压杆稳定设计的名义应力法

本文从压杆稳定条件出发，推导出了压杆截面设计的名义应力法。该方法避免了多次试算，它是压杆截面设计最简便的方法。     

位移约束桁架尺寸优化设计的改进齿形法

该文提出一种改进齿形法应用于具有应力与位移约束的桁架尺寸优化问题。对于应力约束所需的杆件截面积由杆件各工况荷载下的最大内力来确定。对于位移约束所需的杆件截面积,按当前迭代位移比最大的位移约束、采用桁架满位移设计准则确定。分别计算应力约束和位移约束的杆件截面积比,取二者较大者并施加松弛系数作为准则步时杆件截面积更新的参数。对三杆及十杆平面桁架的算例进行了优化设计研究,结果表明该文提出的方法稳定性好、收敛速度快、优化效果好、应用简单。     

钢管桁架拱平面内失稳与破坏机理的数值研究

对两铰圆弧形钢管桁架拱的弹性及弹塑性失稳机理及承载性能进行了深入研究,考虑了全跨和半跨水平均布荷载、跨中及1/4跨集中荷载等多种类型的荷载效应。分析了钢管桁架拱在不同荷载作用下的失稳破坏机理,指出其会发生整体失稳、弦杆局部失稳、腹杆局部失稳以及局部与整体的相关失稳等多种破坏模式。考察了矢跨比、腹杆尺寸、腹杆夹角和截面宽高比等不同参数对钢管桁架拱稳定承载力的影响,为桁架拱稳定设计方法的建立奠定了重要基础。     

基于智能优化算法的机场航站楼桁架结构设计

进行更加安全稳定和轻质量的桁架结构设计,对机场航站楼的安全稳定高效运营具有十分重要的意义。该文从宏观万有引力出发,对桁架结构中粒子级别的应力关系进行了分析,建立了启发式的智能优化算法。针对桁架结构设计和优化过程进行数学建模,以质量更轻为优化目标,配置应力条件、位移条件、横截面条件以及频率条件等组合约束。最后以10杆桁架结构为研究对象进行试验研究,试验结果显示：该文提出的优化设计方法可以获得更轻的桁架结构和更快的收敛速度。     

钢桁架结构稳定性与两层面强度优化设计研究

现行桁架结构优化设计方法难以同时满足构件和体系两层面强度需求。鉴于此,利用弹性模量缩减法研究建立了考虑稳定性影响的桁架结构两层面强度优化设计的改进均匀承载法。在桁架杆件的截面轴向强度中引入压杆稳定系数,据此建立考虑稳定性影响的桁架杆件单元承载比计算表达式。根据弹性模量缩减法迭代首步与末步的构件承载比分别确定桁架在构件和体系两个层面的强度系数,建立构件与体系两层面强度之间的显性关系式按照两层面强度系数的目标值调整各构件的截面强度,利用构件承载比均匀度建立桁架结构优化设计的迭代收敛判据。通过对比分析,验证了该文方法建立的结构设计方案,取得了较好经济效果,克服了现行桁架结构优化设计方法难以满足桁架两层面强度需求的缺陷。     

横向力作用下的悬臂桁架结构拓扑优化

研究了应力约束下最小重量悬臂梁桁架结构的拓扑优化设计。根据Michell理论,首先用解析方法和有限元方法建立满应力类桁架连续体结构。然后选择其中部分杆件形成离散桁架作为近最优结构,并建立桁架的拓扑优化解析表达式。采用解析方法证明最优拓扑结构的腹杆中间结点在节长的四分之一位置。最后采用解析和数值方法对自由端受集中力和侧边受均布力作用的桁架进一步拓扑优化,确定了桁架的节数和每节的长度,最后得到拓扑优化桁架结构。得到的拓扑优化桁架比工程上普遍采用的45°腹杆桁架的体积少20%以上。     

基于信息熵改进的粒子群算法在桁架结构

提出了信息熵改进的粒子群优化算法用于解决有应力约束、位移约束的桁架结构杆件截面尺寸优化设计问题.首先介绍了信息熵基本理论和基本粒子群优化算法理论,然后对粒子群优化算法作了合理的参数设置,并将信息熵引入粒子群优化算法的适应函数和停机判别准则中.最后对2个经典的优化问题进行求解并与其他算法进行了比较.数据结果表明信息熵改进后的粒子群优化算法在桁架结构优化设计中优于其他同类算法.     

