半刚性钢框架结构研究及优化设计
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摘要
在众多钢结构建筑中,钢框架结构体系不仅可用于民用多高层建筑结构,还广泛地应用于多层工业建筑结构,成为目前主要采用的结构体系之一。随着社会的发展、技术的进步,如何在保证结构安全基础上,减少用钢量、提高结构设计的经济性,实现对结构的优化设计成为钢结构发展过程中的瓶颈问题。本文将依据从节点优化到杆件优化再到结构拓扑优化的思路,详细讨论钢框架结构优化的全过程。
传统钢结构设计中,为简化计算通常将梁柱节点简化成理想铰接或完全刚接；事实上,绝大多数钢框架结构梁柱节点的连接性能介于两者之间,呈半刚接特性。大量实验表明,节点的半刚接尤其对钢框架结构影响很大,不能忽略。为实现对钢框架结构的合理优化,本文在考虑节点半刚接基础上建立了钢框架结构静、动力有限元分析程序,这是实现钢框架结构合理优化设计的第一步,也是实现钢框架结构细致优化的关键。
钢框架结构优化设计是非常复杂的问题,既包含杆件尺寸优化,又涉及支撑体系拓扑优化；根据静、动力相关要求,既包含单目标优化,又涉及多目标优化。本文针对钢框架结构优化变量离散性和多约束的特点,对遗传算法和基结构法进行改进,依据钢框架结构静、动力优化设计的相关要求,详细讨论半刚性钢框架静、动力尺寸优化和支撑体系拓扑优化。
本论文主要研究工作如下：
(1)根据钢框架结构静、动力分析的需要,基于零长度弹簧节点模型、转角位移方程和位移形函数,编制了可考虑节点半刚接和P-Δ二阶效应情况的半刚性钢框架静、动力有限元分析程序；并基于工程实例研究了节点连接性能及P-Δ二阶效应对静、动力作用下钢框架结构及杆件力学性能的影响。
(2)根据钢框架结构优化多约束和离散性的特点,针对传统遗传算法借助罚函数处理约束问题易陷入局部收敛或出现非可行解的情况,提出一种新的动态分群免罚函数遗传算法,通过自适应交叉概率和变异概率、多进化体系等相应策略,提高了遗传算法的优化的全局性。根据钢框架结构静力尺寸优化相关要求,将半刚性钢框架静力分析程序与改进遗传算法相结合,建立了半刚性钢框架静力尺寸优化程序；并基于工程实例研究了节点半刚接及P-Δ二阶效应对钢框架静力尺寸优化结果的影响。
(3)根据结构抗震设计多个目标期望值的要求,提出以多目标函数比例和值为偏好准则的改进多目标遗传算法；然后,将半刚性钢框架动力分析程序与改进多目标遗传算法相结合,建立了半刚性钢框架抗震多目标尺寸优化程序。基于工程实例研究了节点连接性能对钢框架抗震多目标尺寸优化结果的影响。
(4)为提高钢框架结构的抗侧力性能,基于高效、经济的原则,详细研究了钢框架结构支撑体系的拓扑优化。根据工程支撑杆件节点设计合理性和可加工性的要求,对传统基结构法进行改进,提出杆件预先删除准则基结构法；针对拓扑优化过程中涉及尺寸优化与拓扑优化耦合关系,提出了整数与逻辑值混合的遗传算法编码形式；为了提高程序的优化效率,引入灰色关联度分析理论提出了约束关联度逐层判断准则。最后,将改进的遗传算法、基结构法和半刚性钢框架静、动力分析过程相结合,建立了半刚性钢框架支撑结构静、动力离散型拓扑优化程序；并基于工程实例研究了节点连接性能对钢框架支撑结构拓扑优化结果的影响。
通过上述相关工作,为提高钢框架结构设计的安全性和经济性提供了理论依据。
Among familiar steel buildings, steel frame structure system is not only used in multi-storey civil building but also adopted to multi-storey industrial structures, and be one of the main structural systems. With the social development and technological advancement, how to reduce steel consumption and improve the economy of the frame structure design, in other words, to achieve the optimal design of frame structure is a bottleneck question. According to the main line from joint optimization to the bar optimization and then to structure optimization, the paper will discuss in detail the entire optimization process of steel frame structure.
In traditional steel design, the calculation of beam-column joints are usually simplified as an ideal hinge or completely rigid joint; in fact, the connection performance of most beam-column joints is semi-rigid characteristics. A great deal experiments show that the semi-rigid performance of joints has especially great influence on frame structures and can not be ignored. In order to realize the rational optimization on steel frame structures, the paper firstly deduced the static and dynamic finite element analysis process by considering the semi-rigid characteristics, which were the first step of the optimal design and the key of achieving rational optimization.
