A structural topological optimization method for multi-displacement constraints and any initial topology configuration

In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.     

SEMI-ANALYTICAL AND SEMI-NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FOUNDATION

A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb's solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of foundations.     

THE SATELLITE STRUCTURE TOPOLOGY OPTIMIZATION BASED ON HOMOGENIZATION METHOD AND ITS SIZE SENSITIVITY ANALYSIS

With the development of satellite structure technology, more and more design parameters will affect its structural performance. It is desirable to obtain an optimal structure design with a minimum weight, including optimal configuration and sizes. The present paper aims to describe an optimization analysis for a satellite structure, including topology optimization and size optimization. Based on the homogenization method, the topology optimization is carried out for the main supporting frame of service module under given constraints and load conditions, and then the sensitivity analysis is made of 15 structural size parameters of the whole satellite and the optimal sizes are obtained. The numerical result shows that the present optimization design method is very effective.     

THEORETICAL INVESTIGATION ON THE DYNAMIC PERFORMANCE OF CMUT FOR DESIGN OPTIMIZATION

Although many modeling approaches exist for analyzing the behavior of capacitive micro-machined ultrasonic transducers(CMUTs),the relation equation between the design parameters with input and output is still lacking.What there is can only be used to analyze the dynamic performance of CMUT indirectly and qualitatively,such as stiffness and sound pressure.A lumped-parameter theoretical model based on the dynamic theory is proposed in this paper.The relation equations between the design parameters with inputs and outputs are given.The results obtained by the proposed model agree well with those by finite element method(FEM)simulation.The dynamic and static behavior of CMUT can be clearly depicted,which is helpful for design and optimization iterations.This shows that the proposed model makes it easier to optimize the parameters of a CMUT with respect to output and bandwidth directly and to better understand the influence of each parameter.     

Transverse vibrations of arbitrary non-uniform beams

Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.     

THREE-DIMENSIONAL EXACT MODELING OF GEOMETRIC AND MECHANICAL PROPERTIES OF WOVEN COMPOSITES

A formulation for the prediction of the influence of various parameters on the elastic moduli of three-dimensional （3D） orthogonally woven composites has been given. These parameters can be classified into different groups according to their properties, such as input design and material parameters, structural parameters etc. Some, by their nature, can be well controlled during the design and manufacture of the composite. The composite is assumed to be homogeneous and orthotropic macroscopically. With a selected representative unit cell and the stiffness model developed by author in 2000, the influence of all of these parameters can be determined. Results showing the influence of the main design geometric parameters are presented. They demonstrate that an optimal design is possible for the through-the-thickness stiffness of the composites. The methodology used can be generalized to predict the behavior of other kinds of 3D woven structures.     

THE CONVERGENT CONDITION AND UNITED FORMULA OF STEP REDUCTION METHOD

The step reduction method was first suggested by Prof. Yeh Kai-yuan. This method has more advantages than other numerical methods. By this method, the analytic expression of solution can he obtained for solving nonuniform elastic mechanics. At the same time. its ealculuting time is very short and convergent speed very fast. In this paper, the convergent condition and nited formula of step reduction method are given by mathemutical method. It is proved that the solution of displacement and stress resultants obtained by this method can eonverge to exact solution uniformly, when the convergent condition is sutisfied. By united formula, the analytic solution solution can be expressed as matrix form, and therefore the former complicated expression can be avoMed. Two numerical examples are given at the end of this paper which indicate that. by the theory in this paper, a right model can be obtained for step reduction method.     

FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables , was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.     

A DISCRETE NONLINEAR STEPPING OPTIMIZATION METHOD AND ITS APPLICATION

Most of the practical design variables should always be discrete quantity within engineering optimization design problems. To obtain the true optimization solution, a discrete optimization method must be used. In this paper, a new method called step optimization search method is presented to solve the discrete quantity mathematic programming problems. The basic idea oft his method is to find out an initialfeasible point and then to search the optimum point step by step in the neighbouring region of this point so as to obtain an improved new discrete point. Respectively, the new point can be taken us initial one, and the whole process can be carried out once more until the optimum solution of the problem is obtained. Some results of numerical examples of practical problems show that this new method can solve problems quickly and simply and can be applied in a lot of engineering design problems.     

