双轴对称截面薄壁圆弧曲梁的弹性稳定平衡方程

基于薄壁构件分析的基本假定,采用双轴对称截面薄壁圆弧曲梁的精确翘曲位移表达式,导出了曲梁考虑几何非线性情况下的总势能,根据欧拉公式得到了曲梁的稳定平衡方程。推导中采用横截面线性和非线性总应变为零的假定,从而无需考虑横向应力的影响,对应变高阶项采用合理的简化处理,使理论推导过程简单明了。在理论推导的基础上分析了简支拱在均布径向荷载和两端等弯矩荷载作用下的平面内和平面外屈曲问题,并与其他研究者的结果进行了比较,追溯了各理论结果存在差别的根源,论证了本文理论推导过程的合理性。使用通用有限元软件ANSYS进行了模拟,与本文的分析结果一致,证明了所得公式的正确性。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。

Elastic Stability Equations for Thin Walled Curved Beam with Biaxially Symmetric Cross Section

Based on the fundamental assumptions of thin walled structure,the geometrically nonlinear total potential energy was obtained by adopting an exact warping displacement of curved beam with biaxially symmetric cross section.The governing differential equations of curved beam were established by using of Euler equation.The sum of linear strains and nonlinear strains is assumed to be zero,so the radial stresses aren't considered.The higher order terms of strains are rationally neglected,and the process of theory derivation is concise.Based on the theory,the in-plane and out plane stability of arch under uniformaly distributed radial load or uniform bending were discussed and compared with other results.The sources of discrepancies were traced,and the rationality of derivation was demonstrated.Correspondence with the result calculated by finite element software ANSYS,the equations are verified accurately.The equations are simple enough to apply in engineering.