带损伤简支梁力学响应的解析  

An analytical study on mechanics response of simply supported beams with damages

作　　者：董文奇 杨怡[1] 王玉爽 黄炽辉 DONG Wenqi;YANG Yi;WANG Yushuang;HUANG Chihui(School of Civil Engineering and Transportation,South China University of Technology, Guangzhou 510641,China)

机构地区：[1]华南理工大学土木与交通学院,广东广州510641

出　　处：《中山大学学报（自然科学版）》2018年第6期77-87,共11页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11627802;51678249;118721852);科技部国家重点研发计划项目(2017YFC0806000)

摘　　要：利用有限元法和U变换法相结合,对带损伤简支梁的力学响应进行了解析研究。首先把简支梁均匀划分为具有n个子结构的周期结构,构造一个等效的循环周期结构系统,将损伤部分看作一个局部荷载项,建立其控制方程,然后对控制方程应用U变换进行解耦,得到节点挠度的解析表达式;在求出损伤单元的位移之后,可以得到整个简支梁的所有节点位移;然后,讨论了单元的损伤程度以及损伤位置对简支梁挠度的影响,并给出了结构固有频率的计算公式。This paper presents an analytical study on the mechanics response of simply supported beams with stiffness damage by combining the finite element method with the U-transformation method.Firstly,a simply supported beam is divided into n substructures,and an equivalent structure with cyclic periodicity is constructed,and the governing equations are established,in which stiffness damage is treated as a loading.Then U-transformation technic is applied to the equations and the analytical expression of nodal deflections of the beam are derived.The influences of damage location and damage degree on these solutions are discussed.Moreover,the natural frequencies of damaged beam are solved.

关 键 词：简支梁 U变换法 损伤 静力分析 固有频率 

分 类 号：O343.1[理学—固体力学]