基于二阶理论的弹性约束变截面悬臂梁刚度与稳定性分析

从计入二阶效应的挠曲微分方程出发，对惯性矩沿轴向二次变化的变截面Bernoulli-Euler梁在弹性约束下的刚度和稳定性进行了分析，推导了在弹性约束下变截面悬臂梁在复合载荷作用下的挠度和稳定性的精确表达式，给出轴向压力引起的挠度影响系数。在极端情况下，该文公式可相应退化为根部固支的变截面梁及等截面梁之刚度与稳定表达式。将该文的计算结果与用ANSYS软件密分单元的计算结果进行分析比较，分析比较结果验证了该文推导的刚度和稳定性表达式的正确性，该文方法可广泛应用于弹性约束下变截面悬臂梁的刚度和稳定性分析。

THE STIFFNESS AND STABILITY ANALYSIS OF A TAPERED BEAM WITH ELASTIC RESTRAINT CONSIDERING SECOND-ORDER EFFECTS

Started from the governing differential equation with second-order effect,the stiffness and stability of a tapered Bernoulli-Euler beam with elastic constraints are analyzed,whose profile is assumed linear variation.Then the exact expression of deflection and critical load of elastic tapered beam with composite loads are proposed;while the deflection coefficients caused by axial force are derived.In extreme situations,the proposed stiffness formulas can degenerate into the stiffness of tapered cantilever and uniform cantilever,respectively.Comparison with the results of ANSYS in the numerical examples indicates that the proposed method can lead to accurate results for stiffness and stability analysis of a tapered Bernoulli-Euler beam with elastic constraints.