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

杨怡; 刘济科

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

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- Effect of a Small Rectangular Hole on Stress Concentration of Thin Plate under Bending Loads
- 矩形小孔对薄板弯曲应力集中的影响
- Vol. 31, Issue 4, Pages: 338-343(2010)
- 作者机构：
  
  1. 华南理工大学土木与交通学院
  2. 中山大学力学系
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2010
- 稿件说明：
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杨怡, 刘济科. Effect of a Small Rectangular Hole on Stress Concentration of Thin Plate under Bending Loads[J]. 2010, 31(4): 338-343.
DOI：

杨怡, 刘济科. Effect of a Small Rectangular Hole on Stress Concentration of Thin Plate under Bending Loads[J]. 2010, 31(4): 338-343. DOI：

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.

Abstract

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.

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Keywords

references

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