Comparative seismic design optimization of spatial steel dome structures through three recent metaheuristic algorithms

Steel dome structures, with their striking structural forms, take a place among the impressive and aesthetic load bearing systems featuring large internal spaces without internal columns. In this paper, the seismic design optimization of spatial steel dome structures is achieved through three recent metaheuristic algorithms that are water strider (WS), grey wolf (GW), and brain storm optimization (BSO). The structural elements of the domes are treated as design variables collected in member groups. The structural stress and stability limitations are enforced by ASD-AISC provisions. Also, the displacement restrictions are considered in design procedure. The metaheuristic algorithms are encoded in MATLAB interacting with SAP2000 for gathering structural reactions through open application programming interface (OAPI). The optimum spatial steel dome designs achieved by proposed WS, GW, and BSO algorithms are compared with respect to solution accuracy, convergence rates, and reliability, utilizing three real-size design examples for considering both the previously reported optimum design results obtained by classical metaheuristic algorithms and a gradient descent-based hyperband optimization (HBO) algorithm.     

基于改进序列线性规划法的空间桁架结构优化设计

在空间桁架的优化设计中,仅把截面面积作为设计变量并不能得到结构的最优解。只有把桁架结构的截面面积和节点坐标作为设计变量,才能大幅降低结构重量及造价。空间桁架结构的优化设计多为复杂的非线性问题,序列线性规划法是解决非线性规划问题的典型算法。本文作者将改进的序列线性规划法结合SAP2000 API功能,对空间桁架进行优化设计。数值结果表明,改进的序列线性规划法具有良好的收敛性和稳定性,可以有效地进行空间桁架结构的形状优化设计。     

索穹顶结构全面优化设计方法的研究

通过线性规划、齿形片、模态搜索及一维搜索片的联合应用,提出了索穹顶结构的预应力、截面、矢高、圈数同时优化设计的方法,优化效果明显。可在优化的过程中完成对索穹顶结构的设计。编制了索穹顶结构优化设计的计算程序,并进行了算例分析。     

Optimal design of steel frames under seismic loading using two meta-heuristic algorithms

In this paper, optimal design of steel frames is performed under seismic loading. The variables of the problem are taken as the cross-sectional areas of the members. These variables are considered as discrete, and are selected from a list of existing cross sections. Here, the charged system search and improved harmony search algorithms are utilized for optimization. For optimal design of steel frames in the first phase a time history analysis with the relative lateral displacement constraints is performed, and in the second phase a simultaneous dynamic–static analysis with the relative displacement and stress constraints is utilized using two meta-heuristic algorithms. Moment frames and their shear frame counterparts are considered, and their performances are compared for optimal design. In the case of moment frames, apart from the columns, the cross sections of the beams are also considered as design variables. The results indicate a good performance of the optimized moment frame and show that considering the effect of both drift and stress constraints, instead of only drift constraints, one obtains a better design. These results also show the suitability of the charged system search algorithm for optimal design of frames under seismic loading, as an extremely nonlinear problem.     

基于鲁棒性的索穹顶结构截面优化设计

针对索穹顶结构缺乏有效的基于鲁棒性能的截面优化设计理论现状,基于H∞范数极小控制方法,利用非线性系统运动方程构建输入变量到输出响应的系统传递函数,通过引入L2性能准则并结合随机理论建立索穹顶结构非线性鲁棒性定量评价指标IR,在此基础上,利用MATLAB和ANSYS软件交互算法给出基于遗传算法的截面优化设计的具体步骤,并以内蒙古伊旗一实际肋环型索穹顶工程结构为分析对象,采用遗传算法开展基于结构鲁棒性的截面优化设计。研究表明,杆件截面变化对结构鲁棒性具有不同的敏感性,在保持质量不增加的前提下,通过增加对结构鲁棒性影响敏感构件的截面面积及减少对结构鲁棒性影响不敏感构件的截面面积,可有效提高结构鲁棒性,经优化后鲁棒性提高了39.2%,有效提升了结构抵抗产生不相称破坏的能力。     

空间网格结构基于离散变量的优化设计

空间网格结构离散变量的优化设计是空间网格结构的截面尺寸优化、形状优化、拓扑优化和布局优化的理论基础。本文在建立空间网格结构离散变量优化设计问题数学模型的基础上,分析了空间网格结构离散变量优化设计的特点和算法效率。文中采用相对差商法。对空间网格结构杆件截面尺寸的离散变量优化设计问题进行了研究和探讨。文章最后给出了两个算例,计算结果验证了本文理论的正确性和有效性。     

System reliability of suspension bridges

Provisions for the design of existing suspension bridges often rely on a deterministic basis. Consequently, the reliability of these bridges cannot be assessed if current provisions are applied. In order to develop cost-effective design and maintenance strategies for suspension bridges a system reliability-based approach has to be used. This is accomplished by a probabilistic finite element geometrically nonlinear analysis approach. This study forms part of an investigation into the system reliability evaluation of geometrically nonlinear large span bridges recently undertaken at the University of Colorado. A brief review of reliability analysis of geometrically nonlinear elastic structures allows for the determination of its relevance to the assessment of suspension bridges. A probabilistic finite element geometrically nonlinear elastic code is used for system reliability evaluation of suspension structures. The allowable stress design procedures used by the Honshu Shikoku Bridge Authority for the design of suspension bridges are presented along with their application to the design of an existing bridge. This bridge is studied from a system reliability viewpoint to evaluate its reliability under different loading and damage scenarios. Such information calls attention to the fact that the reliability of cables, hanger ropes and girders are very different. Therefore, optimal maintenance decisions for suspension bridges designed according to allowable stress method are not consistent with those based on equal component reliability values.     

