轴向压力下侧向弹性约束压杆的稳定分析

以弹性力学最小势能原理为基础,采用级数形式的压杆挠度曲线,利用迈克劳林级数简化分析了最小势能方程中的第一类曲线积分,并推导出了具有一定精度的压杆临界压力和侧向约束刚度的平衡方程。通过对比三角级数和多项式级数的压杆挠度曲线方程可知,前者在取多项级数时计算量较小且各项正交,后者取高阶形式时各项非正交其求解矩阵较为复杂。通过对实际算例的对比分析可知,不同级数的挠度型函数,即使只取首项,对于给定压杆临界荷载的情况下,其侧向约束刚度的计算结果同样是较为精确且结果相近的。

Stability of Column Member with Lateral Elastic Constraint under Axial Force

Based on the principle of minimum potential energy in elasticity, the interaction equation for critical pressure and lateral elastic constraint of compression bar has been deduced. If compression bar’s deflection is expressed by trigonometric series, its axial deformation, which is derived from first form curve integral and simplified by Taylor series, will fit that equation well. With deflection results expressed by trigonometric and polynomial series, for the trigonometric series, its terms are orthogonal, so the potential matrixes are diagonal ones, which are different from polynomial forms. Therefore, the computational complexity of trigonometric form is lower than that of polynomial form. The stiffness of lateral elastic constraint deduced from both the series is nearly the same for the given critical load of compression bar, even if only the first term of these series is taken.