摘要
根据变分原理推导了任意开口薄壁截面曲梁的稳定平衡方程。单轴对称截面圆弧拱在均布径向荷载(均匀受压)或两端作用大小相等、方向相反的端弯矩(均匀弯曲)作用下,平衡方程中曲率平面内的变形和曲率平面外的变形相互独立,故要么发生曲率平面内弯曲失稳,要么发生曲率平面外的弯扭失稳。给出单轴对称截面圆弧拱在这两种受力情况下平面外屈曲荷载的理论解答。通过一些无碍结果的近似使所得公式形式简洁,便于在工程中应用。最后给出了计算实例,与已有的文献进行比较,并使用通用有限元软件ANSYS进行了模拟,分析结果与该文计算结果吻合,证明了所得公式的正确性。
The differential equations of stability are derived by the principle of variation for arbitrary thin-walled curved beams. When mono-symmetric arch is subjected to uniformly distributed radial load （uniform compression） or to equal but opposite end moments （uniform bending）, its in-plane displacements are uncoupled with out-plane displacements, so it undergoes either in-plane flexural buckling or out-plane flexural-torsional buckling. Theoretic solutions are obtained for mono-symmetric circular arches under uniform compression and under uniform bending respectively. The equations are simple enough to be applied in engineering. Numerical examples are presented to validate the equation, observing good agreement with the result calculated by finite element software ANSYS and previous theoretical.
出处
《工程力学》
EI
CSCD
北大核心
2012年第3期27-32,共6页
Engineering Mechanics
基金
上海高校选拔培养优秀青年教师科研专项基金项目(RE652)
上海师范大学重点学科<结构工程>资助项目(A-7001-12-002007)
关键词
圆弧拱
单轴对称截面
平面外稳定
稳定平衡方程
弯扭屈曲荷载
理论解
circular arches
mono-symmetric
out of plane stability
governing differential equations
flexural-torsional buckling load
theoretic solution
