摘要目前，结构抗震领域的一个重要的研究方向是，研究如何提高计算效率，缩短计算时间，并在此基础上寻求更有效的结构建模和计算方法。如今，多体系统传递矩阵法正逐渐受到越来越广泛的运用，其优点有很多，如无需建立系统总体动力学方程、计算速度快。但与多体系统传递矩阵法在其他领域的应用研究相比，在土木工程领域的应用仍处于探索阶段。65345

本文首先基于多体系统传递矩阵法的基本理论，分析三种单层两跨门式刚架工业厂房结构，推导所需相关元件的线性传递矩阵和离散时间传递矩阵，建立振动方程，同时，对其进行多遇地震作用下的弹性时程分析，具体计算时采用MATLAB语言编制相关的计算机程序。然后，将计算出的结果与有限元ANSYS计算所得的结果进行对比，主要得到了以下成果：

1.求解三种单层两跨门式刚架工业厂房结构周期时，两种方法计算得到的基本周期误差最大为3.15%，利用多体系统传递矩阵法计算大约耗时4秒，而利用有限元ANSYS计算大约耗时30秒。计算时间越短，越有利于结构减震主动控制。

2.求解三种单层两跨门式刚架工业厂房结构在多遇地震作用下顶部位移时，柱顶最大位移平均值误差最大为3.69%；屋脊最大位移平均值误差最大为4.25%。利用多体系统传递矩阵法计算耗时不到60秒，而利用有限元ANSYS计算耗时约为900秒。

3.求解单层两跨门式刚架工业厂房结构在多遇地震作用下底部剪力时，边柱A柱的柱底最大剪力平均值的误差最大为4.94%；中柱B柱的柱底最大剪力平均值的误差最大为4.74%。利用多体系统传递矩阵法计算耗时不到60秒，而利用有限元ANSYS计算耗时大约为900秒。

毕业论文关键词：线性多体系统传递矩阵法、多体系统离散时间传递矩阵法、有限元分析、弹性时程分析

毕业设计说明书（论文）外文摘要

Title  Response Analysis of the Portal Frame Structure under  Seismic Action                                                   

Abstract

At present, improving the calculation efficiency is an important research direction in the seismic research field. Many researchers devote to shorten the computing time and seek some more effective structural modeling and calculating methods. The transfer matrix method for multibody system dynamics is widely used now because it does not need to establish the equation of multibody system dynamics and the calculate progress is concise. Unfortunately, compared with the use in other fields the transfer matrix method for multibody system dynamics is still at the exploration stage in the field of civil engineering.

In this paper, based on transfer matrix method for multibody system dynamics, I have developed the linear transfer matrix and discrete time transfer matrix of the relevant components in civil engineering. And also, the vibration equation is established and the analysis is carried out in the environment of MATLAB software. I take the single-layer two-span gantry rigid frame industrial plant structure for the engineering example. The main results are as the following: 

1. The natural periods of structures are calculated both with the transfer matrix method for multibody system dynamics and the method of finite element (ANSYS). For the three single-layer two-span gantry rigid frame industrial plant structure, the largest error value of the basic period is 3.15% in these two methods. When calculating, the transfer matrix method for multibody system dynamics takes about 4 seconds, while the ANSYS takes about 30 seconds.

2. The seismic response of the structures subjected to frequently occurring earthquake are carried out both using the transfer matrix method for multibody system dynamics and the finite element method (ANSYS). For the three single-layer two-span gantry rigid frame industrial plant structure, the largest error value got by these two methods for the maximum average displacement of the column cap is 3.69%; the largest error value for the maximum average displacement of the roof ridge is 4.25%. The transfer matrix method for multibody system dynamics takes less than 60 seconds, but the ANSYS software takes approximately 900 seconds.