具有动应力、位移和稳定性约束的离散变量桁架结构布局优化设计算法

给出了在动应力、动位移和动稳定约束下离散变量结构布局优化设计问题的数学模型,用“拟静力”算法,将具有动应力约束、动位移约束和动稳定约束的离散变量结构布局优化设计问题化为静应力、静位移和静稳定约束的优化问题,然后利用两级优化算法求解该模型．优化过程由两级组成,拓扑级优化和形状级优化．在每一级,都使用了综合算法,并且在搜索过程中都根据两类设计变量的相对差商值进行搜索．对包含稳定约束和不包含稳定约束的优化结果做了比较,结果显示稳定性约束对优化结果产生较大的影响．     

基于可靠性的工程结构动力响应优化设计

在考虑结构物理参数和作用荷栽同时具有随机性的情况下,建立了具有动应力、动位移可靠性约束和设计变量上下限约束的工程结构优化设计数学模型;分别对结构动力响应的数字特征和基于可靠性的结构动力响应的灵敏度进行了推导.利用内罚函数法求解.算例表明文中构建的优化模型和提出的求解方法是合理与可行的.     

应力和位移约束下连续体结构拓扑优化

同时考滤应力和位移约束的连续体结构拓扑优化问题,很难用现有的均匀方法或变密度方法等求解。主要困难在于难以建立应力和位移约束与拓扑设计变量间显式关系式;即使建立了这种关系,也由于优化问题规模过大,利用常规的数学规划方法难以求解。隋允康、杨德庆曾提出了基于独立连续拓扑变量及映射变换（ＩＣＭ）的桁架结构拓扑优化模型。本文在此基础上,建立了以重量为目标,考虑应力和位移约束的连续体结构拓扑优化模型,并推导出     

基于多点自由度约束的方向性保形拓扑优化设计方法

保持飞行器气动面、功能面等型面的精确外形是飞行器刚度设计的重要内容.为控制飞行器结构局部区域的翘曲变形模式,抑制特定方向上有害的翘曲变形,提出考虑结构方向性保形约束的拓扑优化设计新方法.一方面,引入由保形区域内有限控制点生成的人工附加弱单元(artificial weak elements,AWEs),使控制点各自由度位移通过多点自由度约束(multi-point constraints,MPCs)传递到AWEs上,约束AWEs的变形能可以实现对保形区域翘曲变形的抑制;另一方面,合理配置多点自由度约束,将需要抑制的特定方向上自由度耦合到AWEs上,从而实现方向性保形优化设计.数值算例证明所提出的优化设计方法能在结构刚度拓扑优化设计的基础上实现对局部保形区域在特定方向上翘曲变形的有效控制,与已有约束所有自由度翘曲变形的保形拓扑优化设计相比,方向性保形优化设计在变形控制效果上更加具有灵活性.     

下期目录预告

陈立群　刘曾荣　一类超混沌离散系统的控制肖　潭　刘人怀　斜放四角锥扁网壳的非线性弯曲理论张洪武　钟万勰　顾元宪　三维弹塑性有摩擦接触问题求解的一个新算法周振功　王　彪　双Ⅰ＿型裂纹断裂动力学问题的非局部理论解黄永念　任意二阶张量的特征张量及其特性分析石连栓　孙焕纯　冯恩民　具有动应力和动位移约束的离散变量结构拓扑优化设计方法夏铁成　张鸿庆　闫振亚　一类非线性演化方程新的显式行波解柴　山　张耀明　马　浩　曲庆文　赵又群　汽轮机调节级的气流激振力分析张伟亿　Ｋ·侯赛因　叶　敏　一种改进的范式方法的应…     

离散变量结构优化设计的组合算法*

本文首先给出了离散变量优化设计局部最优解的定义,然后提出了一种综合的组合算法.该算法采用分级优化的方法,第一级优化首先采用计算效率很高且经过随机抽样性能实验表明性能较高的启发式算法─—相对差商法,求解离散变量结构优化设计问题近似最优解 X ;第二级采用组合算法,在 X 的离散邻集内建立离散变量结构优化设计问题的(-1,0.1)规划模型,再进一步将其化为(0,1)规划模型,应用定界组合算法或相对差商法求解该(0,1)规划模型,求得局部最优解.解决了采用启发式算法无法判断近似最优解是否为局部最优解这一长期未得到解决的问题,提高了计算精度,同时,由于相对差商法的高效率与高精度,以上综合的组合算法的计算效率也还是较高的.     

