Fonksiyonel derecelendirilmiş ortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi

Abstract

Bu çalışmada, fonksiyonel derecelendirilmiş konsol bir kirişin statik ve serbest titreşim davranışları ortotropik malzeme modeli kullanılarak incelenmiştir. Fonksiyonel derecelendirilmiş kirişin incelenmesinde düzlem parçalı sürekli ortam modeli kullanılmış olup, sonlu elemanlar yöntemi uygulanmıştır. Probleme ait yönetici denklemleri, virtüel yer değiştirmeler prensibi ile elde edilmiştir. Kirişin malzeme özellikleri, kiriş yüksekliği boyunca belli bir fonksiyona bağlı olarak belirlenmiştir. Ele alınan kirişin boyutları, levha modeli olacak biçimde seçilerek düzlem gerilme problemi uygulanmıştır. Söz konusu problemin, sonlu elemanlar formülasyonları elde edilip, sonlu eleman çözümü için MATLAB programında algoritma ve program yazılarak sonuçlar elde edilmiştir. Ele alınan çalışmada, farklı malzeme dağılımlarının, kirişin statik ve titreşim davranışına olan etkileri incelenmiştir. Değişik malzeme dağılımlarına göre, en büyük yer değiştirmeler ve doğal frekanslar elde edilip, yorumlanmıştır.

Keywords

• Fonksiyonel derecelendirilmiş malzeme,düzlem gerilme problemi,sonlu elemanlar yöntemi,statik analiz,titreşim analizi

Investigation of static and vibration behaviors of a functionally graded orthotropic beam

Abstract

In this paper, static and vibration behaviors of a functionally graded orthotropic beam are investigated. In the solution of the functionally graded beam, plane piecewise solid continua model and finite element method is used. The governing equations of the problems are obtained by using the virtual displacement principle. Material properties of functionally graded beam vary across the height direction. With the dimensions of the functionally graded beam are assumed as plane model and the plane stress problem is implemented. In the solution of the finite element equations, MATLAB program is used. In the study, the effects of the different material distributions on the static and vibration behaviors of the beam are investigated. The maximum static deflections and natural frequencies are obtained and discussed for different material parameters.

Keywords

• Functionally graded materials,plane stress problem,finite element method,static analysis,vibration analysis

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