Structural dynamic optimal design based on dynamic reliability

In this work, dimension and shape optimization of structures under stochastic process excitation is addressed in the context of element or system dynamic reliability constraints, where the structural gross mass is taken to be the objective function. Firstly, based on the dynamic response analysis of truss structures under stochastic process loads, the dynamic reliability constraints are developed and simplified, and the normalization of design variables is discussed to avoid some variables being drowned by others during optimization due to their different dimensions and orders of magnitude. The optimal models of dimension and shape with element or system dynamic reliability constraints are then presented. Two numerical examples are finally used to illustrate the results of different optimal designs, which demonstrate that the efficiency to solve the structural optimization with dynamic reliability constraints can be significantly improved if the design variables and their initial values are selected properly.     

Robust design and optimization procedure for piled-raft foundation to support tall wind turbine in clay and sand

A geotechnical design and optimization procedure for piled-raft foundations to support tall wind turbines in clayey and sandy soil are presented in this paper. From the conventional geotechnical design, it was found that the differential settlement controlled the final design and was considered as the response of concern in the optimization procedure. A parametric study was subsequently conducted to examine the effect of the soil shear strength parameters and wind speed (random variables) on the design parameters (number and length of piles and radius of raft). Finally, a robust design optimization procedure was conducted using a Genetic Algorithm coupled with a Monte Carlo simulation considering the total cost of the foundation and the standard deviation of differential settlement as the objectives. This procedure resulted in a set of acceptable designs forming a Pareto front which can be readily used to select the best design for given performance requirements and cost limitations.     

Integrated wind‐induced response analysis and design optimization of tall steel buildings using Micro‐GA

This paper presents an integrated procedure for wind‐induced response analysis and design optimization for rectangular steel tall buildings based on the random vibration theory and automatic least cost design optimization technique using Micro‐Genetic Algorithm (GA). The developed approach can predict wind‐induced drift and acceleration responses for serviceability design of a tall building; the technique can also provide an optimal resizing design of the building under wind loads to achieve cost‐efficient design. The empirical formulas of wind force spectra obtained from simultaneous measurements of surface pressures on various rectangular tall building models in wind tunnel tests are verified testified using a published example. Upon the known wind force spectra, the equivalent static wind loads for every storey, such as along‐wind, across‐wind and torsional loads, are then determined and applied for structural analysis including estimation of wind‐induced responses. An improved form of GAs, a Micro‐GA, is adopted to minimize the structural cost/weight of steel buildings subject to top acceleration and lateral drifts constraints with respect to the discrete design variables of steel section sizes. The application and effectiveness of the developed integrated wind‐induced response analysis and design optimization procedure is illustrated through a 30‐storey rectangular steel building example. Copyright © 2009 John Wiley & Sons, Ltd.     

有支撑钢框架离散型拓扑优化设计

为了研究离散型拓扑优化理论在实际工程中的应用,在遗传算法和渐进结构优化算法的基础上对有支撑钢框架的离散型拓扑优化设计进行了分析.通过引入拓扑变量并修改无效杆件的弹性模量,提出了一个能适用于桁架结构、刚架结构和桁架刚架混合结构的离散型拓扑优化问题统一数学列式.该统一数学列式能解决桁架拓扑优化问题中以截面面积作为设计变量而...     

Optimal design of Schwedler and ribbed domes via hybrid Big Bang-Big Crunch algorithm

An optimum topology design algorithm based on the hybrid Big Bang-Big Crunch optimization (HBB-BC) method is developed for the Schwedler and ribbed domes. A simple procedure is defined to determine the Schwedler and ribbed dome configuration. This procedure includes calculating the joint coordinates and element constructions. The nonlinear response of the dome is considered during the optimization process. The effect of diagonal members on the results is investigated and the optimum results of Schwedler domes obtained by the HBB-BC method demonstrate the efficiency of these domes to cover large areas without intermediate supports.     

A simulation-based method for reliability based design optimization problems with highly nonlinear constraints

Reliability-based design optimization (RBDO) is a topic of interest in the design of economical structures. It allows designers to effectively reach a balanced cost-safety configuration in the design of structures. In this study, a simulation-based method is presented for RBDO problems in which the design variables are treated as random variables. The method works by uniformly distributing samples in the design space and employing a feature that allows the designer to obtain the optimum design solution by performing only one simulation run. Moreover, the proposed feature also helps the designer to use the results of aforementioned run to provide multi-level design solutions when the arrangement of the design problem is changed. The robustness and accuracy of the method are examined by solving design problems with highly nonlinear constraints and comparing with the results of common RBDO methods. The results confirm the robustness of the method for highly nonlinear problems with different design arrangements.     

