Fonksiyonel Derecelendirilmiş Malzeme Plakların Statik Analizinde Mikro-Mekanik Modellerin Katkısı

Year 2023, Volume: 5 Issue: 1, 23 - 37, 30.06.2023

Emrah Madenci

Abstract

Yeni nesil mühendislik malzemelerinden biri olarak bilinen fonksiyonel derecelendirilmiş malzemeler (FDM), tabakalı yapılarda ortaya çıkan arayüz problemlerini kaldırarak modern mühendislik uygulamalarında yüksek mukavemet ve ısıl direnç sağlar. Tipik FDM'nin karakteristik özellikleri, yüksek eğilme-gerilme bağlantısı ve bileşen malzemelerin hacim oranının kademeli olarak değişmesi gibi mekanik özelliklerinden dolayı termal dirençtir. Bu çalışmada; FDM plakların malzeme özelliklerini belirlemek için kullanılan "Voigt, Reuss, Tamura, yerel temsili hacim elemanı (LRVE) ve Mori-Tanaka" gibi çeşitli mikro-mekanik modellerin kalınlık koordinatı boyunca malzeme özelliği değişen FDM plakların eğilme davranışına tepkisi üzerindeki etkisi analitik çözüm ile araştırılmıştır. FDM plak elemanının kinematik bağıntıları için birinci dereceden kayma deformasyonu plak teorisi kullanılmış ve virtüel yer değiştirme ilkesinin yardımıyla alan denklemleri elde edilmiştir. Basit mesnetli FDM plakların analitik çözümü için Navier yöntemi kullanıldı. Her bir mikro-mekanik modelden elde edilen sonuçlar literatürde bulunan referans çözümler ile karşılaştırıldı ve uyum içinde oldukları görüldü. Elde edilen sonuçlara göre hacim oranı indeksinin yer değiştirme konusunda modeller arasında farklılık ortaya koyduğu görülmüştür.

Keywords

FGM Plak, Mikro-mekanik model, Birinci mertebe kayma deformasyon teorisi, Eğilme.

Contribution of Micro-Mechanical Models to Static Analysis of Functionally Graded Material Plates

Abstract

The Functionally graded materials (FGM) which are known one of the next generation of engineering materials, renovate interface problems due to graded structures and provide high strength and thermal resistance in modern engineering applications. The characteristic properties of typical FGM are high bending-stretching coupling and thermal resistance due to their mechanical properties such as the volume fraction of constituent materials changes gradually. In this study; the effect of various micro-mechanical models such as "Voigt, Reuss, Tamura, LRVE and Mori-Tanaka" on the response of FGM plates to the bending behavior of FGM plates, which are used to determine the material properties of FGM plates with varying properties throughout the thickness, have been analyzed by analytical solution. First order shear deformation plate theory was used for the kinematic relations of the FGM plate element and the governing equations were obtained with the help of the virtual displacement principle. Navier method was used for the analytical solution of the simple-supported FGM plate. The results obtained from each micromechanical model were compared with the reference solutions found in the literature and it was found that they were in good agreement. According to the results, it was seen that the volume fraction index revealed a difference between models on displacement.

Keywords

FGM plates, Micro mechanical models, First order shear deformation theory, Flexure

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