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

Öz

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.

Anahtar Kelimeler

• Kalın cidarlı silindir
• Dairesel delik
• Gerilim konsantrasyon faktörü
• Sonlu eleman analizi

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

Öz

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.

Anahtar Kelimeler

• Thick-walled cylinder
• Circular hole
• Stress concentration factor
• Finite element analysis

Kaynakça

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