用能量法计算双模量深梁的弯曲挠度  

Calculating Bending Deflection of Bimodulous Deep Beam by Energy Method

作　　者：吴晓[1] 刘奇元[1] 罗佑新[1] 

机构地区：[1]湖南文理学院机械工程学院,湖南常德415000

出　　处：《力学季刊》2017年第3期586-591,共6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：为了得到双模量深梁弯曲变形挠度的实用计算方法,在考虑剪切变形的基础上,采用能量法研究了双模量深梁在外载荷作用下的弯曲变形挠度计算问题,并推导出了双模量深梁弯曲挠度的计算公式.把能量法的挠度计算结果与弹性理论方法的挠度计算结果进行比较,可知用能量法研究双模量深梁的弯曲变形不但计算过程简便,而且计算精度也很高.研究结果表明,双模量深梁的剪切形状因子与双模量材料的拉压弹性模量有关,而各向同性材料深梁的剪切形状因子却与它的弹性模量无关,所以双模量深梁的剪切形状因子与各向同性材料深梁的剪切形状因子有着本质上的区别.In order to obtain the practical calculation method of the flexural deformation deflection in the bimodulus deep beam, computational problems of calculating the bending deflection in the bimodulus deep beam under external loads were investigated on the basis of the shear deformation. The calculation formula of the bending deflection was deduced. Comparing the results calculated by the energy method with those by the elastic theory, it shows that the energy method possesses a simpler calculation process and a higher calculation accuracy for calculating the bending deflection in the bimodulus deep beam. The results prove that the shear shape factor of the bimodulous deep beam is related to the elastic modulus of the bimodulous material, and the shear shape factor of isotropic deep beam is independent of the elastic modulus. As a result, there is an essential difference between the shear shape factor of the bimodulous deep beam and that of the isotropic deep beam.

关 键 词：能量法 双模量 梁 弯曲挠度 弹性模量 剪切形状 

分 类 号：O341[理学—固体力学]