含损伤缺陷悬臂梁的应力求解  

SOLUTION FOR STRESS OF CANTILEVER BEAM WITH DAMAGE FLAW

作　　者：刘敏杰[1,2] 王银邦[1] 梅宁[1] 

机构地区：[1]中国海洋大学工程学院,青岛266100 [2]青岛理工大学汽车与交通学院,青岛266033

出　　处：《工程力学》2010年第3期79-84,共6页Engineering Mechanics

基　　金：863计划项目(2007AA09Z317)

摘　　要：对单侧承受双曲余弦分布压力的含损伤缺陷矩形截面悬臂梁,用弹性理论进行了应力分析。应用叠加原理,将构件分解为无损伤缺陷构件和含损伤缺陷的半无限平面分别求解,将外载荷根据其特点展开成三角级数形式,采用半逆解法求出了满足边界条件的近似解析解,得到了构件的应力状态。实例计算结果表明:损伤缺陷附近将产生较大的应力集中,且应力值随损伤缺陷尺寸的减小而增大。This paper considered a cantilever beam with rectangle section,whose stress due to hyperbolic cosine distributed load in damaged flaw side was computed by elasticity theory.The problem was converted into the superposition of two cases：absence of damaged flaw and semi-finite plane with damaged flaw.The load was expanded into trigonometric series based on its feature,and the approximate analytic solution meeting boundary conditions was obtained by semi-inverse method.Stress concentration was observed in the vicinity of damage flaw,and the value of stress increased along with the reduction of the flaw size.

关 键 词：损伤缺陷 双曲余弦 应力场 解析解 三角级数 

分 类 号：TH123.4[机械工程—机械设计及理论] TB125[理学—工程力学]