考虑摩擦力时受圆柱面约束弹性杆的平衡

Considering the friction equilibrium of an elastic rod constrained to a cylinder

受约束弹性杆作为农作物根茎、植物纤维的力学模型,其平衡问题已成为力学与农业植物交叉学科的研究热点。基于Kirchhoff理论讨论受圆柱面约束弹性杆在光滑接触与非光滑接触时的平衡问题。首先以描述截面姿态的欧拉角为变量,建立形式简明且物理意义明确的数学模型及平衡方程。接下来考虑在光滑接触与非光滑接触两种情况下,分别讨论弹性杆在特殊状态时的平衡,给出其解析积分和数值积分,并画图分析外力对受圆柱面约束弹性杆形状的影响。

The investigations on the problems of equilibrium of an elastic rod constrained to a cylinder as model of plant roots have became an interdisciplinary area of classical mechanics and molecular biology with full of activities.Based on the Kirchhoff theory,it was discussed balance problems of elastic rod constrained to the cylindrical surface with smooth and non-smooth contact.Firstly it was took Euler angles as variables which describe the shape of the cross section,established a simple and clearly physical meanings mathematics model and balance equations.Then it was considered smooth and no smooth contact,discussed the balance of an elastic rod constrained to a cylinder under special condition,given its analytical integration and numerical integration,drawn and analyzed the influence of force to the shape of an elastic rod constrained to a cylinder.