SavedAdd your journal

Journals / Politeknik Dergisi / 2026 / Cilt: 29 Sayı: 5

Numerical Re-evaluation of Stress Concentration in Solid-Walled Pressure Vessels with Circular Holes under Internal Pressure

İç Basınca Maruz Kalan Dairesel Delikli Kalın Cidarlı Basınçlı Kaplarda Gerilim Konsantrasyon Faktörlerinin Değerlendirilmesi

Fulya Erdemır(Gazi University, Turkey)0000-0002-1383-6857
Pages
1–11
Publication Date
2026-09-14
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These findings suggest that while traditional formula-based approaches remain useful for preliminary design, their applicability may be limited under certain geometric conditions and should be reassessed using high-fidelity numerical analysis for improved design accuracy.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, stress concentration factors (Kt) were investigated for solid-walled cylinders and pressure vessels with and without circular holes under internal pressure.
📊
Key Findings & Data:Parametric models were generated by varying inner-to-outer diameter ratios and hole geometries, and three-dimensional finite element analyses were conducted using ANSYS.
💡
Conclusion & Impact:These findings suggest that while traditional formula-based approaches remain useful for preliminary design, their applicability may be limited under certain geometric conditions and should be reassessed using high-fidelity numerical analysis for improved design accuracy.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Kalın cidarlı silindir · Dairesel delik · Gerilim konsantrasyon faktörü

Abstract

In this study, stress concentration factors (Kt) were investigated for solid-walled cylinders and pressure vessels with and without circular holes under internal pressure. Peterson’s widely used stress concentration charts were digitized and re-evaluated using modern numerical techniques. Parametric models were generated by varying inner-to-outer diameter ratios and hole geometries, and three-dimensional finite element analyses were conducted using ANSYS. Maximum stresses were computed for each configuration to determine the corresponding Kt values. The numerical results were compared with chart-based and experimental data through regression analysis. The coefficient of determination (R²) ranged from 0.9977 to approximately 1.000, indicating excellent agreement. The mean error percentage (MEP) remained below 1.96%, decreasing to 0.003% in certain cases. RMSE values were low relative to stress magnitudes, confirming the high reliability of the developed finite element models. However, systematic deviations were observed in some classical analytical formulations, particularly at higher thickness ratios. These findings suggest that while traditional formula-based approaches remain useful for preliminary design, their applicability may be limited under certain geometric conditions and should be reassessed using high-fidelity numerical analysis for improved design accuracy.

Özet

Bu çalışmada, dairesel delikli ve deliksiz kalın cidarlı iç basınçlı silindirler ve kaplar için gerilim konsantrasyon faktörleri (Kt) ayrıntılı olarak incelenmiştir. Literatürde yaygın biçimde kullanılan Peterson gerilim konsantrasyon faktörü çizelgeleri sayısallaştırılarak modern bilgisayar destekli analiz yöntemleriyle yeniden değerlendirilmiştir. Farklı iç ve dış çap oranları ile delik geometrilerine sahip parametrik modeller oluşturulmuş ve üç boyutlu sonlu eleman analizleri ANSYS yazılımı kullanılarak gerçekleştirilmiştir. Duvar kalınlığı ve iç basınç değerleri sistematik olarak değiştirilerek her bir durum için maksimum gerilmeler hesaplanmış, bu değerler üzerinden gerilim konsantrasyon faktörleri elde edilmiştir. Sayısal analiz sonuçları, literatürde yer alan grafik tabanlı ve deneysel verilerle regresyon analizi yardımıyla karşılaştırılmıştır. Regresyon sonuçları, R² değerlerinin 0.9977-1.0000 aralığında değiştiğini göstermektedir. Ortalama hata yüzdesi (MEP) %1.96’nın altında kalmış, bazı durumlarda %0.003 seviyesine kadar düşmüştür. Kök ortalama kare hata (RMSE) değerleri, karşılık gelen gerilme büyüklüklerine kıyasla düşük seviyelerde kalmıştır. Bu istatistiksel göstergeler, sonlu eleman analizleri ile grafik tabanlı Kt değerleri arasında oldukça yüksek bir uyum bulunduğunu ve geliştirilen modelin güçlü bir doğruluk seviyesine sahip olduğunu ortaya koymaktadır. Buna karşılık, bazı klasik istatistiksel formülasyonlardan elde edilen Kt değerlerinde sistematik sapmalar gözlemlenmiş ve bu durum, geleneksel analitik ifadelerin modern sayısal analiz teknikleri ışığında yeniden değerlendirilmesi gerektiğini göstermiştir.

