精确几何模型下杆的压弯大变形

Large Deformation of a Rod with Compress and Bending Moment Load Using Accurate Geometric Model

摘要: 采用精确的几何模型，研究了一端固定一端自由约束的细长弹性杆在外部荷载作用下的压弯变形问题。在大变形过程中的精确几何关系下，建立几何方程和平衡方程，建立机械荷载作用下弹性压弯杆几何精确的大变形基本方程。采用打靶法数值对该边值问题进行求解，获得了在数值意义下问题的精确解。绘出该模型下弹性杆的压弯大变形特性曲线。研究外部载荷对弹性杆弯曲大变形的影响，分析压弯杆的力学特性。

Abstract: Based on accurate geometric model, the large deformation of a rod with free-fixed edges subjected to compress and bending moment loads was studied. Considering the precise geometric relation-ships across the deformation process, the geometric equations and equilibrium equations were es-tablished, and the basis equations of exact geometry under large deformation with linear constitu-tive relationship were established. Using shooting method to numerically solve the boundary value problem, the exact solution in the numerical sense was obtained, and the characteristic figures of the elastic large deformation with compress and bending moment loads were drawn, the influence of the large deformation elastic rod with external load was studied, and the mechanical characteris-tics of the rod were analyzed.