On Normal Stresses in Elastic Media Containing Two Neighboring Hollow Fibers with Periodic Curvature

Öz

In this paper, the distribution of normal stresses at the fiber-matrix interface in the case of two neighboring hollow fibers with infinite length periodic curvature embedded in an infinite elastic body is investigated. The concept of neighborhood is used to express the interaction between hollow fibers. The case where the midlines of the fibers are in the same plane and have the same phase initial curvature with respect to each other is considered. It is thought that uniformly distributed normal forces are applied to the elastic medium in the direction of the fibers and ideal contact conditions are provided between the fibers and the matrix. In the study, linearized three-dimensional equations of the theory of elasticity is used within the framework of the piecewise-homogeneous body model. Thus, the mathematical model of the boundary value problem is established, and the boundary form perturbation method is applied to the solution of this model. Accordingly, by writing the governing field equations and the complete conditions in series form in terms of the small parameter defined to express the bending, separate boundary value problems containing the solutions of the previous approaches are obtained for each approach. Obtained boundary value problems are solved for the zeroth and first approaches. Thus, numerical results are obtained regarding the normal stresses at the matrix interface with hollow fibers with periodic curvature and these results are interpreted. The effects of the interaction of hollow fibers with each other, thickness changes of fibers and material constants on the values of these normal stresses are investigated.

Anahtar Kelimeler

• Two Neighboring Hollow Fibers
• Fibrous Composites
• Normal Stresses
• Periodic Curvature
• Composite Materials

Periyodik Eğrilikli İki Komşu İçi Boş Lif İçeren Elastik Ortamdaki Normal Gerilmeler Üzerine

Öz

Bu makalede, sonsuz elastik cisme gömülü, sonsuz uzunluklu periyodik eğrilikli birbirine komşu içi boş iki lif olması durumunda lif-matris arayüzeyinde normal gerilmelerin dağılımı incelenmiştir. Komşuluk kavramı, içi boş lifler arasında etkileşim olduğunu ifade etmek için kullanılmıştır. Liflerin orta çizgilerininin aynı düzlemde ve birbirlerine göre aynı fazlı başlangıç eğriliklerine sahip oldukları durum ele alınmıştır. Elastik ortama, lifler yönünde düzgün dağılmış normal kuvvetler etkidiği ve lifler ile matris arasında ideal temas koşullarının sağlandığı düşünülmüştür. Çalışmada, elastisite teorisinin lineerize edilmiş üç boyutlu kesin denklemleri, parçalı-homojen cisim modeli çerçevesinde kullanılmıştır. Böylece, sınır değer probleminin matematiksel modeli kurulabilmiş, bu modelin çözümü için ise sınır formu pertürbasyon yöntemi uygulanmıştır. Buna göre, alan denklemleri ile tamas koşulları, eğilmeyi ifade edecek şekilde tanımlanan küçük parametre cinsinden seri formda yazılarak her bir yaklaşım için, önceki yaklaşımların çözümlerini içeren, ayrı ayrı sınır değer problemleri elde edilmiş ve bu problemler sıfırıncı ve birinci yaklaşımlar için çözülmüştür. Böylece, periyodik eğriliğe sahip içi boş lifler ile matris arayüzeyinde normal gerilmelerle ilgili sayısal sonuçlar elde edilebilmiş ve bu sonuçlar yorumlanmıştır. İçi boş liflerin birbirleri ile etkileşimlerinin, liflerin kalınlık değişimlerinin ve malzeme sabitlerinin, bu gerilme değerlerine etkisi incelenmiş ve tartılmıştır.

Anahtar Kelimeler

• İçi Boş komşu iki Lif
• Lifli Kompozitler
• Normal Gerilmeler
• Periyodik Eğrilik
• Kompozit Malzeme

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