🔖

Cite This Article

Erdemır, F. (2026). Numerical Re-evaluation of Stress Concentration in Solid-Walled Pressure Vessels with Circular Holes under Internal Pressure. Politeknik Dergisi, Cilt: 29 Sayı: 5, 1–11. https://doi.org/10.2339/politeknik.1883902

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (39)

  1. Megyesy E.F., “Pressure Vessel Handbook”, 14. Baskı, PV Publishing, Oklahoma, (2001).
  2. ASME Boiler and Pressure Vessel Code, “Section VIII, Division 2 – Alternative Rules”, (2019).
  3. Busuioceanu S., Paraschiva G.A., “Study of Stresses and Stress Concentrations in Pressure Vessels”, Mechanical Engineering Journal, (2016).
  4. Timoshenko S., Goodier J.N., “Theory of Elasticity”, McGraw-Hill, New York, (1970).
  5. Ugural A.C., Fenster S.K., “Advanced Strength and Applied Elasticity”, Prentice Hall, New Jersey, (2003).
  6. Gross D., Seelig T., “Fracture Mechanics: With an Introduction to Micromechanics”, Springer, Berlin, (2011).
  7. Murakami Y., “Stress Intensity Factors Handbook”, Pergamon Press, Oxford, (1987).
  8. Frocht M.M., “Photoelasticity”, Wiley, New York, (1948).
  9. Zienkiewicz O.C., Taylor R.L., “The Finite Element Method for Solid and Structural Mechanics”, Butterworth-Heinemann, Oxford, (2005).
  10. Hussain S., “Analysis of Stress Concentration in a Solid-walled Cylinder”, Master Thesis, Bangladesh University of Engineering and Technology, (2006).
  11. Gerdeen J.C., “Analysis of Stress Concentrations in Thick Cylinders with Side holes and Cross holes”, Journal of Engineering for Industry, 94 (3): 815–824, (1972).
  12. Gerdeen, J.C., Smith, R.E., “Experimental determination of stress-concentration factors in solid-walled cylinders with crossholes and sideholes”, Experimental Mechanics 12: 530–536, (1972).
  13. L.M. Masu,"Cross bore configuration and size effects on the stress distribution in solid-walled cylinders", International Journal of Pressure Vessels and Piping, 72(2): 171-176, (1997).
  14. Dulieu-Barton S., Quinn S., “Determination of Stress Concentration Factors Using Thermoelastic Stress Analysis”, Strain, 38: 105-118, (2002).
  15. Comlekci, T., Mackenzie, D., Hamilton, R., & Wood, J.,” Elastic stress concentration at radial crossholes in pressurised thick cylinders”, Journal of Strain Analysis for Engineering Design, 42(6): 461-468, (2007).
  16. Sérgio B. Cunha, Theodoro A. Netto,"Analytical solution for stress, strain and plastic instability of pressurized pipes with volumetric flaws", International Journal of Pressure Vessels and Piping, 89: 187-202, (2012).
  17. Makulsawatudom, P & Mackenzie, D.,” Stress concentration at crossholes in thick cylindrical vessels”, Journal of Strain Analysis for Engineering Design - J Strain Anal Eng Design, 39: 471-481, (2004).
  18. Gerard & Kinoshita, N., Christopher & Masutani, S., “Stress Concentration Factors for Oblique Holes in Pressurized Solid-walled Cylinders”, Journal of Pressure Vessel Technology-transactions of The Asme - J Pressure Vessel Technol, 130: (2008).
  19. Elie A. Badr," Stress concentration factors for pressurized elliptic cross bores in blocks", International Journal of Pressure Vessels and Piping, 83(6): 442-446, (2006).
  20. Faupel, J H, & Harris, D B., “Stress Concentration in Heavy-Walled Cylindrical Pressure Vessels. Effect Of Elliptic and Circular Side Holes”, Industrial and Engineering Chemistry (U.S.) Formerly J. Ind. Eng. Chem. Superseded by Chem. Technol., 49: (1957).
