作　　者： ; ;

机构地区： 华南理工大学土木与交通学院

出　　处： 《中北大学学报（自然科学版）》 2010年第4期338-343,共6页

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： 变换 应力集中 矩形孔 薄板弯曲

领　　域： [理学] [理学] [一般工业技术] [机械工程]