numerical model. The H–Q, P–Q and η–Q graphs are extracted experimentally for the improved impeller, which show good improvement in comparison with original impeller.     

传热结构的多目标拓扑优化设计研究

深入分析了传热结构多目标拓扑优化设计中的几个关键问题。提出了基于结构柔度最小化和结构散热弱度最小化的多目标拓扑优化设计方法,建立了传热结构的多目标拓扑优化设计模型,推导了传热结构多目标拓扑优化中用于迭代分析求解的优化准则算法和敏度分析方程。通过数值计算验证了理论和算法的有效性。     

Dynamic reliability analysis of a cantilever beam during a deterioration process

Considering deterioration process of a beam structure subjected to cyclic load, the reliability and sensitivity analysis is presented. Gamma process is introduced to describe the deterioration of properties and the accuracy of the model is verified by experiments of structures under cycle load. A set of experiments is designed to investigate the deterioration process of the beam under cycle load. For arbitrarily distributed random material and geometric variables, the stochastic perturbation method and Edgeworth series are used to approximate the statistical characteristics of vibration and failure probability. Monte Carlo simulation is employed to show the validity of the method proposed. Additionally, the effects of material and geometric parameters are discussed to provide important information for design and use of beam structures.     

基于移动可变形孔洞方法的超弹性结构拓扑优化

现有隐式拓扑优化方法在进行超弹性结构拓扑优化设计时，具有设计变量多、中间设计有限元分析存在严重的收敛性和设计结果无法直接导入CAD/CAE系统等问题。为解决这些问题，提出了一种基于移动可变形孔洞的显式拓扑优化方法来进行承受大变形的超弹性结构设计，材料本构采用常用的Mooney-Rivlin模型。首先，介绍了移动可变形孔洞方法的基本思想和可变形孔洞的显式描述方法；其次，构造了基于移动可变形孔洞方法的超弹性结构拓扑优化的数学列式，给出了相应的灵敏度结果；最后，通过数值算例验证了本方法的有效性。数值结果表明，该方法可以通过较少的设计变量和非常稳健的优化过程，给出边界由B样条曲线描述且可与CAD/CAE软件无缝连接的超弹性结构设计。     

Load and Boundary Condition Calibration Using Full-field Strain Measurement

For critical load bearing structures, it is often necessary to experimentally determine the load distribution on the structure so that accurate finite element models can be developed for stress and fatigue life predictions. An inverse problem approach is presented here for computing or calibrating the loads and boundary conditions acting on a structure. This enables the creation of more accurate finite element models, especially for structures that have complicated load distribution and compliant boundary conditions. The method presented here involves minimizing the least square error between the strains computed using the finite element model and the strains and displacements obtained experimentally. The nodal loads and the compliance at fixed boundaries are treated as the variables in the optimization problem. The compliance is modeled as springs attached at the nodes that are on the boundary where the structure is restrained. The method is verified by computing the loads and boundary conditions when displacements, maximum shear strain or both are available at large number of points on the surface of the structure. The experimental data set was generated using the luminescent photoelastic coating (LPC) technique.     

Approximate solution for the temperature field of 1-D soil freezing process in a semi-infinite region

Unfrozen liquid water always exists in the humid soil system below freezing point, and the amount of the unfrozen water decreases continuously with the temperature decreasing. This phenomenon is a special characteristic for the freezing of the humid soil system. The temperature field of 1-D soil freezing process in a semi-infinite region has been studied. The problem is a Stefan-like problem. After the continuous phase change process of soil water is divided into a finite number of substeps, the Stefan problem of a multi-phase material is obtained. A similarity solution is found and determined. In order to get the right solution of the nonlinear equations, a variable substitution technique is introduced. The approximate solution is verified by the numerical results of the continuous phase change model of soil freezing process. Finally, for practical purpose, the advancing factor of the freezing front and the mean squared error of the temperature caused by the measurement errors are defined. Computational examples concerning the effect of different parameters on the advancing factor of the freezing front and the effect of the measurement errors on the accuracy of the solution are presented and discussed.     