钢框架结构基于整体优化策略的非线性抗震设计

针对现有抗震优化设计很少考虑结构非线性反应的缺点,提出了整体优化策略,并运用到钢框架结构造价最小的抗震优化设计中。以结构构件截面尺寸为设计变量,结构构件的总体积为目标函数,整体优化策略在以结构弹性强度和弹性变形为约束条件的基础上,增加弹塑性变形为约束条件,与我国抗震设计规范两阶段设计方法相对应,因此基于整体优化策略的优化设计结果可以作为最终的结构设计方案。整体优化策略不仅能够考虑结构的非线性反应,而且可以采用我国抗震规范的相关规定作为约束条件,适用于钢框架结构造价最小的抗震优化设计。     

Application of evolutionary global optimization techniques in the design of RC water tanks

This paper presents evolutionary-based optimization procedures for designing conical reinforced concrete water tanks. The material cost of the tank that includes concrete, reinforcement, and formwork required for walls and floor was chosen as the objective function in the nonlinear optimization problem formulation. The wall thicknesses (at the bottom and at the top), base thickness, depth of water tank, and wall inclination were considered as design variables.Three advanced optimization techniques to solve the nonlinear constrained structural optimization problems were investigated. These methods are: (1) Shuffled Complex Evolution (SCE), (2) Simulated Annealing (SA) and Genetic Algorithm (GA). Several tests were performed to illustrate the robustness of these techniques and results were encouraging for SCE Method. The SCE method proved to be superior to the SA and GA methods in obtaining the best discovered solutions. The paper concludes that the robust search capability of SCE algorithm technique is well suited for solving the structural problem in hand.     

Buckling and imperfection sensitivity in the optimization of shell structures

The subject of the present study is the optimization of structures with geometrically nonlinear behaviour allowing the inclusion of instability phenomena and imperfection sensitivity in the structural design. The proposed optimization procedure is based on the methods of path following, direct computation of bifurcation and limit points and an accurate and efficient sensitivity analysis. The finite element method is used for the structural analysis. These techniques are used together with mathematical programming schemes and methods of computer-aided geometric, design.     

基于非线性有限元的膜结构初始形态设计

阐明了膜结构初始形态设计的内涵，论述了形和态之间的关系。根据非线性大位移理论，推导了膜结构的几何非线性有限元方程，在此基础上，给出了基于非线性有限元法的两种初始形态设计方法。数值算例表明，初始形态设计方法是有效、正确的。     

Crashworthiness optimization design for foam-filled multi-cell thin-walled structures

Foam-filled thin-walled structure and multi-cell thin-walled structure both have recently gained attentions for their excellent energy absorption capacity. As an integrator of the above two kinds of thin-walled structures, foam-filled multi-cell thin-walled structure (FMTS) may have extremely excellent energy absorption capacity. This paper firstly investigates the energy absorption characteristics of FMTSs by nonlinear finite element analysis through LS-DYNA. Based on the numerical results, it can be found that the FMTS with nine cells has the most excellent crashworthiness characteristics in our considered cases. Thus, the FMTSs with cell number n=9 are then optimized by adopting a multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). During the process of multi-objective optimization design (MOD), four kinds of commonly used metamodels, namely polynomial response surface (PRS), radial basis function (RBF), Kriging (KRG) and support vector regression (SVR) for SEA and PCF, are established to reduce the computational cost of crash simulations by the finite element method. In order to choose the best metamodel for optimization, the accuracies of these four kinds of metamodels are compared by employing the error evaluation indicators of the relative error (RE) and the root mean square error (RMSE). The optimal design of FMTSs with nine cells is an extremely excellent energy absorber and can be used in the future vehicle body.     

A multi-objective structural optimization method for serviceability design of tall buildings

Structural optimization design aims to identify optimal design variables corresponding to a minimum objective function with constraints on performance requirements. To this end, many optimization frameworks have been proposed to determine optimal structural systems that are subjected to seismic and wind hazards in isolation. However, some modern tall buildings are sensitive to seismic and wind excitation owing to their complex structural systems and geographic regions. Therefore, a proper structural optimization method for such buildings is required to ensure that the expected performance is achieved in a multi-hazard scenario. This study proposes a multi-objective serviceability design optimization methodology for buildings in multi-hazard seismic and wind environments by combining optimality criteria and the nondominated sorting genetic algorithm II (NSGA-II). Seismic and wind effects can be instantaneously updated due to changes in the structural dynamic properties during the optimal design process. A neural-network-based surrogate model with self-updating is proposed to predict the structural natural frequency so that the overall computation time of the optimization process can be reduced. The proposed method was used to optimize a 50-story frame-tube building and was compared against the general genetic algorithm and general NSGA-II to verify the feasibility and effectiveness.