改进的多目标启发式粒子群算法及其在桁架结构设计中的应用

针对工程结构多目标优化设计中出现的约束条件处理能力差、编程复杂,计算效率低且收敛精度差等问题,对启发式粒子群算法(HPSO)进行改进,提出了多目标启发式粒子群算法(MOHPSO),并与多目标粒子群算法(MOPSO)和改进的多目标群搜索算法(IMGSO)进行比较。通过对15杆平面桁架、40杆平面桁架和72杆空间桁架3个经典算例的计算,证明了所提出的MOHPSO算法的有效性。结果表明:MOHPSO算法具有收敛精度高、约束处理能力强、全局最优解选取更合理、非劣解集维护效率高等特点。     

粒子群优化算法在桁架优化设计中的应用

粒子群优化（PSO）算法是近年来发展起来的一种基于群智能的随机优化算法,具有概念简单、易于实现、占用资源低等优点。为了解决有应力约束和位移约束的桁架的尺寸优化问题,将PSO算法应用于桁架结构的尺寸优化设计。首先介绍了原始的PSO算法的基本原理,然后引入压缩因子改进了PSO算法,并提出合理的参数设置值。对几个经典问题进行了求解,并与传统的优化算法和遗传算法进行了比较。数值结果表明,改进的PSO算法具有良好的收敛性和稳定性,可以有效地进行桁架结构的尺寸优化设计。     

微分演化算法在桁架形状优化中的应用

为了获得全局最优和解决具有应力约束、几何约束以及局部稳定性约束的桁架形状优化问题中2类不同设计变量耦合给优化带来的困难,将1种新型智能优化算法——微分演化(Differential Evolution,DE)应用于桁架结构的形状优化问题中。给出了考虑节点坐标和截面面积两类不同性质的设计变量的桁架结构优化的数学模型,并对几个经典的桁架结构进行优化,将所得结果与其他优化算法结果进行了比较。数值结果表明了DE算法具有良好的收敛性和稳定性,可以有效地进行桁架结构的形状优化设计。     

基于改进双向渐进结构优化法的桁架结构拓扑优化

为了将双向渐进结构优化法应用于桁架结构优化设计中,结合能量原理和满应力设计准则,推导了以结构最小应变能为目标函数的优化计算公式,提出了可以应用于桁架结构优化的桁架-双向渐进结构优化(T-BESO)法.T-BESO法以杆件截面面积为设计变量,以结构应变能为目标函数,以应力约束和满应力设计准则为约束条件.在T-BESO法中...     

满应力齿行法中松弛系数对桁架结构优化的影响

用M ATLAB编制了优化程序,实现带位移约束的桁架满应力优化设计方法,在迭代过程中引入松弛系数,并通过算例分析松弛系数对优化结果的影响及其原因.     

Optimum design of steel truss arch bridges using a hybrid genetic algorithm

The design of steel truss arch bridges is formulated as an optimization problem. The objective function considered is the weight of the steel truss arch bridge. The objective function is minimized subjected to the design constraints of strength (stress) and serviceability (deflection). An efficient, accurate, and robust algorithm is proposed for optimal design of steel truss arch bridges. The proposed algorithm integrates the concepts of the genetic algorithm (GA) and the finite element method. A real-coded/integer-coded method is used to realistically represent the values of the design variables. Three GA operators consisting of constraint aggregate selection procedure, arithmetic crossover, and non-uniform mutation are proposed. Finite element method is used to compute values of implicit objective functions. A numerical example involving a detailed computational model of a long span steel truss arch bridge with a main span of 552 m is presented to demonstrate the applicability and merits of the proposed method.     

基于全局优化设计的桁架结构优化设计研究

桁架结构优化设计中普遍存在约束的作用.现有优化设计一般采用满应力法和遗传优化等优化方法,编程复杂.本文介绍了优化设计软件LINGO10.0的功能、特点、使用方法和使用注意事项等,建立了桁架结构优化设计的数学模型.采用LINGO软件的全局优化方法求解.实例计算表明,采用LINGO的全局优化方法能获得全局优化解,且方法简单,值得推广应用.     

