兩端夾持固定之長度不受限制彈性體
於圓形通道內的變形

本文主要探討兩端夾持固定之長度不受限制彈性體於圓形通道內的變形。在實驗觀測中，我們利用薄長的彈性體做實驗並稱它為「板條」，將板條放入圓形通道裡兩端夾持固定，其中一端，板條可以在夾持處自由滑移改變在通道內之長度，接著觀察它的變形，我們發現對稱與不對稱的變形皆會存在，本文尤其著重於板條與圓形通道因接觸而產生的變形部分。理論分析上，我們利用elastica理論去求解變形曲線，將整段的變形以接觸點為分界，分成數個基本變形(sub-domains)來討論，並將板條變形歸納為14種變形patterns形態。最後的數值結果，我們呈現各個patterns的變形模擬結果，並求得patterns之間的臨界值(critical point)及分支點值(branching point)，最後將不同板條長度內可能出現的變形情況列出來，並圖示板條長度改變量與施力的關係。

關鍵字

夾持固定；板條；圓形通道；彈性理論；變形曲線

並列摘要

In this paper we study the planar deformations of an elastica inside a circular channel with clearance. One end of the elastica is fully clamped, while the other end is partially clamped in the lateral direction and is subject to a pushing force in the longitudinal direction. In the experiment, we observe various deformation patterns after pushing the elastica through the partial clamp. Both symmetric and asymmetric deformations are recorded. Special attention is focused on the contact conditions between the elastica and the circular channel. In order to analyze the elastica deformation theoretically, we first divide the elastica into several elementary sub-domains depending on the contact condition between the elastica and the circular channel. In each sub-domain the elastica is either only loaded at the ends or in full contact with the outer wall. Armed with these basic equilibrium analyses, we proceed to calculate and classify the loaded elastica into several different deformation patterns. Finally, we present the load-deflection curves which relate the external pushing force to the elastica length increase inside the channel. The branching phenomena exhibited by these load-deflection curves agree qualitatively with the experimental observations.

並列關鍵字

parially clamped ； elastica ； circular channel ； sub-domains ； deformation patterns

參考文獻

[1] Chai, H., 2002. On the post-buckling behavior of bilaterally constrained plates. International Journal of Solids and Structures, 39, 2911-2926.

[2] Chai, H., 2006. On the crush worthiness of a laterally confined bar under axial compression. Journal of Applied Mechanics, 73, 834-841.

[3] Chen, J.-S., Li C.-W., 2007. Planar elastica inside a curved tube with clearance. International Journal of Solids and Structures, (in press).

[4] Cunha, J.C., 2004. Buckling of tubulars inside wellbores: Review on recent theoretical and experimental works. SPE Drilling and Completion, 19, 13-19.

[5] Domokos, G.., Holmes, P., Royce, B., 1997. Constrained Euler buckling. Journal of Nonlinear Science, 7, 281-314.

國際替代計量

兩端夾持固定之長度不受限制彈性體於圓形通道內的變形

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