多重约束下空间桁架结构抗风优化

目前复杂结构的抗风优化研究大多集中于高层建筑,很少针对风敏感的大跨屋盖结构．考虑强度、刚度和几何尺寸等多重约束,基于虚功原理和Lagrange乘子将抗风优化转化为无约束问题,编制数值程序整合有限元计算和优化分析两部分,然后对杆件数为10080的实际双层柱面网壳进行优化设计,讨论了设计变量可行域、初始值和调整步选择等对优化结果的影响．研究表明,采用本文方法可实现对空间桁架结构进行多重约束下的高效抗风优化设计,网壳总重降低约37%,风致响应分布不均使得有必要设定可行域下限,而设计变量初值和调整步选择不影响最后的优化结果．     

基于对偶二次规划的大型框架结构优化方法

将准则法和数学规划相结合,对于不同的约束采用不同的处理方法:应力约束作为局部性约束,用0阶近似进行处理,借助满应力准则将其转化为动态尺寸下限;位移约束作为全局性约束,根据单位虚载荷法将其显式化,从而建立了满足应力和位移约束的框架结构截面优化的显式模型．为了提高模型的求解效率,根据对偶理论将大规模的框架结构优化问题转化为仅仅几个对偶变量的对偶问题,采用二次规划方法求解,算例证明该方法能极大的提高模型的求解效率．采用近似射线步既能减小计算量又能使迭代过程更加平稳,采用删除无效约束技术能减小优化模型的规模. 以MSC/Nastran软件为结构分析的求解器,以MSC/Patran软件为开发平台,完成了满足刚度和强度的多工况、多变量的框架截面优化软件．算例结果表明上述程序算法的高效性．     

非完整约束Hamilton动力系统保结构算法

基于变分积分的思想和对偶变量表示的Lagrange-d’Alembert原理,构造了一类求解非完整约束Hamilton动力系统的高阶保结构算法.基于变分积分法,选取适当的多项式及数值积分方法,将对偶变量形式的Lagrange-d’Alembert原理进行离散.在此离散原理的基础上,以积分区间两端位移为独立变量,同时要求在区间端点处及区间内部的控制点处严格满足非完整约束,从而得到数值积分方法.给出了算法的对称性证明.数值算例表明算法具有高阶收敛性,严格满足非完整约束,且在长时间仿真后,依然能保持良好的数值性质.     

基于对偶混合变分形式的Uzawa型算法

基于弹性接触问题的三变量（应力，位移，接触边界位移）对偶混合变分形式，对混合有限元离散化的单边约束问题，提出了一种Uzawa型算法。首先证明了迭代算法的收敛性，然后用数值例子验证了迭代算法的有效性。     

Optimization of arches using genetic algorithm

An optimization procedure is presented for the minimum weight and strain energy optimization for arch structures subjected to constraints on stress, displacement and weight responses. Both thickness and shape variables defining the natural line of the arch are considered. The computer program which is developed in this study can be used to optimize thick, thin and variable thickness curved beams/arches. An automated optimization procedure is adopted which integrates finite element analysis, parametric cubic spline geometry definition, automatic mesh generation and genetic algorithm methods. Several examples are presented to illustrate optimal arch structures with smooth shapes and thickness variations. The changes in the relative contributions of the bending, membrane and shear strain energies are monitored during the whole process of optimization.     

