İki Enklüzyon ve Bir İç Çatlak İçeren Sonsuz Silindir

Bu çalışmada elastik ve izotropik malzemeden imal edilmiş, halka şeklinde bir iç çatlak ve daire şeklinde iki adet rijit enklüzyon içeren sonsuz bir silindir incelenmiştir. İncelenen silidir iki ucundan eksenel yüke tabi tutulmuştur. Eksenel yüklenmiş sonsuz silindiri içeren karmaşık problem iki problemin süperpoze edilmesiyle çözülmüştür. Bu problemler: (i) çatlak veya enklüzyon içermeyen sonsuzda yüklenmiş bir sonsuz silindir, (ii) yükleme altında olmayan, halka şeklinde bir iç çatlak ve iki daire şekilli enklüzyon içeren sonsuz silindirdir. İlgili Navier eşitlikleri, Hankel ve Fourier dönüşümleri kullanılarak çözülerek, ilgilenilen probleme yönelik genel ifadeler elde edilmiştir. Sonra, problem üç adet tekil integral denklemine indirgenmiş ve ilgili doğrusal cebrik denklem takımı Gauss- Lobatto integrasyon formülleri kullanılarak sayısal yöntemlerle çözülmüştür.

Anahtar Kelimeler:

İç Çatlak, Sonsuz Silindir, Gerilme Yığılma Faktörü, Rijit Enklüzyon

Infinite Cylinder with an Internal Crack and Two Inclusions

An infinite cylinder, of isotropic and linearly elastic material, with an internal ring shaped crack and two penny shaped rigid inclusions was considered in this study. The considered cylinder was subjected to axial tensile forces from its two ends. The complex problem of the axially loaded infinite cylinder was solved by using the superposition of two problems including: (i) an infinite cylinder, without any cracks or inclusions, loaded at infinity and (ii) an infinite cylinder with an internal ring shaped crack and two penny shaped inclusions and free of loading. Associated Navier equations are solved with Fourier and Hankel transforms to obtain general expressions for the considered problem. Then, the considered problem is reduced to three singular integral equations and numerically solved by using Gauss-Lobatto integration formula with associated system of linear algebraic equations.

Keywords:

Internal Crack, Infinite Cylinder, Stress Intensity Factor, Rigid Inclusion,

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