The Influence of Mean Curvature on the Collapse of Sharp-Notched Circular Tubes under Cyclic Bending

尖銳凹槽圓管在循環彎曲負載時平均曲率對崩塌影響之研究

李國龍(Kuo-Long Lee) ； 徐建民(Chien-Min Hsu) ； 潘文峰(Wen-Fung Pan)

《中國機械工程學刊》 34卷5期 (2013/10) Pp. 461-468

摘要

本文旨在實驗探討尖銳凹槽圓管在循環彎曲負載時平均曲率對圓管的反應與崩塌的影響。為了彰顯平均曲率的影響，六種不同的曲度率r（最小曲率／最大曲率）進行實驗的測試。我們發現當r=-1時，彎矩－曲率迴圈會呈現循環硬化且經過一些循環圈數後迴圈會呈現穩定的狀態。然而，當r≠-1時，彎矩－曲率迴圈會呈現循環鬆弛且經過一些循環圈數後迴圈也會呈現穩定的狀態。此外，不論任何的r值，橢圓化－曲率的曲線皆隨著循環圈數的增加呈現不對稱、棘齒狀且漸漸增加的趨勢狀態。最後，我們將Pan and Lee（2002）所提出的實驗經驗公式加以修改，使得該公式可用來描述控制曲率範圍與循環至皺曲圈數的關係。比較結果顯示，實驗與模擬的結果相當契合。

並列摘要

This study discusses an experimental investigation of the effect of the mean curvature on the response and collapse of sharp-notched circular tubes subjected to cyclic bending. To highlight the influence of the mean curvature effect, six different curvature ratios r (minimum curvature/maximum curvature) were experimentally investigated. We found that the moment-curvature loop cyclically hardens, and stabilizes after a few cycles for r = -1. However, the moment-curvature loop cyclically relaxes and also stabilizes after a few cycles for r≠-1. In addition, the ovalization-curvature curve shows unsymmetrical, ratcheting and increasing manner with the number of cycles for any r. Finally, the empirical formulation proposed by Pan and Lee (2002) was modified to simulate the relationship between the controlled curvature range and the number of cycles necessary to produce buckling. The results of the experimental investigation and the simulation were in good agreement with each other.

並列關鍵字

sharp-notched circular tube ； cyclic bending ； mean curvature effect ； ovalization ； collapse