带有弹性不可伸长杆涂层的弹性圆盘的分岔
Bifurcations of an elastic disc coated with an elastic inextensible rod
AI总结：
本文推导了受等周Cosserat涂层约束的弹性圆盘分岔的解析解，采用复势函数和增量拉格朗日方程处理圆盘内部与预应力涂层杆，揭示了分岔模式随刚度比变化的规律，适用于涂层纤维、机械轧辊及植物形态发生等领域。
摘要：
本文推导了边界受等周Cosserat涂层约束的弹性圆盘分岔的解析解。后者被视为弹性圆环杆，可以是完全粘结或部分粘结（后者情况下具有滑移界面），并承受三种不同类型的均匀分布径向载荷（包括静水压力）。所提出的求解技术采用复势函数处理圆盘内部，并采用增量拉格朗日方程描述模拟涂层的预应力弹性杆。圆盘的分岔以不同环向波数表征的模式发生，范围从椭圆化到高阶波纹，其取决于圆盘弹性刚度与其涂层弯曲刚度之比。所提出的结果可应用于多个领域，如涂层纤维、机械轧辊以及植物和果实的生长与形态发生。
英文摘要：
An analytical solution is derived for the bifurcations of an elastic disc that is constrained on the boundary with an isoperimetric Cosserat coating. The latter is treated as an elastic circular rod, either perfectly or partially bonded (with a slip interface in the latter case) and is subjected to three different types of uniformly distributed radial loads (including hydrostatic pressure). The proposed solution technique employs complex potentials to treat the disc's interior and incremental Lagrangian equations to describe the prestressed elastic rod modelling the coating. The bifurcations of the disc occur with modes characterized by different circumferential wavenumbers, ranging between ovalization and high-order waviness, as a function of the ratio between the elastic stiffness of the disc and the bending stiffness of its coating. The presented results find applications in various fields, such as coated fibres, mechanical rollers, and the growth and morphogenesis of plants and fruits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
