THE CONTACT MECHANIC FOR FUNCTIONALLY GRADED LAYER RESTING ON HALF PLANE

Abstract

In this study, a contact mechanic of a functionally graded (FG) layer resting on a half plane and pressed with distributed load from the top was considered according to theory of elasticity. The problem is solved under the assumptions that all surfaces are frictionless, the effect of gravity forces is neglected. The problem is reduced a system of integral equation in which the contact pressure are unknown functions by using integral transform technique and applying boundary conditions on equilibrium equations, constitutive equations and strain-displacement equations. The numerical solution of the integral equation was carried out with Gauss-Jacobi integration formulation taking into account the equilibrium condition and contact lengths and stresses have been found. In addition, in this study, the effect of the Application width of distributed load and the functional change of material properties on the stress distribution will be investigated. 

Keywords

• Contact mechanics,Functionally graded layer,Theory of elasticity,Integral equation

YARIM DÜZLEM ÜZERİNE OTURAN FONKSİYONEL DERECELENDİRİLMİŞ TABAKANIN DEĞME MEKANİĞİ

Abstract

Bu çalışmada, yarım düzlem üzerine oturan ve üstten yayılı yükler ile bastırılan fonksiyonel derecelendirilmiş (FD) bir tabakanın eksenel simetrik değme mekaniği elastisite teorisine göre ele alınmıştır. Değme yüzeyleri sürtünmesiz olup, kütle kuvvetlerinin etkisi ihmal edilmiştir. Denge denklemlerine, bünye denklemlerine ve şekil değiştirme-yer değiştirme bağıntılarına sınır şartları uygulanıp problemde integral dönüşüm teknikleri kullanılarak değme gerilmelerinin bilinmeyen olduğu integral denklemine indirgenmiştir. İntegral denklemin sayısal çözümü, denge şartı da dikkate alınarak, Gauss-Jacobi integrasyon formülasyonuyla gerçekleştirilmiş, değme uzunlukları ve değme gerilmeleri bulunmuştur. Ayrıca çalışmada, yayılı yükün uygulama genişliği ve malzeme özelliklerinin fonksiyonel değişiminin tabakada oluşacak gerilme dağılışlarına etkisi incelenmiştir.    

Keywords

• Değme mekaniği,Fonksiyonel derecelendirilmiş tabaka,Elastisite teorisi,İntagral denklem

References

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