GEP在桁架结构优化中的应用

介绍基因表达式编程(GEP)算法的基本原理和在参数优化中的实现过程,并将该算法应用于桁架结构的优化设计。针对标准GEP容易陷入局部最优解,且收敛速度慢的缺陷,对算法引入回溯机制,用停滞前一代的精英个体替换当前种群中所有适应度最差的个体,使较优个体有更多机会向不同方向进化,扩大最优解的搜索空间。25杆空间桁架的截面优化设计结果证明:算法改进后,搜索效率得到明显提高,并通过72杆空间桁架算例,证明了该方法在结构优化中的可行性和有效性。     

倒三角截面空间桁架拱平面外弹塑性稳定设计方法研究

该文研究了倒三角截面两铰桁架拱和固支桁架拱的平面外稳定性能:首先介绍了倒三角形桁架拱的平面外弹性屈曲荷载,此后采用大挠度弹塑性有限元方法,通过引入纯压正则化长细比和纯弯正则化长细比,分别建立了纯压和纯弯桁架拱的平面外弹塑性稳定设计方法。在此基础上,研究了杆件的变形对桁架拱平面外整体稳定性能的影响,并通过两个相关系数将该影响体现在稳定承载力设计方程中。进一步,依据有限元数值计算结果,提出了全跨水平均布荷载或半跨水平均布荷载作用下桁架拱的轴力和弯矩稳定承载力设计方程,供倒三角截面桁架拱平面外稳定性设计。     

基于类桁架材料模型的不确定荷载下结构拓扑优化

用区间分析方法研究了不确定荷载下结构拓扑优化方法。采用类桁架材料模型建立拓扑优化类桁架连续体结构。根据区间变量运算法则推导出不确定荷载下应力约束体积最小类桁架结构的拓扑优化方法。首先采用区间分析方法得到任一点的最不利荷载工况下应变状态。在此应变状态下,利用满应力准则优化类桁架材料中杆件的方向和密度。如此反复分析和优化,直至迭代收敛。最后由类桁架中杆件分布场可以近似离散得到桁架结构。通过几个数值算例验证了方法的有效性。数值算例显示了不确定荷载下的结构拓扑优化布局更合理。     

A mixed integer programming for robust truss topology optimization with stress constraints

This paper presents a mixed integer programming (MIP) formulation for robust topology optimization of trusses subjected to the stress constraints under the uncertain load. A design‐dependent uncertainty model of the external load is proposed for dealing with the variation of truss topology in the course of optimization. For a truss with the discrete member cross‐sectional areas, it is shown that the robust topology optimization problem can be reduced to an MIP problem, which is solved globally. Numerical examples illustrate that the robust optimal topology of a truss depends on the magnitude of uncertainty. Copyright © 2010 John Wiley & Sons, Ltd.     

基于SAND列式的桁架结构优化问题序列线性规划算法

该文提出了一种基于协同分析和设计列式(即SAND 列式,Simultaneous Analysis and Design)和序列线性规划(Sequential Linear Programming)技术的桁架结构优化新方法。与传统列式下将隐式响应函数(如位移、应力等)于设计变量(如杆件截面积等)处作线性展开的做法不同,以桁架结构为例,该文在SAND 列式下,采用杆件截面积和结构节点位移同时作为设计/分析变量,仅对杆件协调条件这一显式双线性函数予以线性近似并构造LP子问题。通过求解一系列LP子问题,可以得到优化问题的近似最优解。与传统优化列式下的SLP 方法相比,该文方法不仅设计变量运动极限的选取相对容易,而且线性近似的误差可以精确估计。数值算例表明,采用该文算法可以快速、稳定地得到优化问题的近似最优解。     

An integrated approach to the synthesis of geometrically non-linear structures

An integrated approach to the minimum weight design of geometrically non-linear three dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The non-linear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the contraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically non-linear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.     

Practical design optimization of truss structures using the genetic algorithms

Truss structures are widely employed in the industrialized world. They appear as bridges, towers, pylons, roof supports, building exoskeletons or high technology light space structures. This paper investigates the simultaneous size, geometry and topology optimization of real life large truss structures using genetic algorithms (GAs) as optimizer and finite element method as analyzer. In general, the large truss structures are constructed for practical reasons from the duplication of some basic structures called bays. Thus, the final optimum design may be reached by optimizing the characteristics of the basic bays instead of optimizing the whole structure. Both single and multiobjective functions based on the mass of the structure and the maximum nodal displacement have been considered as the cost functions. In order to obtain realistic optimal designs, the cross-sectional areas have been extracted from the standard profiles according to AISC codes and practical conditions are imposed on the bays. The design optimization problem is also constrained by the maximum stress, maximum slenderness ratio and the maximum and minimum cross-sectional area of the truss members. To accommodate all these constraints, two different penalty functions are considered. The first penalty function considers the normalization of violated constraints with respect to the allowable stress or slenderness ratio. The second penalty function is a constant function which is used to penalize the violations of the slenderness ratio. Three illustrative examples of realistic planar and space truss structures have been optimized to demonstrate the effectiveness of the proposed methodology. However, other criteria such as cost and/or manufacturability could be quantified and included in the optimization formulation.     

