基于近似模型辅助智能算法的变截面点阵结构优化设计方法EI北大核心CSCD

桁架类点阵结构具有质量轻、比强度/比刚度高、减振吸能性好,且拓扑构型简单、增材成型可靠性高等优点,被广泛应用于航天器各关键承载部件设计。传统桁架类点阵设计大多囿于等截面设计约束,严重制约了优化设计的寻优潜能,难以满足航天器结构超轻质、高强度的性能要求。为突破传统点阵的等截面形状约束,构建基于显式拓扑描述函数的变截面几何描述模型,实现变截面点阵几何形状的自由描述;采用能量均匀化方法精确计算变截面点阵单胞宏观等效弹性张量,并建立变截面点阵几何描述参数关于其宏观等效弹性张量的近似响应模型;以变截面点阵的几何描述参数为设计变量,材料用量为约束条件,最大体积模量或最大剪切模量为目标函数,建立变截面点阵几何描述参数的优化数学模型,并采用基于近似模型辅助的粒子群优化算法实现上述优化模型的高效求解。数值算例表明,相较于等截面点阵,在相同材料用量下,优化后的变截面点阵的体积模量和剪切模量性能更优。所提方法进一步拓展了桁架类点阵的设计空间,有效提升其力学性能,在航天器结构轻量化设计方面具有应用推广前景。     

结构优化设计的几个方法

本文阐明作者提出的几个结构优化设计方法。全文分为四部分。第一部分给出复杂结构满应力设计的浮动指数法、冻结内力法和拱坝的满应力设计方法,利用这些方法可对各种复杂结构进行满应力设计。第二部分给出一个边界搜索法,收敛速度较快。第三部分给出结构几何优化的混合方法。第四部分给出结构重分析的内力线性化方法,和两阶段优化方法。     

求解实对称矩阵区间特征值问题的直接优化法

提出了一种用于对称区间矩阵特征值问题求解的直接优化法。将区间矩阵中为区间量的各元素作为优化设计变量,将区间量的分布区间作为相应的设计变量的边界约束,运用约束优化法求出区间矩 最大特征值和最小特征值,从而获得区间矩阵特征值问题的解。本文提出的直接优化法适用于对称区间矩阵的标准特征值问题和广义特征值问题。文中给出的两个计算实例显示了该法的有效性。     

基于Newmark法敏度计算的刚架结构动力优化

提出一种有效的求解结构最小质量设计,同时满足动位移和动应力约束的二阶优化设计方法。在有限元法和纽马克法基础上导出一种高效的动应力、动位移对设计变量一阶导数和二阶导数的算法。建立含时间参数,以结构质量最小化为目标,同时满足动位移、动应力和设计变量约束的优化数学模型,通过积分型内点罚函数将含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题。利用动位移、动应力对设计变量一阶导数和二阶导数的信息计算内点罚函数的梯度和海森矩阵,利用梯度和海森矩阵构造求解优化设计问题高效有效的二阶优化算法。算例结果表明该文的优化设计方法能获得刚架结构的局部最优设计,优化的效率高于增广拉格朗日乘子法。     

一种高层混凝土建筑结构的优化设计方法

本文提出了一种有效实用的，对多层及高层混凝土建筑结构进行自动优化设计的算法，这种算法以有限元分析为基础，有机地结合了目前较流行的优化方法－一种严格推导的优化准则进工程师强有力的设计工具，它将结构构件的截面尺寸作为设计变量，在构件单元的强度，多层间的偏转角和位移，以及构件单元尺寸的限制等约束条件下，求解以结构重量为目标函数的最优解，一些算例表明此算法十分有效，可靠，可适用于大型高层混凝建筑结构的分析     

基于有理逼近和灵敏度分析的结构动力重分析方法

提出了一种新的结合特征灵敏度直接法和向量值函数有理逼近的结构动力重分析方法。给出了直接法简单特征对n阶灵敏度分析的一般表达式。利用向量值函数有理逼近，减小固有振型n阶Taylor展开的截断误差。数值算例表明，对结构设计参数作大修改时，该方法能够给出高精度的逼近结果。新方法不需要系统的全部模态，因此，适用于大型复杂结构的动力重分析。     

