薄壁圆筒强度计算的相对误差分析  

Relative Errors Analysis of Calculation of Thin-walled Cylinder Strength

作　　者：黄云[1,2] 林鸿志 杜长城 HUANG Yun;LIN Hongzhi;DU Changcheng(School of Mechanical Engineering,Southwest Petroleum University,Chengdu 610500,China;School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南石油大学机电工程学院,成都610500 [2]西南交通大学力学与工程学院,成都610031

出　　处：《长春大学学报》2019年第8期10-13,45,共5页Journal of Changchun University

基　　金：西南石油大学校级项目(134)

摘　　要：讨论了薄壁圆筒受扭和薄壁圆筒受内压的精确解以及在材料力学中的近似解,通过对比分析得到了在材料力学近似公式中取不同直径的相对误差。如果用材料力学中的近似公式计算来解决薄壁圆筒的工程问题,应选择合理的直径,否则相对误差将大于5%。最后得出:薄壁圆筒受扭时近似计算应选择平均直径,薄壁圆筒受内压时近似计算轴向应力应选择内径,计算周向应力和四种强度理论的等效应力应选平均直径。The exact solution of the thin-walled cylinder subjected to torsion or internal pressure and the approximate solution in material mechanics are discussed.The relative errors with different diameters of the approximate formula in material mechanics are obtained by comparative analysis.If the engineering problem of thin-walled cylinder is solved by the approximate formula of material mechanics,the reasonable diameter should be chosen,otherwise the relative error will be larger than 5%.Finally,it is concluded that when the thin-walled cylinder is under torsion,the approximate calculation should choose average diameter,and when the thin-walled cylinder is under internal pressure,the approximate calculation of the axial stress should choose internal diameter,the approximate calculation of the circumferential stress and the equivalent stress of the four kinds of strength theory should choose average diameter.

关 键 词：薄壁圆筒 内压 扭转 轴向应力 周向应力 等效应力 

分 类 号：TH49[机械工程—机械制造及自动化]