Evolutionary Algorithm Integrating Stress Heuristics for Truss Optimization

The optimal truss design using problem-oriented evolutionary algorithm is presented in the paper. The minimum weight structures subjected to stress and displacement constraints are searched. The discrete design variables are areas of members, selected from catalogues of available sections. The integration of the problem specific knowledge into the optimization procedure is proposed. The heuristic rules based on the concept of fully stressed design are introduced through special genetic operators, which use the information concerning the stress distribution of structural members. Moreover, approximated solutions obtained by deterministic, sequential discrete optimization methods are inserted into the initial population. The obtained hybrid evolutionary algorithm is specialized for truss design. Benchmark problems are calculated in numerical examples. The knowledge about the problem integrated into the evolutionary algorithm can enhance considerably the effectiveness of the approach and improve significantly the convergence rate and the quality of the results. The advantages and drawbacks of the proposed method are discussed.     

A GA‐based technique for layout optimization of truss with stress and displacement constraints

Various developments of increasing complexity involved in layout optimization are discussed. The use of conventional GA in layout optimization is briefly mentioned with emphasis on its limitations and conditions imposed in finding the optimal design. The proposed new technique is applied to the benchmark example of Michell's truss for verification. The approach has also been applied to new examples of bridge truss and crane truss problems in order to demonstrate the generality and robustness for topology optimization. The approach is extended to include dual stress‐displacements constraints since many practical problems involve these two constraints simultaneously. Two‐bar and 10‐bar trusses are solved as examples for layout optimization with both stress and displacement constraints with satisfactory results. The effect of mutation on the final topology is also discussed. The major drawbacks of the ground structure approach are overcome in this proposed new method. The optimal designs obtained demonstrate the ability, robustness and generality of using the proposed new technique in layout optimization problems. Copyright © 2001 John Wiley & Sons, Ltd.     

基于并行混沌和复合形法的桁架结构形状优化

针对多工况下受应力、位移和局部稳定性约束的桁架形状优化问题,提出了基于并行混沌优化算法和复合形法的混合优化算法。该算法综合利用了并行混沌的全局搜索能力,复合形法的快速局部搜索能力和混沌细搜索。首先,利用并行混沌优化算法快速搜索到全局最优解附近,然后应用改进复合形法以并行混沌的优化解为初始复形进行搜索,提高了最优解的搜索速度,最后应用混沌细搜索策略提高最优解的精度。两个典型数值算例验证了该混合优化方法对桁架形状优化问题的有效性和稳定性。     

基于遗传算法的离散型结构拓扑优化设计

采用遗传算法求解包括桁架结构和框架结构的离散型结构拓扑优化问题。在遗传算法的基础上,通过引入拓扑变量并修改被删除杆件的材料弹性模量,提出了一个受多工况荷载作用,能同时考虑应力、稳定及位移等约束的离散型结构拓扑优化问题统一数学模型。该模型不但能同时适用于桁架结构和框架结构等离散型结构拓扑优化问题,而且还能解决奇异最优解问题。结合上述统一数学模型和遗传算法,给出了求解离散型结构拓扑优化问题的优化方法。算例结果表明,采用该文提出的拓扑优化方法可有效、方便地对桁架结构、框架结构等离散型结构进行拓扑优化设计。     

Optimization of truss topology using tabu search

A design procedure for integrating topological considerations in the framework of structural optimization is presented. The proposed approach is capable of considering multiple load conditions, stress, displacement and local/global buckling constraints, and multiple objective functions in the problem formulation. Further, since the proposed method permits members to be added to or deleted from an existing topology and the topology is not defined by member areas, the difficulty of not being able to reach singular optima is also avoided. These objectives are accomplished using a discrete optimization procedure which uses 0–1 topological variables to optimize alternate designs. Since the topological variables are discrete in nature and the member cross-sections are assumed to be continuous, the topological optimization problem has mixed discrete-continuous variables. This non-linear programming problem is solved using a memory-based combinatorial optimization technique known as tabu search. Numerical results obtained using tabu search for single and multiobjective topological optimization of truss structures are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that the optimum topologies obtained using tabu search compare favourably, and in some instances, outperform the results obtained using the ground–structure approach. However, this improvement occurs at the expense of a significant increase in computational burden owing to the fact that the proposed approach necessitates that the geometry of each trial topology be optimized.