Su içeresindeki çubuğun stabilite analizi için diferansiyel dönüşüm yöntemi ve dunkerley formülünün uygulanması

Bu çalışmada su içerisinde olan ve P tekil kuvvet ve yayılı kendi ağırlığı etkisinde burkulan çubukların kritik burkulma yükünün bulunması için iki yöntem önerilmiştir. Çalışmada üç farklı Euler durumu dikkate alınmıştır. Sunulan yöntemlerden ilkinde su içerindeki çubuğun stabilite diferansiyel denklemin çözümü Diferansiyel dönüşüm yöntemi (DTM) ile çözülürken, ikinci yöntemde Dunkerley Formula su içerisinde burkulan çubuğun kritik burkulma yük faktörünün belirlenmesi için uygulanmıştır. Çalışmanın sonunda bir örnek önerilen iki yöntem ile çözülerek elde edilen sonuçlar sonlu elamanlar yöntemi ile karşılaştırılmıştır. Sonlu elemanlar yöntemi ile analiz için SAP 2000 programı kullanılmıştır. Elde edilen sonuçlardan iki yönteminde sonlu elemanlar yöntemine yeter uygunlukta sonuç verdiği gözlenmiştir.

Anahtar Kelimeler:

Stabilite, Burkulma, DTM, Dunkerley, Suda kolon

APPLICATION OF DIFFERENTIAL TRANSFORMATION METHOD AND DUNKERLEY FORMULA FOR STABILITY ANALYSIS OF BARS IN WATER

In this study, two methods have been proposed to find the critical buckling load of bars that are in water and buckled under the effect of P singular force and distributed self-weight. Three different Euler's cases were taken into account in the study. In the first method, the solution of the stability differential equation of the bar in water is solved by the Differential Transformation Method (DTM), while in the second method, the Dunkerley formula is applied to determine the critical buckling load factor of the buckled bar in water. Finally, the results obtained by solving an example with the two proposed methods were compared with the finite element method. SAP 2000 program was used for finite element analysis. From the results obtained, it was observed that the two methods gave results in good agreement to the finite element method.

Keywords:

Stability, Buckling, DTM, Dunkerley, Bar in water,

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