离散变量结构优化设计的最优综合效能法

针对结构优化问题的位移约束,引入关键约束的界约参数,提出了结构位移统一约束的缩减形式,从而简化了结构优化模型。根据离散变量结构优化问题的特点,提出了效能系数的概念,它衡量设计变量在离散邻域范围内变化对目标函数与约束函数值的影响,并研究了基于效能系数取值分类的四种主要调整方式。根据结构应力和位移约束的影响区域属性,以综合效能最大化为引导,提出了求解离散变量结构优化问题的最优综合效能法。算例结果显示该算法具有良好的优化效率,可求得问题的最优解或获得历史上的最优记录。     

大跨拱支预应力网壳结构的模糊优化设计研究

针对武汉长江防洪模型展示大厅采用的大跨拱支预应力网壳结构,考虑优化目标函数与约束条件的模糊性,建立了该类结构体系的模糊优化设计数学模型;求解时首先通过约束水平截集法,将模糊优化模型转化为一系列确定性优化模型;然后基于拱支预应力网壳的结构特点,将预应力构件(拉索和吊杆)截面尺寸、预应力作用取值(构件初始应变)以及非预应力构件截面尺寸等优化设计变量分别归为不同的优化级别,采用分级优化思想对确定性优化模型进行求解;最后依据结构经济性与安全性平衡的目标求出结构的最优约束水平,从而得到最优的结构设计方案,并同时确定结构的合理预应力分布,由此形成了拱支预应力网壳结构的两阶段三级模糊优化设计方法。     

空间反射镜轻量化结构的拓扑优化设计

为满足较高面形要求,实现空间反射镜的高度轻量化设计,在直径500 mm 圆反射镜的设计过程中引入拓扑优化方法.依据变密度法建立SIMP模型,在反射镜光轴方向重力的工况下,以结构整体柔度为设计约束,最小体积为设计目标,经过选代,得到了RMS值小于5nm,轻量化率达到75.83%的结构.在同等质量下,传统的三角形孔轻量化结构的RMS值为8.17nm,轻量化率为67.39%.并对优化后的结构与三角形轻量化结构在径向重力工况下进行了面形对比,计算结果满足设计要求.拓扑优化的轻量化方式在面形和轻量化率上都优于传统形式.     

卷边槽钢纯弯构件畸变屈曲板组约束系数的直接强度法分析

现行国家规范《冷弯薄壁型钢结构技术规范》（GB50018-2002）提出适用于各种型钢构件板组的约束系数统一计算公式。针对冷弯薄壁卷边槽钢纯弯构件畸变屈曲运用直接强度法计算受压翼缘板组约束系数,并与GB50018-2002计算结果比较,得到一些有价值的结论,供设计研究参考。     

机械弹性车轮径向刚度特性及影响因素研究

为解决充气轮胎爆胎的问题,提高车辆防刺破及越野路面的行驶性能,对非充气结构机械弹性车轮径向刚度特性及影响因素进行研究。建立了机械弹性车轮非线性有限元模型,并通过负荷特性试验验证了模型的有效性;分析了使用条件和车轮结构等因素对机械弹性车轮径向刚度的影响,揭示了地面约束、材料、垂直载荷及力矩对车轮固有频率和振型的影响规律,为机械弹性车轮结构及整车动力学特性优化提供了参考。     

多工况下杆系结构的概率优化设计

研究了基于概率的杆系结构多工况优化设计问题。建立了以杆系截面积为设计变量,结构位移、单元应力可靠度和尺寸限为约束条件,使结构重量极小化设计的数学模型。通过将概率约束等价化处理使之转变为常规约束形式,以紧约束处理策略确定有效约束。最后利用齿行法求解。算例表明文中的模型和方法是合理的和有效的。     

A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables

A search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems. This procedure, known as a genetic algorithm (GA). utilizes a blending of the principles of natural genetics and natural selection. A lack of dependence on the gradient information makes GAs less susceptible to pitfalls of convergence to a local optimum. To model the multiple objective functions in the problem formulation, a co-operative game theoretic approach is proposed. Examples dealing with single and multiobjective geometrical design of structures with discrete–continuous design variables, and using artificial genetic search are presented. Simulation results indicate that GAs converge to optimum solutions by searching only a small fraction of the solution space. The optimum solutions obtained using GAs compare favourably with optimum solutions obtained using gradient-based search techniques. The results indicate that the efficiency and power of GAs can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency.     

