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研究生: 戴貝亘
Dai, Bei-Xuan
論文名稱: 含槽口的有限寬板受張力之研究
Study of Finite Width Plate with Notches Subjected by Tension
指導教授: 徐文信
Shyu, Wen-Shinn
學位類別: 碩士
Master
系所名稱: 工學院 - 土木工程系所
Department of Civil Engineering
論文出版年: 2023
畢業學年度: 111
語文別: 中文
論文頁數: 77
中文關鍵詞: 有限元素軟體有限寬板半圓槽口半橢圓槽口應力集中
外文關鍵詞: finite element software, finite width plate, semi-circular notch, semi-elliptical notch, stress concentration
DOI URL: http://doi.org/10.6346/NPUST202300019
相關次數: 點閱:18下載:5
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  • 結構設計中有時因為人為或其他因素,使得構件表面出現缺陷;若一有限寬板的表面具有缺陷時,產生的幾何不連續將導致應力集中現象發生。針對應力集中的現象,本研究利用有限元素軟體進行寬板含有半圓或半橢圓槽口受張力作用的模擬分析,因半圓的形狀可透過解析解進行計算,故可提供有限元素軟體分析結果之比對使用。本研究並探討槽口為單一、上下對稱與上下錯位三種案例,透過變數為板寬、槽口間距離進行應力集中係數影響之探究。經驗證後的模型可確認有限元素軟體的可行性,進而討論半橢圓槽口長軸變化對應力集中的影響。分析結果顯示隨著板寬、上下槽口間的距離增加,應力集中係數會逐漸趨於定值;而半橢圓槽口之長軸逐漸增大,應力集中係數則會由小變大。依照有限元素軟體能有效得出結果的特性,未來可更深入進行不規則形狀槽口、不同材料或槽口數量對應力集中產生影響之研究。

    Sometimes in structure design because of human or other factors, the surface of the component defects; If the surface of a finite width plate is defective, the resulting geometric discontinuity will result in stress concentration. In order to solve the stress concentration phenomenon, the finite element software is used to simulate the tension of wide plates with semi-circular or semi-elliptical notches. Since the shape of semi-circular can be calculated by analytical solutions, the comparison of the finite element software analysis results can be provided. In this study, three cases of notch being single, symmetrical up and down, and dislocation up and down were discussed. The influence of stress concentration factor was explored through the variables of plate width and notch distance. The verified model can confirm the feasibility of the finite element software, and then discuss the influence of the change of the major axis of the semi-elliptical notch on the stress concentration. The results show that the stress concentration factor tends to a constant value with the increase of plate width and the distance between upper and lower notch. The stress concentration factor increases from small to large when the major axis of the semi-elliptical notch increases gradually. The effect of irregular notches, different materials, or the number of notches on stress concentration can be further studied in the future based on the effective results obtained by finite element software.

    第1章 前言 1
    1.1 研究動機 1
    1.2 研究目的 1
    第2章 文獻回顧 3
    2.1 應力集中現象 3
    2.2 有限元素法 7
    2.3 有限元素軟體 10
    第3章 研究方法 12
    3.1 問題描述 12
    3.2 單一半圓形槽口與解析解之比對 15
    第4章 板含半圓形槽口受張力之分析 23
    4.1 上下對稱半圓形槽口受張力之作用 23
    4.2 上下錯位半圓形槽口受張力之作用 29
    第5章 板含半橢圓形槽口受張力之分析 36
    5.1 單一橢圓槽口受張力之作用 36
    5.2 上下對稱橢圓槽口受張力之作用 43
    5.3 上下錯位橢圓槽口受張力之作用 49
    第6章 結論 71
    6.1 結論 71
    6.2 未來展望 72
    參考文獻 73
    附錄一 單一槽口理論解 76