Large scale structural synthesis

A general purpose optimization program is coupled to a large scale finite element program to provide an efficient tool for structural synthesis. The resulting interface program may be used to design structures for minimum weight, subject to constraints on stress, displacement, and vibration frequencies. A variety of state-of-the-art techniques are employed, including design variable linking, constraint deletion, reciprocal variables, and formal approximations. The capability is demonstrated with the design of a gear housing using 30 design variables and over 5000 nonlinear inequality constraints. The finite element model consists of over 1600 elements and 7000 displacement degrees of freedom. The design required six detailed finite element analyses and approximately one hour on a Cray-1s supercomputer. It is concluded that structures of practical size and complexity can be efficiently designed using numerical optimization.     

Multiple-Load Truss Topology and Sizing Optimization: Some Properties of Minimax Compliance

This paper considers the mathematical properties of discrete or discretized mechanical structures under multiple loadings which are optimal w.r.t. maximal stiffness. We state a topology and/or sizing problem of maximum stiffness design in terms of element volumes and displacements. Multiple loads are handled by minimizing the maximum of compliance of all load cases, i.e., minimizing the maximal sum of displacements along an applied force. Generally, the problem considered may contain constraints on the design variables. This optimization problem is first reformulated in terms of only design variables. Elastic equilibrium is hidden in potential energy terms. It is shown that this transformed objective function is convex and continuous, including infinite values. We deduce that maximum stiffness structures are dependent continuously on the bounds of the element volumes as parameters. Consequently, solutions to sizing problems with small positive lower bounds on the design variables can be considered as good approximations of solutions to topology problems with zero lower bounds. This justifies heuristic approaches such as the well-known stress-rationing method for solving truss topology problems.     

An evolutionary programming approach to mixed-variable optimization problems

Many engineering optimization problems frequently encounter discrete variables as well as continuous variables and the presence of nonlinear discrete variables considerably adds to the solution complexity. Very few of the existing methods can find a globally optimal solution when the objective functions are non-convex and non-differentiable. In this paper, we present a mixed-variable evolutionary programming (MVEP) technique for solving these nonlinear optimization problems which contain integer, discrete, zero-one and continuous variables. The MVEP provides an improvement in global search reliability in a mixed-variable space and converges steadily to a good solution. An approach to handle various kinds of variables and constraints is discussed. Some examples of mixed-variable optimization problems in the literature are tested, which demonstrate that the proposed approach is superior to current methods for finding the best solution, in terms of both solution quality and algorithm robustness.     

Optimización mixta de estructuras de transporte de energía: aplicación del algoritmo de recocido simulado

A general methodology to optimize the weight of power transmission structures is presented in this article. This methodology is based on the simulated annealing algorithm defined by Kirkpatrick in the early ‘80s. This algorithm consists of a stochastic approach that allows to explore and analyze solutions that do not improve the objective function in order to develop a better exploration of the design region and to obtain the global optimum. The proposed algorithm allows to consider the discrete behavior of the sectional variables for each element and the continuous behavior of the general geometry variables. Thus, an optimization methodology that can deal with a mixed optimization problem and includes both continuum and discrete design variables is developed. In addition, it does not require to study all the possible design combinations defined by discrete design variables. The algorithm proposed usually requires to develop a large number of simulations (structural analysis in this case) in practical applications. Thus, the authors have developed first order Taylor expansions and the first order sensitivity analysis involved in order to reduce the CPU time required. Exterior penalty functions have been also included to deal with the design constraints. Thus, the general methodology proposed allows to optimize real power transmission structures in acceptable CPU time.     

多周期多种设备公用工程系统优化模型的改进及应用

本文提出了多周期多种设备公用工程系统改进的混合整数双线性优化模型,它含有两种优化变量和系统运行过程的离散动态约束,期望系统总设备投资(含设备折旧)与全周期运行操作费用之和最小。针对改进优化模型求解上的困难,给出将改进优化模型分解成有限多个关于连续变量的线性规划。论述了改进优化模型与分解模型的等价性以及两种模型的主要数学性质,并在此基础上提出了求解策略。最后将改进优化模型应用于某石化企业的蒸汽动力系统最优设计与运行优化集成实例。