【作者】 蒋晓静；

【导师】 赵金城；

【作者基本信息】 上海交通大学 ， 结构工程， 2007， 博士

【摘要】 多高层建筑的大量建设使得结构优化设计一直以来都是结构领域力求探索的研究课题之一。尽管结构优化理论的研究历史悠久,并有了相当多的优化实践,但一般只是针对小型结构而建立。相对而言,针对大型结构的优化算法与程序还比较匮乏。这一方面是受到以前计算速度条件的制约,另一方面大型结构约束复杂,荷载组合种类繁多,截面与构件形式丰富,要建立一个全面而实用的算法涉及面非常广。同时,桩筏基础以其承重大、适应性强的优点,随着建筑物日益向高、重、大方向发展,被愈来愈多地采用。但传统的“满堂布桩”、“等承载力布桩”的布桩方式使得桩越来越长、基础底板厚度越来越大,基础造价节节攀升。基于以上背景,本文针对多高层建筑的上部结构和桩筏基础的优化设计,主要进行了以下几方面工作。采用上部结构-筏板-桩土体系共同作用理论,运用子结构法将上部结构的刚度和荷载凝聚到基础边界处,将群桩和地基简化支撑在筏板各节点处的弹簧系统,根据静力平衡条件、竖向位移连续条件和节点对应关系,建立多高层建筑与地基基础共同作用分析的基本方程,通过求解方程和回代,计算各部分的内力和变形,以此作为上部结构和桩筏基础优化分析的理论基础。针对多高层建筑截面形式丰富,约束条件复杂的情况,将结构约束条件分为局部约束和整体约束两大类,提出两级优化策略,即在满足第一级约束条件的最优解的基础上,进行第二级约束条件验算,若不满足则根据相应的优化准则进行调整。建立了多高层建筑结构的截面优化模型,在尽可能减少优化变量又保证与约束对应的前提下,将优化变量全部归结为截面的高和宽,并分别根据钢筋混凝土构件和钢结构构件的特点,将目标函数、局部约束条件和整体约束条件作了大量工程化的处理。针对钢筋混凝土梁柱和钢结构构件约束的不同特点,在处理局部约束条件时采用不同的算法进行优化搜索。对混凝土梁柱,将0.618一维搜索法改造为适合梁柱截面高宽同时变化的二维搜索;对钢结构构件,基于拟满应力法和遗传算法,采用拟满应力遗传算法,并对拟满应力法进行离散性和收敛方式的改造;针对整体约束条件,采用虚功准则法,将Lagrange乘子法与其结合;结合以上三个方面编制优化模块,通过不同结构形式的算例系统地验证了优化模型和优化算法的可行性,并对结果进行分析比较。建立了以桩筏基础总造价和基础差异沉降双控的多目标函数优化模型,通过权重系数自行调整优化的重点;运用在选择优化变量时,由于本文的主要目标是在差异沉降最小的同时达到造价最低,为简化优化计算量,将对目标函数影响最大的桩坐标和桩数作为变量进行处理,满足强度要求、变形要求和构造要求三类约束条件;提出运用筏板变形后位移梯度的范数平方的积分和作为差异沉降部分的目标函数,既评价了基础的差异沉降量,又能与桩坐标相关,为优化过程带来方便。采用序列二次规划法对差异沉降部分的目标函数进行处理,采用修正后的牛顿迭代下降法和0.618黄金分割一维搜索法进行布桩和桩数的综合优化。运用算例验证优化模型和算法的可行性,并通过将总造价的权重系数设为0,将多目标函数变为单一控制差异沉降的目标函数,着重于分析本优化程序所实现的布桩形式优化对于差异沉降的贡献,优化结果说明“外弱内强”的布桩形式是合理的,采用这种布桩方式可以得到较高的经济效益。在上部结构和桩筏基础优化理论和模型的基础上,建立二者的整体优化模式,在优化中体现二者的相互作用,并运用算例进行验证,同时与不考虑共同作用的常规计算方法进行比较,说明进行共同作用分析的必要性。更多还原

【Abstract】 Many tall buildings’construction makes the issue of structure optimization one of the most popular problems in the field of structural research. Although the structure optimization theory has a long history and a lot of optimization practice, it is mostly used to small structures. Relatively speaking, for large structure optimization algorithms and programs are still relatively scarce. It was mostly limited by the previous computer calculation capacity, large amount of structural constraints, complex loading combinations, and rich section forms of the components. It is also necessary to establish a comprehensive and practical algorithm involves a very wide scope. Meanwhile, the piled raft foundation is used more and more for its great adaptability advantage However, the traditional“full uniform”,“equal supporting capacity”pile arrangement make pile length growing, foundation raft thickness increasing and costs spiraling. Based on the background mentioned above, this paper is worked on optimization on tall building superstructure and piled raft foundation.First this paper adopts substructure method to condense the stiffness and load of the whole structure on the foundation and couples with soil and piles for establishing the basic equation of interaction according to the static equilibrium conditions, vertical displacement coordination principles and nodal corresponding relations. The theory of interaction is taken as the theoretic base of the optimization on superstructure and piled raft foundation.According to the rich section form and complex constraints, static determinant and constraint monotonic assumptions are used to divide structural constraints into local and integral constraints and a two-level optimization algorithm is presented, that is to do the second-level optimization based on the optimal result of first-level.This paper established a tall building structure optimization model. In order to minimizing optimization variables but also cooperating to the constraints, this paper make optimization variables all boil down to H and B. According respectively reinforced concrete components and the characteristics of steel structure components, the objective function, local and integral conditions of a large number of projects were handled practically. Because reinforced concrete beams and columns and steel component have different constraints characteristics, their local constraints are dealed with different optimization algorithm. A two-dimensional search technique based on the golden section method is used to concrete components; to the steel structures, an imitative full-stress method with genetic algorithms is used and also proposed for discrete variables and converged means. To integral constraints, it is used Lagrange rule method combined with virtual work criteria. This paper established the virtual work equation with wall element model, and expanded the rule to the wind and seismic loads; finally, this paper realized them in the program and used three different structural forms examples to test the optimization model and optimization algorithm.The objective function for the piled raft foundation optimization is defined as a multi-object with minimizing cost and differential settlements, which could adjust the emphasis of the design with weight coefficient. The variables are the number and coordinates of the piles. Since the norm of the gradient vector of the deflected surface of the raft becomes smaller as the differential settlement of a raft becomes smaller in a global sense, the squared L2 function norm of the gradient vector of the deflected surface of the raft is selected as the objective function which represent the degree of differential settlement of a raft indirectly. Since the objective function is a nonlinear function with respect to the coordinates of piles, the recursive quadratic programming, revised Newton method and a line search technique based on the golden section method are employed to solve the optimization problem.Four examples with different weight coefficients and loading conditions are adopted to test the optimization program. Based on the result of optimization, this paper discussed the two different pile arrangement form of“outwardly weak and inwardly powerful”and“outwardly powerful and inwardly weak”.Based on the optimization theory and models of superstructure and piled raft foundation, the paper establishes an integral optimization program, which could consider the interaction between superstructure and foundation during doing optimization. Then a twelve stories concrete frame is used to test the program and the differences of internal force of superstructure are investigated using conventional method and interaction analysis method.更多还原