四川轻化工大学学报（自然科学版）2025，Vol.38Issue(5)：29-39,11.DOI:10.11863/j.suse.2025.05.04
轴向均布和集中荷载的压杆临界荷载数值解
Numerical Solution for Critical Load of Slender Column Under Combined Axial Uniform and Concentrated Loads
摘要
Abstract
Determining the critical load of a slender column under combined axial uniform and concentrated loads using the equilibrium method involves solving the Bessel equation,which poses challenges in obtaining an analytical solution.Based on rigorous mathematical and mechanical theories and a graphical approach for solving the stability equation,numerical solutions for the critical load of such slender columns are derived.First,the fourth-order Bessel equation governing the buckling behavior is established.Using Maple18 mathematical software,the equation is solved,and the stability equation for eigenvalue buckling is derived by applying four boundary conditions including displacement and internal forces under ten working conditions.The stability equation is then solved graphically to obtain numerical solutions for the critical load.Next,by employing a rapid mirroring algorithm,numerical solutions for the critical load under another ten working conditions after reversing the direction of the axial distributed load are computed.Finally,the numerical solutions for the critical load under all twenty working conditions obtained in this study are compared with those derived using ANSYS Parametric Design Language(APDL),demonstrating excellent agreement between the two sets of results.A systematic investigation of this classical problem is conducted,and the results can be used as fundamental data for other related research.关键词
压杆/均布荷载/稳定方程/临界荷载/APDL解Key words
slender column/uniform load/stability equation/critical load/APDL solution分类
力学引用本文复制引用
黄开志,丁剑平,陈小亮,郑恒伟..轴向均布和集中荷载的压杆临界荷载数值解[J].四川轻化工大学学报（自然科学版）,2025,38(5):29-39,11.基金项目
重庆市科技局基础与前沿研究项目(cstc2019jcyj-msxmX0317) （cstc2019jcyj-msxmX0317）