Total Optimal Synthesis Method for Truss Structures Subject to Static and Frequency Constraints

Abstract: In a previous study, we presented an efficient optimal structural synthesis method for truss structures in which the design variables are coordinates of the panel points, cross-sectional areas, and discrete material kinds subjected to stress and displacement constraints. In this paper, the synthesis method is extended to solve design problems subject to stress, displacement, and fundamental natural-frequency constraints. The design problem is formulated in terms of discrete material kinds and continuous shape and sizing variables and which are approximated by a convex and separable subproblem. The approximate subproblem is expressed in direct and/or reciprocal design variables and shape, material, and sizing sensitivities. Each subproblem is solved by a two-stage minimization process. In the first stage, the continuous shape and sizing variables are optimized by a dual method. Second, the discrete material and continuous sizing variables are improved by a discrete sensitivity analysis. Using the proposed two-stage minimization procedure, both the discrete material kinds and the continuous shape and sizing variables can be systematically improved to obtain an optimal solution. The rigorousness, reliability, and efficiency of the method are illustrated by applying it to the minimum cost design of truss structures subject to stress, displacement, and fundamental natural-frequency constraints.     

Two-stage Optimization Based on Force Method for Damage Identification of Planar and Space Trusses

In this study, an efficient two-stage optimization procedure based on the force method is proposed to properly identify the sites and extents of multiple damages in the planar and space truss structures. In the first stage, the elements which have the higher probability of damages are selected by using the anti-optimization (AO) method and the weighed sum procedure. In the second stage, the genetic algorithm (GA) is performed to determine the actual damage sites and their extents based on the force method. The accuracy and effectiveness of the proposed method are proved through the planar and space truss structures. The results from the present study indicate that the combination of the first stage with the second one can provide a reliable tool to accurately and efficiently identify the multiple damages of truss structures.     

Generalized inverse approach for static behaviour of constrained structures

The problem of structure subjected to certain external causes is established by a mathematical system consisting of equilibrium equations and prescribed constraint conditions. The satisfaction of constrained trajectories depends on an exact calculation of constraint forces required for satisfying the constraints. Most work related to this subject calculate the constraint forces using a numerical approach including undetermined Lagrange multipliers. However, the Lagrange multipliers method has difficulty in handling systems subjected to several tens of constraints. Starting from the difference in potential energy of structures with and without constraints, this study derives the equilibrium equation of constrained structures. It is shown that the derived equations coincide with the results obtained from previous work. The effectiveness and simplicity of the proposed method are illustrated through the static control of continuous structure and the reanalysis of a simple truss structure with a floating substructure. Copyright © 2005 John Wiley & Sons, Ltd.     

Reliability-based optimization of steel truss arch bridges

A reliability-based optimization approach is developed and applied to minimize the weight of steel truss arch bridges subject to probabilistic (the overall probability failure of the structure) and deterministic (stress and deflection) constraints. The method intelligently integrates the genetic algorithm (GA), the finite element method and the first order reliability method. A real-coded/integer-coded method is used to realistically represent the values of the design variables. Three GA operators consisting of constraint aggregate selection procedure, arithmetic crossover, and non-uniform mutation are proposed. The finite element method (FEM) and the first order reliability method are used to compute the value of the probabilistic and deterministic constraint functions. A numerical example involving a detailed computational model of a long span steel arch bridge with a main span of 550 m is presented to demonstrate the applicability and merits of the present method. Finally, several important parameters in the present method are discussed.     

