文档介绍：毕业论文
考虑畸变时三室薄壁箱梁的约束扭转分析
院
2013年06月01日
摘要
随着薄壁杆件在土木工程领域中的应用日益广泛,以及对薄壁杆件的研究日益深入,薄壁杆件截面变形(畸变)的影响也越来越受到工程人员的重视。在一些箱形梁桥中,经常看到某些横截面产生较大的畸变作用而产生明显变形,严重的影响了桥梁的正常使用。所以,考虑畸变的影响在一些工程中是必不可少的,不可忽略的。
本文是在广义坐标法的假定下,基于拉格朗日方程和哈密顿对偶求解体系,利用薄壁杆件扭转变形的广义坐标法,建立了考虑畸变时薄壁箱型截面梁扭转分析的哈密顿正则方程,并利用精细积分法对薄壁箱梁的约束扭转进行分析,编制相应的MATLAB分析程序并调试来求解体系的高精度数值解。所得结果说明哈密顿正则方程的正确性和精细积分法的适用性。
本文对三室薄壁箱梁结构算例进行分析计算,得出结果与实际算例的结果进行对比从而验证本文的理论和公式推导的正确性。而且研究三室薄壁结构更具有其实际工程意义,虽然所研究的为弹性理论的经典问题,但是哈密顿正则方程的建立和精细积分法的应用具有创新性,为该经典问题的求解和分析提供了一个新的途径。
关键词: 薄壁箱型梁;约束弯扭;畸变;广义坐标法;哈密顿理论;精细积分法
Abstract
As long as the application of thin-walled box beam increasing widespread in the field of civil engineering, as well as deepening study of thin-walled box beam, more and more engineering staff pay attention to the affection of thin-walled box beam cross-section deformation (distortion) In a number of box girder bridges, significant deformation of some cross-sectional distortion generated are often seriously affect the normal use of the bridge. So, considering the impaction of the distortion in some projects is essential, not to be ignored.
This article is under the assumption of the generalized coordinate method ,based on Lagrange equations and Hamilton duality solution system,using the generalized coordinate method of reverse deformation in thin-walled box beam, Hamilton canonical equation of thin walled box section beam torsion analysis when considering the distortion was established, and use the precise integration method analyze the constraint reverse of the thin-walled box girder, prepare the corresponding MATLAB analysis program and debug it to solve the high-precision numerical solution. The results indicate the correctness of the Hamilton canonical equations and the applicability of the precise integration method.
This article contains the arithmetic to three-room box beam, the results of pared show this method is validation. What`s more,researching the three-room box beam is of great significance to the engineering.