基于拓扑与形状优化的小型化金属天线设计方法

天线小型化设计需要基于先进的设计方法,基于拓扑优化的设计往往存在灰度单元,因此设计结果无法直接应用,需要进一步规整设计。而对于电磁金属结构,粗糙的规整方法会引起结构性能的很大变化以致偏离最优结果。提出一种拓扑优化和形状优化相结合的方法,用于金属天线结构的小型化设计。该方法通过拓扑优化获得金属天线结构的概念构型,进而利用形状优化对概念构型进行边界规整和精细化设计。形状优化方法采用多控制点贝塞尔曲线描述拓扑概念构型,通过贝塞尔曲线控制点的移动实现天线构型的调控。给出了贝塞尔曲线控制点的设置原则,基于拓扑优化得到场量分布结果,利用较少的贝塞尔曲线控制点实现天线拓扑构型结构特征的有效调控。该方法可以获得无灰度单元残留的拓扑结果,同时可有效避免密度阈值规整方法中天线性能改变的问题,并且获得的拓扑构型边界光滑。数值算例表明拓扑优化和形状优化相结合方法的有效性。此外,该方法可拓展到其他类型电磁器件的优化设计中。     

基于应力及其灵敏度的结构拓扑渐进优化方法

在导出应力灵敏度的基础上，建立了一种改进的基于应力及其灵敏度的结构拓扑双方向渐进优化算法．该方法是对传统ESO和BESO方法的改进和完善．算例表明该方法能较大程度减少解的振荡状态数，获得更佳的拓扑结构．具有概念上的简洁性和应用上的有效性。     

基于拓扑描述函数的连续体结构拓扑优化方法

提出了一种利用拓扑描述函数(TDF)作为拓扑设计变量求解连续体结构拓扑优化问题 的新方法. 优化问题的目标函数是结构的整体柔顺性，约束条件为对于可利用材料的体积限 制. 这种方法不仅可以消除拓扑优化中经常出现的棋盘格式等数值不稳定现象，而且能够有 效地抑制传统算法处理此类优化问题时所引发的边界扩散效应. 与其它的基于水平集描述函 数的拓扑优化方法相比，所提出的算法不仅无需求解控制水平集函数演化的双曲守恒方 程，而且合理地考虑了目标函数的拓扑导数信息，因而使得算法的计算效率有了显著的提高.     

一种基于应力的双方向结构拓扑优化算法

基于传统的渐进结构优化方法，提出了一种基于应力的双方向渐进拓扑优化算法。该方法是对传统方法和目前的双方向法的改进和完善。算例表明该方法能避免目前的双方向法具有的解的振荡问题，具有更高的可靠性，能获得更佳的拓扑结构。     

蜂窝夹芯圆环的拓扑优化设计及尺度效应研究

采用尺度关联的一体化设计方法开展了旋转周期圆环结构的拓扑优化设计研究，以宏观 结构的最大刚度为目标，研究了材料表征体胞尺度、构型以及不同载荷作用形式对蜂窝夹芯 圆环结构优化结果的影响. 所提出的无量纲结构构型因子实现了优化结构的结构效率量化评 估. 结合SIMP材料模型和周长控制方法，实现了宏观结构和细观表征体胞的优化设计，获得 清晰的材料分布. 数值算例表明，尺度关联的一体化设计方法能有效地完成圆环结构的拓扑 优化设计，设计结果充分反映体胞尺度效应对旋转周期圆环结构夹芯构型的影响.     

