2017 年 2017 巻 62 号 p. 27-35
In recent years, large deformation analyses of flexible spring materials have attracted attention considerably. However, there is not sufficient analysis for practical problems such as large deformation of a cable within a channel (or a pipe), or of a drill inserted in a drilling hole in rock engineering and petroleum production, or of a medical guide wire (catheter) within a blood vessel, and so on. When a thin flexible beam material is pushed through the narrow space, the beam may buckle since the leading edge of the material strikes an obstacle (or a barrier) and cannot proceed any more. The large deformation behavior will be of great concern in handling these flexible materials.
This paper deals with large deformations of a flexible elastic beam contained within a rigid channel with friction under the action of axial compressive forces at each end. Three different deformation stages in a channel are prescribed for our analysis. Using the nonlinear deformation theory, nondimensionalized analytical solutions are derived in terms of elliptic integrals. In this study, several experiments were presented and the experimental results were compared with the theoretical formulas.
As a result, the relation between the applied axial force and the pushed-in beam length is similar to that of predicted calculation by the analytical theory. Furthermore, it is made clear that the existence of friction between the beam and the wall causes a nonuniform large deformation. Incidentally, the analysis presented in this paper would be applied to the medical guide wire (catheter) and the design of machinery for handling flexible elastic materials such as sheets, tapes, films, papers, cloths and so on. In addition, designers of machines for drill , tubing strings, and sewing machines should find the results useful and easy to apply.