Constrained minimization of vibrational magnitudes using a modal reduction method

A numerically effective method is suggested and applied for evaluating objective and constraint functions when so-called vibrational magnitudes of a mechanical structure are minimized. General damped linear structures under external harmonic loading are considered. The magnitude functions studied can relate to displacements, velocities and accelerations and also to sectional and reactive forces. Both magnitudes at a specific frequency and peak magnitudes and averaged magnitudes over a frequency range are investigated. An arbitrary set of magnitude functions can be used in the constraints. Design variables are masses, dampings and stiffnesses of discrete and discretized continuous elements contained in the structure. The objective and constraint functions are expressed by use of the modal parameters (generally complex-valued) of the structural system. A reduced modal model is established and updated during the optimization process. Approximate derivatives (sensitivities) of the objective and constraint functions with respect to changes in design variables are calculated employing perturbed modal parameters. The optimization problem is solved by use of a primal method. Numerical examples demonstrate applications to the classical damped vibration absorber with two design variables and to a beam system used in a light-weight machine foundation with 14 design variables.     

Swarm algorithms for single- and multi-objective optimization problems incorporating sensitivity analysis

Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.     

基于计算智能技术的结构系统可靠性优化设计

利用随机摄动和Edgeworth级数方法,将非正态随机参数可靠性优化设计中的概率约束转化为等价的确定性约束,并运用粒子群算法迅速准确地获得结构系统可靠性优化设计的初始点。针对多失效模式的结构系统,提出了随机模拟-小波神经网络方法(MCS-WNN),有效解决了结构系统的可靠性仿真。并提出了一种便于逆映射的小波神经网络模型,实现了设计参数的可靠性优化。实验结果表明上述方法是行之有效的。     

A hybrid artificial neural network method with uniform design for structural optimization

This paper presents a new hybrid artificial neural network (ANN) method for structural optimization. The method involves the selection of training datasets for establishing an ANN model by uniform design method, approximation of the objective or constraint functions by the trained ANN model and yields solutions of structural optimization problems using the sequential quadratic programming method (SQP). In the proposed method, the use of the uniform design method can improve the quality of the selected training datasets, leading to a better performance of the ANN model. As a result, the ANN dramatically reduces the number of required trained datasets, and shows a good ability to approximate the objective or constraint functions and then provides an accurate estimation of the optimum solution. It is shown through three numerical examples that the proposed method provides accurate and computationally efficient estimates of the solutions of structural optimization problems.     

Multi-objective optimization of fuzzy structural systems

It is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures. Since most practical structural design problems involve several, often conflicting, objectives to be considered, a multi-objective fuzzy programming method is outlined in this work. The fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points. A method of solving a fuzzy multi-objective structural optimization problem using ordinary single-objective programming techniques is presented. The computational approach is illustrated with two numerical examples.     

A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

A bidirectional evolutionary structural optimization algorithm is presented, which employs integer linear programming to compute optimal solutions to topology optimization problems with the objective of mass minimization. The objective and constraint functions are linearized using Taylor's first-order approximation, thereby allowing the method to handle all types of constraints without using Lagrange multipliers or sensitivity thresholds. A relaxation of the constraint targets is performed such that only small changes in topology are allowed during a single update, thus ensuring the existence of feasible solutions. A variety of problems are solved, demonstrating the ability of the method to easily handle a number of structural constraints, including compliance, stress, buckling, frequency, and displacement. This is followed by an example with multiple structural constraints and, finally, the method is demonstrated on a wing-box, showing that topology optimization for mass minimization of real-world structures can be considered using the proposed methodology.