Stress Distribution in Elastic Media Containing Hollow Fiber with Periodic Curvature

Abstract

In the present paper, stress distribution is studied in an infinite elastic body containining low concentration of periodical curved hollow fibers. Taking the low concentration of hollow fibers into account the interaction between them is neglected. So, the considered media is a single periodical curved hollow fiber with an infinite length embedded in an infinite elastic body. Moreover, it is assumed that the body is loaded at infinity by uniformly distributed normal forces which act along the hollow fiber. We suppose that on the inter-medium surfaces the completely cohesion conditions are satisfied. The investigations are carried out within the framework of the piecewise homogeneous body model with the use of the three-dimensional geometrical nonlinear exact equations of the theory of elasticity. In formulation and mathematical solution of the obtained boundary value problem, the boundary form perturbation method is used. In this study, numerical results are obtained in the framework of the zeroth and the first approximations for the normal stress and the self-equilibrium shear stresses on the contact surfaces between hollow fiber and matrix. The numerous numerical results related to the stress distribution in considered body and the influence of geometrical nonlinearity to this distribution are obtained and interpreted. Moreover, the influences of the geometrical and mechanical parameters of problem to these distributions are also analyzed.

Keywords

• Hollow Fiber
• Fibrous Composites
• Stress Distribution
• Periodic Curvature
• Geometrical Non-linearity

Periyodik Eğrilikli İçi Boş Lif İçeren Elastik Ortamda Gerilme Dağılımı

Öz

Bu makalede, düşük yoğunluklu periyodik eğrilikli içi boş lifler içeren sonsuz elastik bir ortamda gerilme dağımılı incelenmiştir. İçi boş liflerin düşük yoğunluğu dikkate alındığında, aralarındaki etkileşim ihmal edilir. Dolayısıyla, dikkate alınan ortam, sonsuz bir elastik gövdeye gömülü sonsuz bir uzunluğa sahip tek bir periyodik eğrilikli içi boş liftir. Ayrıca, ortamın sonsuzda içi boş lif boyunca etkiyen düzgün dağılmış normal kuvvetlerle yüklendiği varsayılmaktadır. Ortamlar arası yüzeylerde ideal temas koşullarının sağlandığını düşünüyoruz. Araştırmalar, parçalı-homoje cisim modeli çerçevesinde elastisite teorisinin üç boyutlu geometrik doğrusal olmayan kesin denklemleri kullanılarak gerçekleştirilmiştir. Elde edilen sınır değer probleminin formülasyonu ve matematiksel çözümünde sınır formu pertürbasyon yöntemi kullanılmıştır. Bu çalışmada, içi boş lif ile matris arasındaki temas yüzeyleri üzerindeki normal gerilme ve kendi kendini dengeleyen kayma gerilmeleri için, sıfırıncı ve birinci yaklaşımlar çerçevesinde sayısal sonuçlar elde edilmiştir. Ele alınan cisimdeki gerilme dağılımı ve geometrik doğrusal olmamanın bu dağılıma etkisi ile ilgili çok sayıda sayısal sonuç elde edilmiş ve yorumlanmıştır. Ayrıca, geometrik ve mekanik problem parametrelerinin bu dağılımlara etkileri de analiz edilmiştir.

Anahtar Kelimeler

• İçi Boş Lif
• Lifli Kompozitler
• Gerilme Dağılımı
• Periyodik Eğrilik
• Geometrik nonlineerite

Kaynakça

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