Tamamlayıcı Fonksiyonlar Yöntemi ile Fonksiyonel Derecelenmiş Sandviç Dairesel Plakların Eğilme Analizi

Öz

Bu çalışmada, Fonksiyonel Derecelenmiş (FD) malzemeli sandviç dairesel plakların eğilme davranışı teorik olarak araştırılmıştır. Malzeme özellikleri kalınlığı boyunca değişen sandviç dairesel plakların, öz tabakası veya çekirdeği izotropik homojen yüzey tabakları ise FD malzemeli olarak kabul edilmiştir. Ele alınan plakların statik davranışını idare eden denklemler Kirchhoff–Love ve Mindlin–Reissner plak teorilerine göre minimum toplam enerji prensibi yardımıyla kanonik halde elde edilmiştir. Elde edilen bu denklemlerin sayısal çözümleri için Tamamlayıcı Fonksiyonlar Yöntemi (TFY) uygulanmıştır. Bu araştırmada, malzeme değişim katsayılarının, yarıçap-kalınlık oranlarının, kayma deformasyon etkisinin ve farklı sınır koşullarının FD sandviç dairesel plakların eğilme davranışı üzerindeki etkileri parametrik olarak incelenmiştir. TFY’nin bu tür problemlere etkin bir şekilde uygulanabilirliği ve yöntemin doğruluğu, elde edilen sonuçların mevcut literatür ile karşılaştırılarak gösterilmiştir.

Anahtar Kelimeler

• Sandviç dairesel plak
• Tamamlayıcı fonksiyonlar yöntemi
• İki noktalı sınır değer problemi
• Fonksiyonel derecelenmiş malzemeler

Bending Analysis of Functionally Graded Sandwich Circular Plates via the Complementary Functions Method

Öz

In this study, the flexural response of sandwich circular plates with Functionally Graded (FG) material is investigated theoretically. The core of the sandwich circular plates, whose material properties change throughout their thickness, is considered to be isotropic homogeneous and the face sheets are assumed to be FG. The governing equations of the static behavior of the considered plates are obtained in canonical form with the aid of the minimum total energy principle based on the Kirchhoff–Love and Mindlin–Reissner plate theories. For the numerical solutions of these equations, the Complementary Functions Method (CFM) is implemented. In this research, the effects of material gradient index, radius-thickness ratios, shear deformation effects and different boundary conditions on the bending behavior of FG sandwich circular plates are parametrically investigated. The efficient applicability of the CFM to this type of problem and the accuracy of the suggested method are demonstrated by comparing the results obtained with the existing literature.

Anahtar Kelimeler

• Sandwich circular plate
• Complementary functions method
• Two-Point boundary value problem
• Functionally graded materials

Kaynakça

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