Frequency-constrained optimization of space frames having general cross-sectional relationships∗

An optimality criteria (OC) method is presented for weight optimization of space frames having general cross-sectional relationships. The space frames support a sizeable amount of non-structural mass, while multiple natural frequency constraints, and minimum and maximum gauge restrictions are imposed on their design. The iterative design method involves alternately satisfying the constraints (scaling) and applying the Kuhn-Tucker (optimality) condition (resizing). The primary sizing variables (cross-sectional areas), and indirectly the secondary ones (two principal moments of inertia and a torsional constant), are uniformly scaled to the constraint surfaces using a nonlinear closed-form formulation. No exact scaling formulation for this class of problem has been proposed and tested in the optimization literature hitherto. The closed-form scaling procedure is united with an adaptable design strategy in which linear extrapolates of past-scaled design vectors are coupled with automatically-tuned OC recursive methods. Elementary design examples are presented to demonstrate the method. On average, the method achieves a stable upper-bound convergence of weight minima, as it quickly dissolves the (sometimes violent) oscillations of scaled weights in the iteration history. Most of all, the present design strategy eliminates the need for adjustments of internal parameters during the redesign phase.     

Constrained mean‐variance mapping optimization for truss optimization problems

Truss optimization is a complex structural problem that involves geometric and mechanical constraints. In the present study, constrained mean‐variance mapping optimization (MVMO) algorithms have been introduced for solving truss optimization problems. Single‐solution and population‐based variants of MVMO are coupled with an adaptive exterior penalty scheme to handle geometric and mechanical constraints. These tools are explained and tuned for weight minimization of trusses with 10 to 200 members and up to 1,200 nonlinear constraints. The results are compared with those obtained from the literature and classical genetic algorithm. The results show that a MVMO algorithm has a rapid rate of convergence and its final solution can obviously outperform those of other algorithms described in the literature. The observed results suggest that a constrained MVMO is an attractive tool for engineering‐based optimization, particularly for computationally expensive problems in which the rate of convergence and global convergence are important.     

A critical evaluation of topology optimization results for strut‐and‐tie modeling of reinforced concrete

Defining a suitable truss model is one of the most important steps of applying the strut‐and‐tie modeling (STM) method to design D‐regions in reinforced concrete (RC) structures. The truss model is a discrete representation of the stress field developed within a region of a concrete element. Topology optimization (TO) methods have been investigated by researchers for about two decades to generate suitable models for the STM method. Several truss models and numerous continuum TO results that could serve as an inspiration for suitable truss models have been proposed. However, limited attention has been paid to the evaluation of various TO results in the perspective of the STM method. As a result, it is at present unclear to what extent TO results offer a benefit for STM modeling, and which method should be preferred. In order to address this gap, an automatic and objective evaluation procedure is proposed in this paper. First, a TO result extraction method is proposed to systematically convert optimized topologies to truss‐like structures. Next, based on the extracted structures, three evaluation measures are formulated to evaluate TO results. These measures indicate whether an analyzable truss model could be extracted, to which extent tensile stress regions are covered by tensile ties and how economical the design will be. The effectiveness of the proposed evaluation procedure is validated using known STM solutions. Subsequently, the evaluation procedure is applied to 23 TO results from the literature, covering three different design problems. Most TO results show a good performance in covering tensile regions and would result in economical designs, and some undesired topologies are also identified by the evaluation method. Nevertheless, the use of continuum TO is most hampered by difficulties in identifying a suitable truss from the TO results.     

Border-search and jump reduction method for size optimization of spatial truss structures

This paper proposes a sensitivity-based border-search and jump reduction method for optimum design of spatial trusses. It is considered as a two-phase optimization approach, where at the first phase, the first local optimum is found by few analyses, after the whole searching space is limited employing an efficient random strategy, and the second phase involves finding a sequence of local optimum points using the variables sensitivity with respect to corresponding values of constraints violation. To reach the global solution at phase two, a sequence of two sensitivity-based operators of border-search operator and jump operator are introduced until convergence is occurred. Sensitivity analysis is performed using numerical finite difference method. To do structural analysis, a link between open source software of OpenSees and MATLAB was developed. Spatial truss problems were attempted for optimization in order to show the fastness and efficiency of proposed technique. Results were compared with those reported in the literature. It shows that the proposed method is competitive with the other optimization methods with a significant reduction in number of analyses carried.     

