矩形小孔对薄板弯曲应力集中的影响  

Effect of a Small Rectangular Hole on Stress Concentration of Thin Plate under Bending Loads

作　　者：杨怡[1] 刘济科[2] 

机构地区：[1]华南理工大学土木与交通学院,广东广州510640 [2]中山大学力学系,广东广州510275

出　　处：《中北大学学报（自然科学版）》2010年第4期338-343,共6页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10772202;10972241);中央高校基本科研业务费专项基金资助项目(2009ZM0236);华南理工大学亚热带建筑科学国家重点实验室资助项目

摘　　要：对于内含矩形小孔的弹性薄板的应力集中问题,传统的解决办法是运用数值计算方法或者保角变换并得到数值解.基于弹性理论和有限元方法,针对矩形薄板的特性建立了具有循环周期性的控制方程,并应用U变换技术,得到具有3个自由度的位移方程,给出级数形式的位移解析解,矩形孔的长宽比是解的一个参数;然后,可以很方便地由结点位移讨论薄板弯曲的内力和应力集中系数.文中给出一个具体的算例,当薄板受到单向弯曲荷载作用时,利用四结点12自由度薄板弯曲非协调单元得到内力的解,并且改变矩形孔的长宽比,讨论了矩形孔形状对于应力集中系数的影响.研究结果表明:当长宽比等于1时,应力集中系数为1.591 1,并且随着长宽比的增大而迅速增大,随着长宽比的减小而平缓下降.The stress concentration due to a rectangular hole in thin plate under bending loads and the effect of the rectangular hole′s shape on the maximum bending moment were studied.In order to establish a governing equation with cyclic periodicity,the disadjust made by the hole may be regarded as an additional loading which including the hole′s displacement.Based on the theory of elasticity,FEM and the U-transformation technique,the displacement equations with 3-DOF of each element′s nodes were derived.The displacement solutions were provided in series form.And then the internal force can be discussed easily.For the plate subjected to unidirectional bending loads,the non-conforming plate bending element with four nodes and 12-DOF was taken as examples.The maximum bending moments under different hole′s shape were discussed.The solutions show that the stress concentration factor equals to 1.591 1 when the ratio of the length to width of the hole is 1,and grows rapidly when the ratio increases,then grows down slowly when the ratio decreases.

关 键 词：U变换 应力集中 矩形孔 薄板弯曲 

分 类 号：TB121[理学—工程力学] TH311[理学—力学]