Steel frame structure optimization design is very complicated problem, which includes not only all rods size optimization, and involves bracing system of topological optimization. According to different design requirements, the problem maybe relate to single objective optimization, also involves multi-objective optimization. This article will consider the particularity of steel frame optimization, such as the discrete variable and multi constraints, to improve traditional genetic algorithm and base-structure method to realize the semi-rigid steel frame structural static and dynamic sizing optimization and topology optimization.
The main research work of this paper is as follows:
1. Based on the zero length spring node model, the angle displacement equation and displacement shape function, the semi-rigid steel frame static and dynamic finite element analysis programs that can consider the effect of the node and the second semi-rigid case on frame were compiled. Then the joint connectivity and the second-order effect on the steel frame and bar mechanical properties were studied through calculating engineering examples.
2. In order to realize single-objective optimization, a new improved dynamic population genetic algorithm without penalty function was proposed. Some improved strategies for the new GA can increase the global convergence and optimization efficiency. Then to combine the semi-rigid steel frame static analysis program with the improved GA, the static 'optimization program for semi-rigid steel frame was compiled. Through calculating engineering examples, the effect of semi-rigid connectivity on static size optimization was studied.
3. According to the requirement of multi-objective anti-seismic design, a new multi-objective GA with multi-objective proportional sum value was proposed. Based on seismic requirements of steel frame structure, the dynamic multi-objective optimization procedure for semi-rigid steel frame was set up by combined the semi-rigid steel frame dynamic analysis procedures and the new multi-objective GA. Through calculating engineering examples, the effect of semi-rigid connectivity on dynamic size optimization was studied.
4. To improve lateral stiffness of steel frame system based on the efficient and economic principles, topological optimization of bracing system was studied in detail. According to the node design requirement, the traditional base structure method was improved, and puts forward the rods beforehand delete criteria. For topological optimization process refers to size optimization and the topological optimization coupling relation, a new genetic algorithm coded form of integer and logic mixed code was proposed. In order to improve the optimization efficiency, the theory of grey relational analysis was introduced to supply constraint correlation step by step judgment criterion. Then, the improved genetic algorithm and base structure method combined with the semi-rigid steel frame static and dynamic analysis procedures to compile steel frame discrete topological optimization program. Based on the engineering examples, the effect of semi-rigid connectivity on bracing topology optimization was studied.
Through the above related work, the theory about how to improve the design safety and economy of steel frame structure was given.
传统钢结构设计中,为简化计算通常将梁柱节点简化成理想铰接或完全刚接；事实上,绝大多数钢框架结构梁柱节点的连接性能介于两者之间,呈半刚接特性。大量实验表明,节点的半刚接尤其对钢框架结构影响很大,不能忽略。为实现对钢框架结构的合理优化,本文在考虑节点半刚接基础上建立了钢框架结构静、动力有限元分析程序,这是实现钢框架结构合理优化设计的第一步,也是实现钢框架结构细致优化的关键。
钢框架结构优化设计是非常复杂的问题,既包含杆件尺寸优化,又涉及支撑体系拓扑优化；根据静、动力相关要求,既包含单目标优化,又涉及多目标优化。本文针对钢框架结构优化变量离散性和多约束的特点,对遗传算法和基结构法进行改进,依据钢框架结构静、动力优化设计的相关要求,详细讨论半刚性钢框架静、动力尺寸优化和支撑体系拓扑优化。
本论文主要研究工作如下：
(1)根据钢框架结构静、动力分析的需要,基于零长度弹簧节点模型、转角位移方程和位移形函数,编制了可考虑节点半刚接和P-Δ二阶效应情况的半刚性钢框架静、动力有限元分析程序；并基于工程实例研究了节点连接性能及P-Δ二阶效应对静、动力作用下钢框架结构及杆件力学性能的影响。
(2)根据钢框架结构优化多约束和离散性的特点,针对传统遗传算法借助罚函数处理约束问题易陷入局部收敛或出现非可行解的情况,提出一种新的动态分群免罚函数遗传算法,通过自适应交叉概率和变异概率、多进化体系等相应策略,提高了遗传算法的优化的全局性。根据钢框架结构静力尺寸优化相关要求,将半刚性钢框架静力分析程序与改进遗传算法相结合,建立了半刚性钢框架静力尺寸优化程序；并基于工程实例研究了节点半刚接及P-Δ二阶效应对钢框架静力尺寸优化结果的影响。
(3)根据结构抗震设计多个目标期望值的要求,提出以多目标函数比例和值为偏好准则的改进多目标遗传算法；然后,将半刚性钢框架动力分析程序与改进多目标遗传算法相结合,建立了半刚性钢框架抗震多目标尺寸优化程序。基于工程实例研究了节点连接性能对钢框架抗震多目标尺寸优化结果的影响。
(4)为提高钢框架结构的抗侧力性能,基于高效、经济的原则,详细研究了钢框架结构支撑体系的拓扑优化。根据工程支撑杆件节点设计合理性和可加工性的要求,对传统基结构法进行改进,提出杆件预先删除准则基结构法；针对拓扑优化过程中涉及尺寸优化与拓扑优化耦合关系,提出了整数与逻辑值混合的遗传算法编码形式；为了提高程序的优化效率,引入灰色关联度分析理论提出了约束关联度逐层判断准则。最后,将改进的遗传算法、基结构法和半刚性钢框架静、动力分析过程相结合,建立了半刚性钢框架支撑结构静、动力离散型拓扑优化程序；并基于工程实例研究了节点连接性能对钢框架支撑结构拓扑优化结果的影响。
通过上述相关工作,为提高钢框架结构设计的安全性和经济性提供了理论依据。