    1. C. Kirsch, 1898, "Die theorie der elastizitat und die bedurfnisse der festigkeitslehre," Zeitschrift des Vereines Deutscher Ingenieure, vol. 42, pp. 797-807.
    2. C. E. Inglis, 1913, "Stresses in a plate due to the presence of cracks and sharp corners," Trans Inst Naval Archit, vol. 55, pp. 219-241.
    3. R. C. J. Howland, 1930, "On the stresses in the neighbourhood of a circular hole in a strip under tension," Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, vol. 229, no. 670-680, pp. 49-86.
    4. A. M. Wahl, Beeuwkes Jr, R., 1930, "Stress concentration produced by holes and notches," Stress, p. 141.
    5. F. G. Maunsell, 1936, "LXII. Stresses in a notched plate under tension," Philosophical Magazine Series 1, vol. 21, pp. 765-773.
    6. C. B. Ling, 1947, "On The Stresses in a Notched Plate Under Tension," Journal of Mathematics and Physics, vol. 26, pp. 284-289.
    7. C. B. Ling, 1985, "On stress concentration of a semi-elliptic edge notch," Journal of the Franklin Institute, vol. 319, pp. 341-357.
    8. O. Tamate, 1952, "Stresses in an Infinite Strip with a Semi-Circular Notch under Uniform Tension and Pure Bending," Transactions of the Japan Society of Mechanical Engineers, vol. 18, pp. 7-15.
    9. M. Isida, 1953, "On the Tension of the Strip with Semicircular Notches," Transactions of the Japan Society of Mechanical Engineers, vol. 19, pp. 5-10.
    10. A. Atsumi, 1954, "Stress Functions for an Infinite Strip with Semicircular Notches," Transactions of the Japan Society of Mechanical Engineers, vol. 20, pp. 699-706.
    11. N. A. Noda, Sera, M., Takase, Y., 1995, "Stress concentration factors for round and flat test specimens with notches," International journal of fatigue, vol. 17, no. 3, pp. 163-178.
    12. I. D. Erhunmwun, Ikponmwosa, U. B., 2017, "Review on finite element method," Journal of Applied Sciences and Environmental Management, vol. 21, p. 999.
    13. C. B. Ling, 1968, "On Stress-Concentration Factor in a Notched Strip," Journal of Applied Mechanics, vol. 35, pp. 833-835.
    14. F. I. Baratta, Neal, D. M., 1970, "Stress-concentration factors in U-shaped and semi-elliptical edge notches," Journal of Strain Analysis, vol. 5, no. 2, pp. 121-127.
    15. C. R. Chiang, 1998, "Stress concentration factors of edge-notched orthotropic plates," The Journal of Strain Analysis for Engineering Design, vol. 33, no. 5, pp. 395-398.
    16. A. Kazberuk, Savruk, M. P., Chornenkyi, A. B., 2016, "Stress distribution at sharp and rounded V-notches in quasi-orthotropic plane," International Journal of Solids and Structures, vol. 85-86, pp. 134-143.
    17. C. B. Ling, 1967, "On Stress Concentration at Semicircular Notch," Journal of Applied Mechanics, vol. 34, no. 2, pp. 522-522.
    18. N. Nao-Aki, Hironobu, N. , 1987, "Stress concentration of a strip with a single edge notch," Engineering Fracture Mechanics, vol. 28, no. 2, pp. 223-238.
    19. S. Ray-Chaudhuri, Chawla, K., 2018, "Stress and Strain Concentration Factors in Orthotropic Composites with Hole under Uniaxial Tension," Curved and layered structures, vol. 5, no. 1, pp. 213-231.
    20. M. Zappalorto, Ricotta, M., 2019, "Effect of material orthotropy on the notch stress intensity factors of sharp V-notched plates under tension," Theoretical and Applied Fracture Mechanics, vol. 104, p. 102375.
    21. M. Zappalorto, 2020, "Universal equations for the mode I stress distribution in finite size orthotropic plates with blunt notches and holes," Theoretical and Applied Fracture Mechanics, vol. 109, p. 102768.
    22. W. D. Pilkey, 1997, "Peterson's stress concentration factors," New York.
    23. H. Neuber, 2013, Kerbspannungslehre: Theorie der Spannungskonzentration Genaue Berechnung der Festigkeit, Springer-Verlag.
    24. C. A. Felippa, 2004, Introduction to finite element methods (University of Colorado).
    25. 薛守義,2005,有限單元法, 中國建材工業出版社.
    26. J. (Ed.). Schijve, 2009, Fatigue of structures and materials, Springer.
    27. O. C. Zienkiewicz, Taylor, R. L., Zhu, J. Z., 2005, The finite element method: its basis and fundamentals, Elsevier.
    28. 中原一郎,2014,彈性力學手册, 西安交通大學出版社.
    29. O. L. Bowie, 1966, "Analysis of edge notches in a semi-infinite region," Army Materials Research Agency Watertown Ma Materials Engineering Div.
    30. J. B. Hanus, 1980, "Stress concentration factors due to flaws near the edge of a plate under tension," Ames Lab., Ames, IA (United States).
    31. K. Klungerbo, 2016, "Stress Concentrations and Stress Gradients at Elliptical Through-Holes and Spheroidal Cavities," NTNU.
    32. 徐文信,2002,震波在含夾物半平面之散射行為,台灣大學土木工程學研究所博士論文,台北。

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