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中南大学学报(自然科学版)

Journal of Central South University

第49卷    第12期    总第292期    2018年12月

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文章编号:1672-7207(2018)12-2972-07
用材料力学方法研究不同模量梁的弯曲变形
吴晓,刘奇元,罗佑新

(湖南文理学院 机械工程学院,湖南 常德,415000)

摘 要: 为得到不同模量梁弯曲正应力及挠度的实用计算公式,采用材料力学方法分析复杂外载荷下的不同模量梁的弯曲变形,将材料力学方法得到的计算结果与弹性理论方法得到的计算结果进行比较。研究结果表明:用材料力学方法研究不同模量梁的弯曲变形不但计算精度较高,而且计算过程也简便,克服了弹性理论存在一题一解及计算过程复杂繁琐的缺陷;不同模量梁的剪切形状因子与不同模量材料的拉压弹性模量有关,而各向同性材料梁的剪切形状因子与材料的弹性模量无关。

 

关键词: 材料力学;模量;梁;弯曲变形;剪切;形状因子

Research of bending deformation of beam with different modulus by material mechanics method
WU Xiao, LIU Qiyuan, LUO Youxin

College of Mechanical Engineering, Hunan University of Arts and Science, Changde 415000, China

Abstract:In order to get the practical calculation formulas of bending normal stress and deflection of the beam with different modulus, the material mechanics method was used to research the bending deformations of the beam with different modulus under external load. The calculation results obtained by the material mechanics method were compared with those obtained by the elastic theory. The results show that the accuracy is high and the procedure is simple for calculating the bending deformations of the beam with different modulus. This method overcomes the defects of elastic theory that one problem is with one solution and that the calculation process is complicated and cumbersome. The shear shape factor of the beam with different modulus is related to the elastic modulus of tension and compression of the different modulus material, and the shear shape factor of the beam with isotropic material is independent of the elastic modulus.

 

Key words: material mechanics; modulus; beam; bending deflection; shear; shape factor

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
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