拉压不同弹性模量薄板上圆孔的应力分析  

Stress Analysis of Round Hole for a Thin Plate with Different Elastic Moduli in Tension and Compression

作　　者：吴晓[1] 

机构地区：[1]湖南文理学院土木建筑工程学院,湖南常德415000

出　　处：《力学季刊》2016年第3期581-589,共9页Chinese Quarterly of Mechanics

基　　金：湖南省"十二五"重点建设学科资助项目(湘教发2011[76])

摘　　要：采用弹性理论研究了拉压不同弹性模量薄板上圆孔的孔边应力集中问题.采用广义虎克定律推导出了拉压不同弹性模量薄板上圆孔边的应力平衡方程,并联合利用应力函数及边界条件得到了拉压不同弹性模量薄板上圆孔边的应力表达式.算例分析表明,当薄板材料的拉压弹性模量相差较大时,采用经典弹性理论研究薄板上圆孔的孔边应力是不合适的,当经典弹性理论与拉压不同弹性模量弹性理论的计算结果间的差别超过工程允许误差5%时,应该采用拉压不同弹性模量弹性理论进行计算.The hole edge stress concentration problem of a thin plate with different elastic moduli in tension and compression is studied by using the elastic theory. Equilibrium equations of the stress around the hole of the thin plate are derived by the generalized Hook’s law with different elastic moduli in tension and compression, and are further combined with the stress functions and the boundary conditions to derive the stress expressions around the hole edge. Through the analysis of several examples, it indicates that the classic elasticity theory is inappropriate to investigate the stress distribution around the hole edge of a thin plate with much different elastic moduli in tension and compression. When the results of the elasticity theory with different moduli in tension and compression differ from those of the classic elasticity theory by more than 5%, the calculation should follow the elasticity theory with different moduli in tension and compression.

关 键 词：拉压不同 弹性模量 薄板 圆孔 应力 弹性理论 

分 类 号：O343[理学—固体力学]