大长度箱形伸缩臂几何非线性变形精确求解

Accurate solution of geometric nonlinear deformation of long box telescopic arm

大长度箱形伸缩臂在吊重较大时表现出很明显的几何非线性,将伸缩臂等效成阶梯梁模型和铰支梁模型,利用微分方程法和坐标转换法对变形后的臂架重新建立平衡方程,推导出臂架端部横纵向位移与载荷的精确数学关系。同时,考虑轴向载荷的二阶效应,针对等效的铰支梁部分在非线性变形过程中对阶梯梁变形的影响展开进一步研究,给出伸缩臂端部变形量在不同载荷和仰角下的精确数值解。此理论分析结果经有限元仿真验证表明,该方法计算精度高,求解速度快。

Based on the obvious geometric nonlinearity of the large-length box telescopic arm when the lifting weight is large,a stepped beam model and a hinged support beam model of the telescopic arm was established.The differential equation method and coordinate transformation method were used to reestablish the equilibrium equation for the deformed arm frame,and the accurate mathematical relationship between the transverse and longitudinal displacement of the end of the arm frame and the load was derived.Meanwhile,considering the second-order effect of axial load and the influence of equivalent hinged beam on the deformation of stepped beam in the process of nonlinear deformation,the exact numerical solution of the deformation of telescopic arm end under different loads and elevation angles was obtained.Finite element simulation results show that the method has high calculation precision and fast solution speed.