在圓管內受扭矩作用下的大變形彈性圓桿

在本篇論文中，我們利用大變形理論來計算，一端固定，另一端受部份夾持，並於端點施加扭矩的彈性圓桿。受到扭矩後的彈性圓桿，其變形限制於直圓管中。在此論文中，我們與多數前人研究不同的地方在於前人的研究，僅考慮整段彈性圓形的變形以線接觸的形式與圓管管壁接觸，在端點的部份也是如此。然而在我們的研究中，彈性圓桿的兩個端點皆位於圓管截面的中心軸上。變形後的彈性圓桿，可能與圓管管壁形成無接觸與點接觸的變形。最後比較大變形理論與小變形理論的結果。在本篇論文中，首先利用shooting method將十個變形圖案，從變形1到10計算求得。利用本篇論文的方法，我們可以發現更多的變形。從施加端點扭矩與端點位移量的平滑軌跡中，我們發現小變形理論的變形過程，僅存在於早期的變形中，從變形1到5。換句話說，由大變形理論得知，當圓桿以扭矩控制或是位移控制時，預測到受圓管限制的彈性圓桿將會發生折斷式挫曲與自我接觸的現象。這些現象不能由小變形的理論中預測到。

關鍵字

彈性圓桿；受圓管限制；端點扭矩； shooting method ；點接觸；線接觸

並列摘要

In this paper we use elastica model to calculate the deformation of a clamped-clamped rod under end twist and constrained inside a straight tube. Unlike most of the previous works, in which only the fully-developed line-contact spiral from end to end was considered, we study the case when both ends of the rod are at the center of the tube cross section. As a consequence, free of contact and point contact may occur in the deformation. The results are compared with those predicted from a previous work using small-deformation theory. Ten deformation patterns from deformation 1 to 10 are calculated by shooting method, with a possibility of finding more. The deformation sequence forms a smooth load-deflection locus. It is found that the small-deformation theory is capable of finding only the early stage of the deformation sequence from deformation 1 to 5. The elastica model, on the other hand, predicts that the constrained elastica may undergo snapping jump and self-contact when it is under load or displacement control. These deformations cannot be found from a small-deformation theory.

並列關鍵字

Elastica ； Constraining tube ； End twist ； Shooting method ； Point contact ； Line contact

參考文獻

[1] Lubinski, A., Althouse, W.S., and Logan, J.L., 1962, “Helical Buckling of Tubing Sealed in Packers,” Journal of Petroleum Technology, 225, pp. 650-670.

[2] Feodosyev, V.I., 1977, Selected Problems and Questions in Strength of Materials. Mir, Moscow. Translated from the Russian by M. Konyaeva.

[3] Mitchell, R. F., 1982, “Buckling Behavior of Well Tubing: the Packer Effect,” Society of Petroleum Engineers Journal, October, pp. 616–624.

[4] Cheatham, J.B., and Pattillo, P.D., 1984, “Helical Postbuckling Configuration of a Weightless Column under the Action of an Axial Load,” Society of Petroleum Engineers Journal, 24, pp. 467-472.

[5] Sorenson, K.G., and Cheatham, Jr., J.B., 1986, “Post-Buckling Behavior of a Circular Rod Constrained Within a Circular Cylinder,” ASME Journal of Applied Mechanics, 53, pp. 929-934.

國際替代計量

在圓管內受扭矩作用下的大變形彈性圓桿

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