南京工业大学硕士学位论文结构随机地震反应时域分析及抗震可靠度优化姓名：孙广俊申请学位级别：硕士专业：结构工程指导教师：李鸿晶20060601- I - 摘 要 地震地面运动过程的随机性以及结构体系本身的不确定性， 导致结构的地震反应必然为随机过程，采用随机振动理论分析结构的地震反应，在概率意义上对结构的地震反应和抗震可靠性做出较为精确的估计是必要的、合理的。结构抗震可靠度应该和结构优化结合起来。 基于结构抗震可靠性分析的优化方法可以解决在给定预期投资条件下结构抗震可靠度的优化问题。本文研究了结构平稳随机地震反应的时域解法；给出了适用于优化算法的抗震可靠度简化分析方法，提出了一种基于“等可靠度”准则的结构优化方法。具体研究内容如下： （1）研究了三种典型的平稳随机地震动模型（理想白噪声、金井清谱、改进金井清谱）的时域统计特性。通过比较，分析了模型的物理概念、频域特征、参数取值以及适用范围。根据地震动模型的过滤方程推导了随机地震动模型自相关函数解析表达式，解决了结构随机振动时域分析中激励过程的描述问题。 （2）给出了结构随机地震反应的时域解法。利用状态空间概念、复模态方法和随机过程相关性理论在时域内推导了结构的随机地震反应， 导出了多自由度体系在多种随机地震模型下的协方差反应的解析式， 通过求解协方差反应矩阵可以直接获得结构的均方位移、均方速度等反应值，并将这种方法推广到二维随机激励的情况。针对工程上常用的框架结构体系，利用静力凝聚技术大幅度缩减了结构的自由度，给出了简化分析方法，大大降低了计算工作量。 （3）给出了结构抗震可靠度的简化计算方法。分别采用承载力准则和变形准则定义了抗震结构的两种极限状态，即承载力极限状态和抗倒塌极限状态。将框架结构视为串联模型，根据首次超越机制，推导了给定地震地面加速度峰值水平下结构两种极限状态的条件失效概率，分别代表结构的“小震”失效概率和“大震”失效概率。在求解抗倒塌条件可靠度时，利用能量等效准则把结构的非线性抗力等效为线性抗力，避免了非线性随机地震反应的计算。 （4）提出了结构抗震可靠度优化的准则算法。从结构的力学概念出发，基于同步失效的思想，提出了“等可靠度”优化准则。从物理上解释了该准则的含义，研究了它与最优解的关系。根据优化准则构造了设计变量的迭代格式，保证了每次迭代的设计点都在约束条件的边界上，按此方法对抗震结构进行优化，可以得到在给定的材料质量上限值和构件截面尺寸下限值的约束条件下具有最小地震失效概率的结构。 关键词：关键词：结构 地震动模型 随机反应 时域 地震可靠性 优化准则 - II - ABSTRACT For seismic structures, there are vast uncertainties and randomness both in earthquake-induced ground motions and in resistance capacity of the structures, so the seismic responses of the structures are usually considered as stochastic processes. Obviously it is reasonable to analyze the responses of earthquake-resistant structures and evaluate quantitatively the structural vulnerability and safety subject to earthquake excitations on the basis of probabilistic methods. Therefore, the optimization for seismic structural design ought to be carried out under due consideration of the uncertainties involved in the load-structure system based on a structural reliability analysis. The methodology of reliability-based optimization for earthquake-resistant structures may be applied to find the optimal solution of seismic reliability when the initial construction cost is given. In this paper, a practical method is developed for the random seismic response analysis of structures in time domain. A simplified approach of reliability analysis for seismic structures is provided. And an optimality criterion method is presented for the reliability-based optimization. (1) In this paper, three models of the stationary Gaussian white noise process, the filtered Gaussian white noise process with a Kanai-Tajimi power spectrum and the twice filtered Gaussian white noise process with a modified Kanai-Tajimi power spectrum are respectively researched for representing the actual earthquake ground accelerations. The models physical meanings, statistical properties in frequency domain, evaluation of the parameters and the application scopes are studied. According to the filter equations of the Kanai-Tajimi spectrum and modified Kanai-Tajimi spectrum, the autocorrelation functions of the stochastic models are deduced in time domain. These results provide a basis for random seismic response analysis and reliability assessment of the seismic structures. (2) A methodology of random seismic response analysis of structures in time domain is presented in this paper. The equations of motion of the structures are represented by the state equations in state space subject to the earthquake ground motions, and the complex vibration characteristics and responses are analyzed. The method of a complex mode superposition is used to deduce the covariance response matrix of linear time-invariant structures under excitation of the three ground acceleration models. The statistic characteristics of the structural displacement and velocity responses may be obtained directly from the covariance response matrix without any efforts of integral calculation. This method can be developed into the application in the random seismic response analysis of structures due to two dimension coherence ground motions. A static condensation technique is used to simplify the frame 硕士学位论文 - III - structure to a stick model with lumped mass at each floor level, and the degrees of freedom are reduced greatly in the process of structural analysis so that the computer efforts are descended enormously. This methodology is distinct in physical conception, all the analyses are carried out in time domain, and the results are simple and clear, so it can be used to analyze the stationary responses of the seismic structures in practice. (3) A simplified approach of reliability analysis for earthquake-resistant structures is provided. Two limit states of seismic structures are respectively defined according to the loading capacity failure criterion and the deformation failure criterion. The reliability model of the multi-story frame structures is assumed as series connection model, the loading capacity and collapse-resistant limit state probabilities are evaluated respectively at different levels of peaks ground acceleration on the basis of the first passage mechanism. The results respectively represent