边界受限下的轴向压缩超弹性圆管的失稳分析

Stability Analysis of an Axially Compressed Hyper-elastic Tube with Confined Boundary

橡胶制品广泛应用于社会生产和日常生活.论文主要研究外边界受限的超弹性圆管受轴向压缩时的稳定性问题,在非线性弹性理论框架下推导控制方程,对其进行线性分岔分析.考虑沿轴向对称分布的失稳模态,得到临界模态以及对应的临界主伸长,同时刻画出临界主伸长以及临界应力与壁厚之间的关系.结果表明,圆管壁越薄,发生分岔时的临界主伸长更小,更不容易发生失稳.此外,结合封隔器的密封原理,推导出封隔器圆筒在进行油液密封时轴向应力与接触应力的表达式,修正了此前的推导结果,为封隔器在密封性能的判断上提供理论依据.

Seals play an important role in modern engineering applications,especially in the oil and gas industry.Compression of a rubber tube where the outer boundary is confined is an important procedure when sealing apacker.Instability leading to a buckling profile may cause the seal to fail.Generally speaking,the rubber tube（or packer）undergoes a relatively large deformation during the whole sealing procedure.In this paper,we study the bifurcations of a hyper-elastic tube with confined outer boundary in the framework of the exact theory of nonlinear elasticity.Due to the restriction,the initial deformed state is no longer homogeneous,the basic state of which is first characterized by solving the equilibrium equation.Then the incremental governing equations and boundary conditions are established for an axial mode and a linear bifurcation analysis is carried out.The bifurcation condition is numerically solved using the determinant method.Then the bifurcation curves are obtained when the geometric parameters are specified.It is found that the critical axial mode number is always finite.In addition,the relation between the critical bifurcation stretch（or stress）and wall thickness of the tube is obtained,from which it is found that a thinwalled tube is more stable compared with a thick-walled one.According to the relation between the axial stretch and stretch on the inner surface,our results may provide insight into designing the gap between the base pipe and the oil pipe in order to avoid instability.On the other hand,we provide the formulae of contact stress in terms of the applied axial stress for both boundaries when a seal is finished,which correct an existing result in literature and also validate the accuracy of results based on the theory of linear elasticity.Finally,the stability analysis for a packer designed by the CNOOC EnerTech-Drilling Production Company is conducted and the lowest stress to achieve a full seal is given.