梁挠曲线方程的精确推导  

Precise Derivation of Beam Deflection Equation

作　　者：刘海波[1,2] 刘玉丽 石祥锋 LIU Haibo;LIU Yuli;SHI Xiangfeng(School of Civil and Environmental Engineering,University of Science and Technology Beijing,Beijing 100083,China;Architectural Engineering College,China Institute of Science and Technology,Beijing 101601,China;College of Science,North China Institute of Science and Technology,Beijing 101601,China)

机构地区：[1]北京科技大学土木与环境工程学院,北京100083 [2]华北科技学院建筑工程学院,北京101601 [3]华北科技学院理学院,北京101601

出　　处：《华侨大学学报（自然科学版）》2018年第6期840-843,共4页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(51178185);中央高校基本科研业务费资助项目(3142014019)

摘　　要：采用数学工具,在不忽略任何高阶微量的基础上,修改原有近似的挠曲线方程,推导出更精确、更符合实际的方程式.通过有限元法验证该方程的可靠性,结果表明:传统的计算方法误差较大,且误差随着梁的跨度、横截面、荷载大小、抗弯刚度变化而变化;文中方法得到的误差较小.Using mathematical tools,without neglecting any high order infinitesimals,the existed approximate deflection equation is modified,a more accurate and realistic equation is derived.The reliability of the equation is verified by finite element method.The results show that the traditional calculation error is obvious,the error varies for different the beam spans,cross sections,the values of the load and bending stiffness,the error of presented method is small.

关 键 词：挠曲线 挠度 弯矩 曲率 有限元法 

分 类 号：TU311.1[建筑科学—结构工程]