  21. Hoogenboom P.C.J., “Shear Stresses Around Cylindrical Openings in Solid-walled Cylinders”, Heron, 55(2): 155-168, (2010).
  22. Dixon, Ricky & Peters, Daniel & Keltjens, Jan., “Stress Concentration Factors of Cross-Bores in Solid-walled Cylinders and Square Blocks”, American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP, 436: (2002).
  23. Aydoğan M., “Silindirik Kabuklarda Delik Etkisi”, Yüksek Lisans Tezi, İstanbul Teknik Üniversitesi, (1981).
  24. Urade, Shildip.,” Stress Analysis of Multilayer Pressure Vessel”, Journal of Applied Mechanical Engineering, (2015).
  25. Lekhnitskii S.G., “Theory of Elasticity of an Anisotropic Body”, Mir Publishers, Moscow. (1981).
  26. Winckler N.T., Tutuncu, N., “Stresses and deformations in solid-walled cylinders subjected to combined loading and a temperature gradient”, Journal of Reinforced Plastics and Composites, 12(2): 198-209. (1993).
  27. Reddy J.N., “Mechanics of Laminated Composite Plates and Shells: Theory and Analysis”, CRC Press, Boca Raton, (2004).
  28. K Magnucki, W Szyc, J Lewiński,"Minimization of stress concentration factor in cylindrical pressure vessels with ellipsoidal heads”, International Journal of Pressure Vessels and Piping, 79(12): 841-846, (2002).
  29. Pilkey W.D., Pilkey D.F., “Peterson’s Stress Concentration Factors”, Wiley, New York, (2008).
  30. H. Kraus, "Chapter 8 - Computer Analysis of Pressure Vessels", The Stress Analysis of Pressure Vessels and Pressure Vessel Components, Pergamon, 367-404, (1970).
  31. E.A. de Carvalho, "Stress concentration factors for an internally pressurized circular vessel containing a radial U-notch”, International Journal of Pressure Vessels and Piping, 82(7): 517-521, (2005).
  32. Bulut N.Z., Cengiz M.T., Özkan M.T., Özdemir V., “FEM and ANN Modeling of Stress Concentration Factors (Kt) of Circular Plates with Various Circular Holes According to Internal and External Pressures”, Materials Testing, 67 (10): 1591–1612, (2025).
  33. Atalay O., Toktaş İ., “Notch (Stress Concentration) Factor Estimation of a Cylinder Under Internal Pressure Using Different Approaches”, Materials Testing, 63 (5): 430–435, (2021).
  34. Nazlım, O., “Dikdörtgen Delikli İzotropik Levhalarda Gerilme Yığılması Faktörünün (GYF) Parametrik Analizi ve Yapay Sinir Ağı Yaklaşımı”, Politeknik Dergisi, 28(6): 1667-1679, (2025).
  35. Eren M., Toktaş İ., Özkan M.T., “Modeling of Stress Concentration Factor Using Artificial Neural Networks for a Flat Tension Bar with Opposite V-Shaped Notches”, Politeknik Dergisi, 26 (3): 1199–1205, (2023).
  36. Toktaş İ., “Eliptik Delikli İnce Cidarlı Küresel Bir Elemanın Basınç Altında Gerilme Yığılma Faktörünün Sonlu Elemanlar Analizi ve Yapay Sinir Ağları ile Modellenmesi”, Politeknik Dergisi, 27 (2): 819–827, (2024).
  37. Akış T., Eren Ö., “Radyal Yönde Basınç Uygulanan Fonksiyonel Derecelendirilmiş Malzemeden Yapılmış Uzun Tüplerde von Mises Kriterine Göre Akmanın Başlaması”, Politeknik Dergisi, 18 (2): 63–71, (2015).
  38. Erdemir F., Özkan M.T., “Determination of Mechanical Properties of Fruit Shell Powders Reinforced Wood Plastic Composite (WPC) Materials and Case Study for I-Type Snap-Fit Model”, Journal of Polytechnic, 26 (3): 1243–1253, (2023).
  39. Erdemir F., Özkan M.T., “Modal Analysis of a Snap-fits Joint Model for Plastic Parts”, Journal of Polytechnic, 22 (4): 927–933, (2019).