Among familiar steel buildings, steel frame structure system is not only used in multi-storey civil building but also adopted to multi-storey industrial structures, and be one of the main structural systems. With the social development and technological advancement, how to reduce steel consumption and improve the economy of the frame structure design, in other words, to achieve the optimal design of frame structure is a bottleneck question. According to the main line from joint optimization to the bar optimization and then to structure optimization, the paper will discuss in detail the entire optimization process of steel frame structure.
In traditional steel design, the calculation of beam-column joints are usually simplified as an ideal hinge or completely rigid joint; in fact, the connection performance of most beam-column joints is semi-rigid characteristics. A great deal experiments show that the semi-rigid performance of joints has especially great influence on frame structures and can not be ignored. In order to realize the rational optimization on steel frame structures, the paper firstly deduced the static and dynamic finite element analysis process by considering the semi-rigid characteristics, which were the first step of the optimal design and the key of achieving rational optimization.
Steel frame structure optimization design is very complicated problem, which includes not only all rods size optimization, and involves bracing system of topological optimization. According to different design requirements, the problem maybe relate to single objective optimization, also involves multi-objective optimization. This article will consider the particularity of steel frame optimization, such as the discrete variable and multi constraints, to improve traditional genetic algorithm and base-structure method to realize the semi-rigid steel frame structural static and dynamic sizing optimization and topology optimization.
The main research work of this paper is as follows:
1. Based on the zero length spring node model, the angle displacement equation and displacement shape function, the semi-rigid steel frame static and dynamic finite element analysis programs that can consider the effect of the node and the second semi-rigid case on frame were compiled. Then the joint connectivity and the second-order effect on the steel frame and bar mechanical properties were studied through calculating engineering examples.
2. In order to realize single-objective optimization, a new improved dynamic population genetic algorithm without penalty function was proposed. Some improved strategies for the new GA can increase the global convergence and optimization efficiency. Then to combine the semi-rigid steel frame static analysis program with the improved GA, the static 'optimization program for semi-rigid steel frame was compiled. Through calculating engineering examples, the effect of semi-rigid connectivity on static size optimization was studied.
3. According to the requirement of multi-objective anti-seismic design, a new multi-objective GA with multi-objective proportional sum value was proposed. Based on seismic requirements of steel frame structure, the dynamic multi-objective optimization procedure for semi-rigid steel frame was set up by combined the semi-rigid steel frame dynamic analysis procedures and the new multi-objective GA. Through calculating engineering examples, the effect of semi-rigid connectivity on dynamic size optimization was studied.
4. To improve lateral stiffness of steel frame system based on the efficient and economic principles, topological optimization of bracing system was studied in detail. According to the node design requirement, the traditional base structure method was improved, and puts forward the rods beforehand delete criteria. For topological optimization process refers to size optimization and the topological optimization coupling relation, a new genetic algorithm coded form of integer and logic mixed code was proposed. In order to improve the optimization efficiency, the theory of grey relational analysis was introduced to supply constraint correlation step by step judgment criterion. Then, the improved genetic algorithm and base structure method combined with the semi-rigid steel frame static and dynamic analysis procedures to compile steel frame discrete topological optimization program. Based on the engineering examples, the effect of semi-rigid connectivity on bracing topology optimization was studied.
Through the above related work, the theory about how to improve the design safety and economy of steel frame structure was given.
引文
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