Decentralized coordination of autonomous swarms inspired by chaotic behavior of ants

In this paper, we propose a decentralized coordination algorithm for a group of mobile nodes, called an autonomous swarm, on a finite two-dimensional space, which can efficiently coordinate cooperatively the autonomous swarm to the optimal solution. Our algorithm is inspired by chaotic behavior of a single ant and self-organization behavior of the whole ant colony. To construct this algorithm, we firstly assume that each agent is a nonlinear oscillator presenting the chaotic behavior of a single ant. Then we establish a self-organization mechanism according to the self-organization behavior of the whole ant colony. Moreover, we analyze the convergence of the proposed algorithm. Finally, we experimentally evaluate the performance of our algorithm with the clustering and dispersion operations of a swarm. Comparison results of the proposed algorithm and the gradient-type one are also presented to illustrate the effectiveness of the proposed scheme in approximately global optimization for swarms.     

晶体生长过程实时监测系统

实时监测晶体生长过程对研究晶体生长动力学以及调控晶体生长过程有着很重要的意义。结合干涉技术、相移技术以及时间序列位相提取技术,建立了一个晶体生长过程实时监测系统。该系统主要由三条光束组成,通过设定快门参数组成不同的Mach-Zehnder干涉光路,可同时用于无机盐晶体和蛋白质晶体生长过程的实时定量监测。利用该系统及时间序列位相提取方法,对NaCl晶体在自然蒸发情况下的生长过程以及溶菌酶蛋白悬滴法结晶过程进行了研究,对该系统和方法在研究晶体结晶过程中的可行性及优势进行了验证。结果表明,该系统不仅可以获得晶体结晶过程中的实时绝对浓度、过饱和度等晶体生长动力学参数;而且对于蛋白质结晶过程,快门系统的引入解决了蛋白溶液多浓度场叠加的分离问题,在一个实验周期内获得了溶菌酶蛋白结晶过程中的实时蛋白浓度演变、实时沉淀剂浓度变化等结晶动力学参数。这些关键参数为下一步探索结晶条件对晶体质量的影响、分析蛋白结晶相图以及优化蛋白质晶体质量提供了定量数据基础。     

Design of microstructure-sensitive properties in elasto-viscoplastic polycrystals using multi-scale homogenization

Evolution of properties during processing of materials depends on the underlying material microstructure. A finite element homogenization approach is presented for calculating the evolution of macro-scale properties during processing of microstructures. A mathematically rigorous sensitivity analysis of homogenization is presented that is used to identify optimal forging rates in processes that would lead to a desired microstructure response. Macro-scale parameters such as forging rates are linked with microstructure deformation using boundary conditions drawn from the theory of multi-scale homogenization. Homogenized stresses at the macro-scale are obtained through volume-averaging laws. A constitutive framework for thermo-elastic–viscoplastic response of single crystals is utilized along with a fully-implicit Lagrangian finite element algorithm for modelling microstructure evolution. The continuum sensitivity method (CSM) used for designing processes involves differentiation of the governing field equations of homogenization with respect to the processing parameters and development of the weak forms for the corresponding sensitivity equations that are solved using finite element analysis. The sensitivity of the deformation field within the microstructure is exactly defined and an averaging principle is developed to compute the sensitivity of homogenized stresses at the macro-scale due to perturbations in the process parameters. Computed sensitivities are used within a gradient-based optimization framework for controlling the response of the microstructure. Development of texture and stress–strain response in 2D and 3D FCC aluminum polycrystalline aggregates using the homogenization algorithm is compared with both Taylor-based simulations and published experimental results. Processing parameters that would lead to a desired equivalent stress–strain curve in a sample poly-crystalline microstructure are identified for single and two-stage loading using the design algorithm.     

