摘要
采用渐进积分法研究了简支梁-柱分别在横向分布力、横向集中力和力偶作用下的弯曲问题.构造了各种荷载作用下梁-柱的四阶微分迭代方程和边界条件.首先选取简支梁只有横向荷载的挠曲线作为梁-柱的初函数,然后将初函数代入梁-柱的四阶微分迭代方程进行积分,得到下一次迭代挠度函数,依次进行迭代积分运算.编程计算出了用轴力放大系数表示的最大挠度、最大转角和最大弯矩的简单多项式解析函数.经过六次迭代,与精确解相比,当梁-柱所受的轴向力是欧拉临界力的1/2以内时,误差可以控制在1%以内,达到了令人满意的工程精度要求.
The bending of simply supported beam-column under continuous transverse load,transverse concentrated load and coupling is studied by using the method of progressive integration.The fourth order differential iterative equations and boundary conditions of beam-column under various loads are constructed.Firstly,the deflection curve of simply supported beam with only transverse load is selected as the initial function of beam-column.Then,the initial function is substituted into the fourth-order differential iterative equation of beam-column for integration,and the next iterative deflection function is obtained,and the iterative integration operation is carried out in turn.Simple polynomial analytic functions of maximum deflection,maximum angle and maximum bending moment expressed by amplification coefficients are calculated.After six iterations,compared with the exact solution,the error can be controlled within 1%when the axial force is less than half of the Euler critical force,which achieves satisfactory engineering accuracy requirements.
作者
郭春霞
李银山
孙永涛
李子瑞
GUO Chunxia;LI Yinshan;SUN Yongtao;LI Zirui(School of Science,Xi′an Univ.of Arch.&Tech.,Xi′an 710055,China;School of Mechanical Engineering,Hebei University of Technology,Tianjin 300401,China;School of Mechanical Engineering,Tianjin University,Tianjin 300072,China)
出处
《西安建筑科技大学学报（自然科学版）》
北大核心
2023年第5期652-660,共9页
Journal of Xi'an University of Architecture & Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(12072222)。
关键词
渐进积分法
梁-柱
最大挠度
最大转角
最大弯矩
progressive integral method
beam-column
maximum deflection
maximum angle
maximum bending moment
