本研究採用 ANSYS 2024R2 模擬軟體進行有限元素分析，探討在循環負載下，不同深度與夾角之局部圓錐形凹槽對不同彎管角度行為的影響。分析材料選用科技廠房中常見於原料輸送管線的不鏽鋼 SUS316，以提升模擬結果之實用性與現實性。模擬條件涵蓋局部圓錐形凹槽的夾角、深度、彎管角度，以及彎管內部壓力等變數，旨在分析上述條件下凹槽尖端所產生之最大應力。具體參數設定如下：局部圓錐形凹槽夾角由 7.5° 起，每級遞增 7.5°，至 82.5° 止，共計十一種變化；凹槽深度分別為 0.1 mm、0.3 mm 與 0.5 mm，共三種；彎管角度由 70度起，每隔 10度 一組，至 110度止，共五種角度；彎管內部壓力則自 2.0 MPa 起，遞增至 5.0 MPa，共四種壓力條件。四項參數相互組合，共建立 660 組模擬模型。經模擬分析整理後，獲致以下結論：(1) 凹槽深度增加或彎管內部壓力上升時，最大應力值亦隨之上升；(2) 當局部圓錐形凹槽夾角介於 52.5° 至 75° 之間時，最大應力值達到峰值，之後逐漸下降；(3) 無論彎管內部壓力為何，彎管角度為 90度時，最大應力值最小，而在 110度時則為最高；(4) 隨著彎管內部壓力升高，不同彎管角度之最大應力值差異趨於縮小。

This study employed the finite element analysis software ANSYS 2024R2 to investigate the effects of localized conical grooves with varying depths and cone angles on the mechanical behavior of bent pipes under cyclic loading. The material selected for simulation was SUS316 stainless steel, which is commonly used in raw material delivery pipelines in high-tech manufacturing facilities, thereby enhancing the practical relevance of the simulation results. The simulation parameters included the cone angle and depth of the localized groove, the bending angle of the pipe, and the internal pressure within the bend. The primary objective was to evaluate the maximum stress occurring at the groove tip under these varying conditions. Specifically, the cone angle of the localized groove ranged from 7.5° to 82.5°, in increments of 7.5°, resulting in a total of eleven angle variations. Groove depths were set at 0.1 mm, 0.3 mm, and 0.5 mm, comprising three depth levels. The pipe bending angle varied from 70-degree to one 110-degree, increasing every 10-degree, total of five angle changes. Internal pressures were set at 2.0 MPa, 3.0 MPa, 4.0 MPa, and 5.0 MPa, resulting in four pressure conditions. A total of 660 simulation models were constructed through the full factorial combination of these four parameters. The simulation results led to the following conclusions: (1) An increase in groove depth or internal pressure resulted in a corresponding increase in maximum stress; (2) The maximum stress peaked when the groove cone angle ranged between 52.5° and 75°, and then gradually decreased beyond this range; (3) Regardless of internal pressure, the lowest maximum stress occurred at a bending angle of 90-degree, while the highest was observed at 110-degree; (4) As internal pressure increased, the variation in maximum stress across different bending angles tended to diminish.

L. Lee. C. Y. Hung and W. F. Pan, Variation of ovalization for sharp-notched circular tubes under cyclic bending, Journal of Mechanics, Vol. 26, No. 3, pp. 403-411 (2010).
K. L. Lee, C. M. Hsu and W. F. Pan, The influence of diameter-to-thickness ratios on the response and collapse of sharp-notched circular tubes under cyclic bending, Journal of Mechanics, Vol. 28, No. 3, pp.461-468 (2012).
K. L. Lee, C. H. Meng and W. F. Pan, The influence of notch depth on the response of local sharp-notched circular tubes under cyclic bending, Journal of Applied Mathematics and Physics, Vol. 2, No. 6, pp.335-341 (2014).
C. C. Chung, K. L. Lee and W. F. Pan, Collapse of sharp-notched 6061-T6 aluminum alloy tubes under cyclic bending, International Journal of Structural Stability and Dynamics, Vol. 16, No. 7, 1550035 [24 pages](2016).
C. C. Chung, K. L. Lee and W. F. Pan, Finite element analysis on the response of 6061-T6 aluminum alloy tubes with a local sharp cut under cyclic bending, Journal of Vibroengineering, Vol. 18, No. 7, pp.4276-4284 (2016).
K. L. Lee, K. H. Chang and W. F. Pan, Effect of notch depth and direction on stability of local sharp-notched circular tubes subjected to cyclic bending, International Journal of Structural Stability and Dynamics, Vol.18, No. 7, 1850090 [23 pages] (2018).
劉政傑，管路彎頭內側裂縫疲勞成長之數值模擬，虎尾科技大學飛機工程系學位論文（2018）。
K. L. Lee, M. L. Weng and W. F. Pan, On the failure of round-hole tubes under cyclic bending, Journal of Chinese Society of Mechanical Engineering, Vol. 40, No. 6 pp. 663-673 (2019).
李鎮修，局部圓錐形凹槽對管路彎頭在循環負載下行為之有限元素分析，工程科學系學位論文(2021)。
K. L. Lee, H. Y. Liu and W. F. Pan, Response of round-hole tubes submitted to pure bending creep and pure bending relaxation, Advances in Mechanical Engineering, Vol. 13, No. 9, pp. 1-17 (2021).
L. H. Chou, Y. C. Chiou, C. C. Wu and Y. J. Huang, Predictions of stress-stain curve and fatigue life for AISI 316 stainless steel in cyclic straining, Journal of Marine Science and Technology, Vol. 24, No. 3,pp. 426-433 (2016).
MatWeb, 316 stainless steel, http://www.matweb.com/search/DataSheet. aspx? MatGUID- 50f320bdldaf4fa7965448c30d3114ad&ckck=1. ANSYS 2020 R2 Engineering Data資料庫內建材料資訊。