Random Seismic Response Analysis Of Structures In Time Domain And Reliability-Based Optimization For Earthquake-resistant Structures

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...