Design of a tuned vibration absorber for a slender hollow cylindrical structure

Abstract

In this paper, details of the design work for a tuned vibration absorber to be used on a hollow cylindrical structure is presented. The vibration problem is of resonant type and the tuned vibration absorber is designed to suppress the displacement vibration response of the free end of the slender hollow structure dominated by the contribution of its lowest transverse vibration modes. The structure is modeled using a commercial finite element software. Finite element model of the structure is verified using experimentally obtained frequency response functions and modal parameters. Effective parameters of the tuned vibration absorber design are then determined based on finite element analysis simulations of the vibration suppression performance of the tuned vibration absorber as it is used on the structure. Details of the tuned vibration absorber design are determined and a prototype is fabricated. Prototype tuned vibration absorber is then characterized experimentally both as a standalone system and also as it is used on the main structure. Vibration reduction performance of the physical prototype of the tuned vibration absorber is also compared with its vibration reduction performance estimated from finite element analysis simulations so that the analysis based design process can be validated.

Communicated by Dumitru Caruntu.     

一种基于自适应单元删除率的BESO方法

在ESO中采用动态删除率能有效地提高优化效率和稳定性，但现有的动态删除率策略都含有经验参数，确定删除率的过程较为复杂。本文提出了一种用于BESO的无经验参数自适应单元删除率确定方法。通过分析单元删除率对优化稳定性的影响，得到了结构优化过程中单元删除率的理想变化规律和单元灵敏度均匀化信息对删除率的影响情况，并据此分析了经验参数引入的原因，从而构造了评价单迭代步的单元灵敏度均匀化程度指标。然后，基于单迭代步的单元灵敏度均匀化程度指标，构造了全部迭代步信息下的单元灵敏度均匀化程度相对指标，结合单元删除率的推荐范围值，给出了一种自适应于结构优化进程的单元删除率自适应函数。最后，给出了基于自适应单元删除率的BESO方法实现流程。经典算例的结果对比说明，本文方法在保证优化质量相近的情况下，具有更好的优化效率和稳定性。     

基于能度可靠性的结构优化设计方法

基于可靠性的结构优化设计是不确定性结构设计的最合理途径。本文提出了基于能度可靠性的结构优化设计方法，将不确定结构的优化设计描述为：在重量或造价约束下，极小化结构的失效可能度；或对确定的容许失效可能度，极小化结构重量或造价。所提方法和传统的基于随机可靠性的结构优化设计是平行和相似的。由于结构的能度可靠性模型对已知数据的依赖性较低，计算过程较为简便。从而可使结构设计阶段获取数据的难度大大降低，并有效降低计算工作量，且可使模糊信息的处理更为合理。实例计算说明了文中方法是有效和可行的。     

几何规划原算法对含多变参数梁单元结构优化设计的统一处理

对于含空间梁单元的复杂结构,给出了同单参数模型不同统一处理途径:采用Duffin缩并公式形成截面多变参数与截面力学量的函数关系,运用分部与整体两级优化策略,并使用几何规划原算法的统一解法。数值算例表明本文方法的有效性。     

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.     

Evaluation of Conformal and Non-Conformal Contact Parameters Using Digital Photoelasticity

Experimental studies to exploit photoelastic data of conformal geometries to extract contact parameters are non-existent because closed-form stress field equations were not available until recently. In this paper, the explicit equations recently reported in the literature for a flat punch with rounded edges are generalized so that a single set of equations can be used for a flat punch with rounded edges and Hertzian contacts with arbitrary radii of curvatures. The generality of the governing equations is verified by plotting isochromatics for conformal and non-conformal contact situations. A generic method to evaluate unknown contact parameters from the whole-field isochromatic data for conformal and non-conformal geometries is implemented. The methodology is initially verified using theoretically generated isochromatic data and is then used to experimentally evaluate two contact situations. In view of high-fringe gradient zones, the suitability of various digital photoelastic methods is compared. A novel four-step phase shifting technique is proposed in which isochromatic and isoclinic data can be evaluated using the minimum number of images.