摘要
变截面压杆是工程结构中应用广泛的承力构件,当压杆所承受的荷载达到临界荷载时,整个结构就会失去稳定性.基于此,研究了变截面压杆弹性稳定的临界荷载解析解,推导了求解二阶线性齐次微分方程的摄动法.然后,采用该方法求出了变截面压杆微弯平衡状态下的微分平衡方程的解析解,结合边界条件得到了变截面压杆弹性稳定的临界荷载.最后,运用研究结果计算了变截面压杆的临界荷载(计算结果与其他文献基本一致).算例分析表明,该方法简便实用,且有良好的近似性.
A variable cross -section compression bar is an important structural member in an engineering structure. When the compression of the bar reaches its critical load, the whole structure will lost the stability. Thus it was studied that the analytical approach for stability of variable cross - section compression bars with a perturbation method. First, the perturbation method of particular importance in solving linear homogeneous differential equation of second order with variable coefficients was derived in detail. Then the analytical solu- tion of the slightly bending differential equation of the variable cross - section compression bar was constructed by using the perturbation method. And the critical load of the variable cross - section compression bar with boundary constraints was obtained. Finally, as the numerical examples, the critical loads of variable cross - section compression bars were calculated, and the calculation result agreed well with the result recorded in other literatures. It is shown by several numerical examples that this method is simple and practicable, and owns good precision.
出处
《河南理工大学学报（自然科学版）》
CAS
北大核心
2013年第1期85-88,共4页
Journal of Henan Polytechnic University（Natural Science）
基金
湖南省"十二五"重点建设学科(机械设计及理论)资助
湖南省科技计划项目(2010SK3051)
常德市科技计划项目(2010ZX18)
关键词
摄动法
变截面压杆
稳定
解析解
perturbation method
variable cross-section compression bar
stability
analytical solution
