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在梁发生大变形后的平衡位置取一微段进行分析,从变形前后的几何关系与变形后的平衡方程出发建立计算模型,推导出求解梁大变形问题的一阶控制微分方程组,为处理梁大挠度变形问题提供了一种新的半数值半解析算法.为保证求解的精确与稳定,文中采用精细积分法与增量优化迭代的方法求解该一阶控制微分方程组.数值算例结果表明,本文的计算模型与求解方法精度高,稳定性好.
Taking a micro-section for analysis of the equilibrium position after the large deformation of the beam, the calculation model is established from the geometric relation before and after the deformation and the equilibrium equation after deformation, and the first-order differential equations governing the beam deformation are deduced. In order to ensure the accuracy and stability of the solution, a precise integration method and an incremental optimization iteration method are used to solve the first-order differential equations.This numerical example results It shows that the calculation model and solution method in this paper have high precision and good stability.