关于剪切变形对等截面梁临界载荷影响的讨论
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摘要
采用平面问题的剪应变与位移分量的几何方程以及材料力学给出的等截面梁剪应力公式,得到了严格满足表面切应力边界条件的轴向位移表达式,推导了等截面梁屈曲时的微分方程,得到了计算等截面梁屈曲时的临界载荷特征方程.研究结果表明剪切变形对等截面梁临界载荷有一定影响.考虑剪切变形的影响时,等截面梁的临界载荷将变小.对于弹性支承圆形空心压杆,当扭簧刚度不十分大时,可以把圆形空心压杆作为简支梁来计算.
Based on the geometric equation about shear strain and displacement components of plane problem, and the shear stress formula of uniform beam in material mechanics, the axial displacement expressions which strictly meet boundary condition of the surface shear stress are obtained, and the differential equations and the critical load characteristic equations are deduced when the uniform beam buckles. The results show that shear deformation has certain influence on the critical load of uniform beam. When considering the effect of shear deformation, the critical load of uniform beam will be smaller. When the stiffness of the torsion spring is not very large, the circular hollow pressure rod with elastic support can be calculated as a simply supported beam.
Based on the geometric equation about shear strain and displacement components of plane problem, and the shear stress formula of uniform beam in material mechanics, the axial displacement expressions which strictly meet boundary condition of the surface shear stress are obtained, and the differential equations and the critical load characteristic equations are deduced when the uniform beam buckles. The results show that shear deformation has certain influence on the critical load of uniform beam. When considering the effect of shear deformation, the critical load of uniform beam will be smaller. When the stiffness of the torsion spring is not very large, the circular hollow pressure rod with elastic support can be calculated as a simply supported beam.
引文
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[2] 张晓霞,钟文生,姚远.初始挠度及中间弹性支撑对压杆稳定的影响分析[J].机械,2011,38(6):1-4.ZHANG Xiao-xia,ZHONG Wen-sheng,YAO Yuan.Buckling analysis for compressive bar with initial deflection and intermediate elastic support [J].Machinery,2011,38 (6):1-4.
[3] 王珂晟,李永东.弹性压杆稳定计算的方块脉冲函数法[J].机械设计与制造,2004,3:5-7.WANG Ke-sheng,LI Yong-dong.Calculation of stability for elastic compression bar using block-pulse functions [J].Machinery Design & Manufacture,2004,3:5-7.
[4] 姚小虎,陈达,欧智成,等.耦合场中轴向压缩碳纳米管的尺度效应[J].华南理工大学学报 (自然科学版),2013,41(8):103-109.YAO Xiao-hu,CHEN Da,OU Zhi-cheng,et al.Small-scale effects on axially-compressed carbon nanotubes in coupled Fields [J].Journal of South China University of Technology(Natural Science Edition),2013,41(8):103-109.
[5] 范慕辉,焦永树,蔡宗熙.斜井中钻柱的稳定性研究[J].工程力学,2007,24(1):167-172.FAN Mu-hui,JIAO Yong-shu,CAI Zong-xi.A study on the stability of tubulars in inclined wellbores [J].Engineering Mechanics,2007,24(1):167-172.
[6] 徐家福,齐德瑄,张义同.轴向可压缩压杆的压缩失稳实验研究[J].实验力学,2009,24(2):115-120.XU Jia-fu,QI De-xuan,ZHANG Yi-tong.Experimental study of compressive buckling for an axial compressible rod [J].Journal of Experimental Mechanics,2009,24 (2):115-120.
[7] 张文俊,蔡明仪,程然.铝合金E形截面轴压杆件屈曲分析方法的探讨[J].机械设计,2012,29(8):83-86.ZHANG Wen-jun,CAI Ming-yi,CHENG Ran.Discussion on methods of buckling analysis for E-section aluminum alloy members under axial compression [J].Journal of Machine Design,2012,29(8):83-86.
[8] 朱炳坤.水平钻柱屈曲载荷的分析计算[J].石油矿场机械,2006,35(4):65-67.ZHU Bing-kun.The analysis of buckling load of the horizontal drill stem [J].Oil Field Equipment,2006,35(4):65-67.
[9] 李红波,郭玉明.小麦茎秆变刚度模型与临界载荷[J].农业机械学报,2012,43(2):70-74.LI Hong-bo,GUO Yu-ming.Mechanical model with varying stiffness and critical grain load of wheat stalk [J].Transactions of the Chinese Society of Agricultural Machinery,2012,43(2):70-74.
[10] 卓曙君.弹性压杆稳定性的一般表达式[J].国防科技大学学报,1990,12(2):50-54.ZHUO Shu-jun.General expression of the stability of elastic compression bar [J].Journal of National University of Defense Technology,1990,12(2):50-54.
[11] 吴晓,李叶林.关于轴向力作用下梁弯曲时中性轴位置的讨论[J].工程与试验,2018,58(3):1-3.WU Xiao,LI Ye-lin.Discussion on the position of neutral axis in bending of beam under axial force [J].Engineering & Test,2018,58(3):1-3.
[12] 卜继玲,周炜,李建林,等.带橡胶球铰的车用推力杆稳定性分析[J].湘潭大学自然科学学报,2016,38(1):39-46.BU Ji-ling,ZHOU Wei,LI Jian-lin,et al..Stability analysis for vehicle torque rod based on the rubber bushing [J].Natural Science Journal of Xiangtan University,2016,38(1):39-46.