摘要
对于变截面细长杆结构的屈曲临界载荷分析问题,传统欧拉公式仅适用于等截面杆件。拟建立轴向受压变截面杆屈曲失稳的控制微分方程,采用Galerkin加权残值法求解其屈曲临界载荷和失稳挠曲线函数的近似解,并给出求解问题的一般格式。通过对比四种典型边界条件下模型的理论解与有限元解,验证该方法的可行性和精确性。进一步分析杆长、初始截面直径、锥度比及壁厚等关键结构参数对锥形压杆屈曲临界载荷的影响规律。结果表明:临界屈曲载荷随杆长增加而显著降低,随初始截面直径增大而显著增大;锥度比增大将导致临界载荷降低;适当增加壁厚可有效提升临界屈曲载荷。
For the buckling critical load analysis of slender rods with non-uniform cross-sections,the traditional Euler formula is only applicable to rods with constant cross-sections.This paper establishes the governing differential equation for the buckling of axially compressed rods with variable cross-sections and employs the weighted residual method(Galerkin method)to solve the problem of the critical buckling load and buckling deflection function.A general format for solving problems is given.The feasibility and accuracy of the proposed method is verified by comparing theoretical solutions with finite element solutions for models under four typical boundary conditions.Furthermore,the influence of key structural parameters-including rod length,initial cross-sectional diameter,taper ratio,and wall thickness-on the critical buckling load is systematically investigated.The results demonstrate that the critical buckling load decreases significantly with increasing rod length and increases significantly with increasing initial cross-sectional diameter.An increase in the taper ratio leads to a reduction in the critical load.The moderate increase of the wall thickness can effectively enhance the critical buckling load.
作者
陈禹廷
李亮
吴青松
Chen Yuting;Li Liang;Wu Qingsong(State Key Laboratory for Safe Mining of Deep Coal Resources and Environment Protection,Anhui University of Science and Technology,Huainan,Anhui 232001,China;School of Civil Engineering and Architecture,Anhui University of Science and Technology,Huainan,Anhui 232001,China;School of Mechanics and Optoelectronic Physics,Anhui University of Science and Technology,Huainan,Anhui 232001,China;School of Mechatronics Engineering,Anhui University of Science and Technology,Huainan,Anhui 232001,China)
出处
《黑龙江工业学院学报(综合版)》
2025年第11期130-137,共8页
Journal of Heilongjiang University of Technology(Comprehensive Edition)
基金
国家自然科学基金项目(项目编号:11902002)
国家自然科学基金项目(项目编号:52227901)
国家重点研发计划项目(项目编号:2024YFC3013805)
2023年安徽省高校中青年教师培养行动—优秀青年教师培育项目(项目编号:134172504)。
关键词
变截面杆
加权残值法
GALERKIN法
边界条件
屈曲临界荷载
non-uniform cross-section rods
weighted residual method
galerkin method
boundary conditions
critical buckling load