强迫谐振动下连续体结构拓扑优化

应用结构拓扑优化ICM(独立连续映射)方法,对强迫谐振动下结构拓扑优化问题建立了以重量极小为目标,位移幅值为约束的优化模型.位移幅值采用一阶泰勒展式近似,由于拓扑优化中设计变量数目通常很多,对强迫谐振动位移幅值的敏度分析推导了伴随法公式,使得一次敏度分析可以计算出对所有设计变量的偏导数,克服了采用直接法敏度分析中一次只能计算出对一个设计变量的偏导数的不足.算例表明用伴随法分析敏度在结构拓扑优化中可以大幅提高计算效率,ICM方法采用独立于截面及形状参数的拓扑优化设计变量更清晰地反映了拓扑优化的本质.     

面向压电智能结构精确变形的协同优化设计方法

智能结构集智能材料与传统材料于一体,能够实现结构的主动控制,在航空航天等领域具有巨大的应用潜力.由于其系统复杂且具有多场耦合效应,智能结构的整体式优化设计方法成为结构控制技术研究的关键之一.为了提高压电智能结构的整体性能和变形精度,提出了同时考虑压电驱动器布局(分布位置及角度)和基体结构拓扑构型的协同优化设计新方法.采用多点约束方法 (multi-point constraints,MPC)建立压电驱动器和基体结构的连接,定义一种与测量点目标位移相关的权重函数,以实现结构的精确变形控制.通过协同优化设计,压电驱动器可以获得最优的分布位置及角度,同时基体结构获得最优的拓扑构型,从而提升了压电智能结构系统的整体驱动性能和变形精度.通过进一步分析,研究了精确变形、体分比约束与结构优化构型和整体刚度的关系,以及优化结果中可能存在的传力路径畸变现象.数值算例的设计结果表明,采用协同优化设计方法,能够扩大结构的寻优空间,有效减小变形误差,实现压电智能结构的精确变形控制.     

基于固定网格和拓扑导数的结构拓扑优化自适应泡泡法

为继承传统拓扑优化泡泡法变量少、精度高等优点,并克服其网格重划频繁、孔洞合并操作繁琐等不足,提出了一种基于固定网格和拓扑导数的自适应泡泡方法.该方法的主要特点是:(1)采用有限胞元固定网格分析方法计算结构力学响应,在优化过程中无需网格更新和重划分,就能保证较高的分析精度;(2)根据拓扑导数信息指导结构区域中孔洞的引入,不仅消除了优化结果对孔洞初始布局的依赖性,还能有效控制设计变量的数量;(3)引入拓扑导数阈值和孔洞影响区域新概念,实现了孔洞引入频次和位置的自适应调节,保证了拓扑优化过程的数值计算稳定性;(4)采用光滑变形隐式曲线描述孔洞边界,不仅设计参数少、变形能力强,而且便于处理孔洞间的融合/分离操作以及与固定网格分析方法的有机结合.理论分析和数值算例表明,改进后的自适应泡泡法能够消除传统泡泡法因采用拉格朗日网格和参数化B样条曲线模型而存在的实施困难,采用很少的设计变量就可获得边界光滑清晰的优化结果.      

基于拓扑描述函数的特定性能材料设计方法

研究了拓扑描述函数在材料设计中的应用,给出了一种基于拓扑描述函数的特定性能材料设计问题的提法和求解方法.将拓扑描述函数表示成含参数的基函数之和,将材料微结构拓扑优化问题转化为设计基函数描述参数的尺寸优化问题,使问题求解更方便.基于拓扑描述函数的方法可以准确确定设计域上任意点的材料分布,避免了变密度法常出现的棋盘效应、设计变量和有限元单元相关的缺点;与传统的水平集方法相比,其优化模型可以利用现有的优化方法求解,避免了差分法求偏微分方程.具有正泊松比和负泊松比的特定弹性性能材料的设计算例,说明了基于拓扑描述函数的材料设计方法的有效性.