大型结构局部非线性随机地震响应分析

【作者】 张春宇；

【导师】 林家浩；

【作者基本信息】 大连理工大学 ， 工程力学， 2002， 硕士

【摘要】 本文对于在平稳随机地震激励下部分构件进入非线性弹塑性状态工作的大型复杂结构(如桥梁、高层建筑等)进行抗震分析。采用Bouc-Wen等提出的微分方程模型描述进入非线性构件的滞变特性，运用虚拟激励法结合等效线性化进行结构非线性随机振动分析。求解受平稳随机激励的剪切型非线性滞迟系统，并研究了工程结构局部非线性随机地震响应问题。 对于剪切型滞迟系统作了以下工作：ⅰ)运用虚拟激励法结合等效线性化法分析了单自由度滞迟系统在不同强度激励下的响应性态，与基于李亚普诺夫方程的结果及用Monte-Carlo法计算的结果作了比较，非常吻合。ⅱ)运用虚拟激励法结合等效线性化法分析了此类遭受地震激励的多自由度滞迟系统在不同的非线性系数下的平稳随机响应，与时程积分方法的计算结果相比较，比较吻合。 对于工程结构地震作用下局部非线性随机振动，将离散塑性铰模型与虚拟激励法和等效线性化法相结合，求解这一类局部发生弯曲型滞迟效应的非线性问题。以上的算法已在有限元分析软件DDJ—W中实现，可以处理具有复杂边界条件的三维结构在地震激励下的局部非线性随机响应分析，并计算了工程中的实际桥梁，得到了比较合理的结果。 在此基础上，探讨了用虚拟激励法分析非线性随机振动问题应用在工程实际中的适用性和精度。本文方法充分利用了虚拟激励法求解复杂线性结构高效、精确的优点，以一系列线性问题的迭代分析，迅速地求得原非线性问题合理的近似解。是一个有实用价值的非线性抗震分析方法。更多还原

【Abstract】 In this paper seismic analysis method of large complex structures such as bridges, tall buildings, subjected to stationary random ground excitations is investigated for which the non-linear elasto-plastic characters of some components is taken into account. The Bouc-Wen differential equation model is used in modeling the hysteretic characteristics of these components. The PEM(Pseudo Excitation Method) combined with the ELM(equivalent linearization method) is used to analyze the non-linear random vibration of such structures. The shear-type non-linear hysteretic system subjected to stationary excitation and local non-linear random vibration of engineering structure under earthquake excitation are studied.The research work about the shear-type hysteretic system includes: i ) Random response of SDOF hysteretic system under variant excitation intensities are analyzed using the PEM combined with the ELM. The results are all in good agreement with those of the Liapunov differential equations and the Monte-Carlo simulation; ii ) The stationary random responses of such MDOF hysteretic systems subjected to earthquake excitation under variant non-linear coefficients are studied using the PEM combined with ELM; The results are compared with those calculated by using integration, the difference is not obvious.The research work about the local non-linear random vibration of engineering structure under earthquake excitation includes; Discrete hinge model combined with the PEM and the ELM is used to solve such non-linear problem which the bend-type hysteretic effect of some components is taken into account. Algorithm above has been implemented in finite element program DDJ-W, and can analyze non-linear random response of 3-D structure which has complex boundary conditions under earthquake excitation. Practical bridges of engineering are calculated and the results are reasonable.Finally, the possibility of engineering application and accuracy of the PEM in analyzing the random response of non-linear structures are discussed based on the work outlined above. Method presented in this paper makes full use of the merits of the PEM, i.e. its high efficiency and accuracy in solving the linear random vibration of complex structures. The solution of the original nonlinear problem is reasonably approximated by means of a series of random vibration analyses for the linearized structure using the pseudo excitation method.更多还原