钢管混凝土组合桁梁桥近、远场抗震性能

基于对传统预应力混凝土连续刚构桥的优化,提出了钢管混凝土组合桁梁桥结构形式,即上部结构采用矩形钢管混凝土组合桁梁,下部结构采用圆形钢管混凝土格构式桥墩。采用数值分析手段对比研究了传统预应力混凝土连续刚构桥、连续刚构优化桥型及新型钢管混凝土组合桁梁桥在近、远场地震作用下的抗震性能。结果表明:钢管混凝土组合桁梁桥、连续刚构优化桥型抗震性能要明显优于传统混凝土连续刚构桥,且钢管混凝土组合桁梁桥抗震性能更佳,近场地震作用下桥墩弯矩下降达41.9%,剪力下降达66.1%,远场地震作用下桥墩弯矩下降达37.5%,剪力下降达76.4%;相较远场地震,近场地震作用致使结构输入的地震能量大幅增加,相同桥型桥墩位移最大增幅达5.7倍,桥墩弯矩最大增幅达3.5倍;钢管混凝土组合桁梁桥是一种抗震性能优越的桥梁结构形式,可为西部地区装配式钢混组合桥梁的设计选型提供参考。     

预应力钢管混凝土桁架应用与研究探讨

通过总结国内外对于预应力结构、钢结构以及钢管混凝土组合结构的研究和应用成果,在简要论述基础上,提出一种新的组合结构型式———预应力钢管混凝土组合结构。本文针对预应力钢管混凝土桁架,通过其受力机理分析,阐述了其设计方法和构造措施,给出了工程应用实例。并对目前正在进行的研究工作及发展方向作了简单探讨。     

Optimal Layout of Bridge Trusses by Genetic Algorithms

In this paper we present an approach to the layout and shape-optimization problem of bridge truss structures using genetic algorithms. The objective is to find an optimal layout design that will have minimum weight or material volume, subject to performance constraints related to member stresses, joint displacements, and member buckling. An automated two-stage optimization search process, which integrates structural analysis by finite-element method, genetic algorithms, and cognitive topology patterns (domain knowledge), is developed to solve the optimal problem. Two examples concerning bridge truss structure are investigated to demonstrate the effectiveness of the proposed method in solving these layout-optimization problems.     

A particle swarm ant colony optimization for truss structures with discrete variables

In this paper, a particle swarm optimizer with passive congregation (PSOPC), ant colony optimization (ACO) and harmony search scheme (HS) are combined to reach to an efficient algorithm, called discrete heuristic particle swarm ant colony optimization (DHPSACO). This method is then employed to optimize truss structures with discrete variables. The DHPSACO applies a PSOPC for global optimization and the ant colony approach for local search, similar to its continuous version. The problem-specific constraints are handled using a modified feasible-based mechanism, and the harmony search scheme is employed to deal with variable constraints. Some design examples are tested using the new method and their results are compared to those of PSO, PSOPC and HPSO algorithms to demonstrate the effectiveness of the present method.     

基于约束多目标优化算法的盾构隧道设计方法

当前盾构隧道的设计仍主要依托于经验确定设计参数,然后对其安全性进行校核,难以定量的考虑成本和控制指标(收敛变形等)的关系。以衬砌厚度、截面配筋率、横向接头螺栓直径为设计参数,以成本及结构的水平收敛变形为优化目标,结合多目标优化的算法,进行了盾构隧道的横断面设计。采用非支配原理,通过引入约束违反函数,实现了基于NSGA-Ⅱ算法的复杂约束条件处理。最后通过具体算例,完成了满足截面安全性要求的限制条件下,完整Pareto前沿面的获取工作,并与无约束优化结果进行了分析对比,说明了迭代过程的收敛性,阐述了所得Pareto前沿面的价值意义,得到了不同设计条件下的最优解。