Nano Kirişlerin Değiştirilmiş Sonlu Elemanlar Taşima Matrisi Yöntemi ile Stabilite Analizi

Öz

Bu çalşmada değiştirilmiş Sonlu elemanlar–taşıma matrisi yöntemi nano kirişlerin stabilite analizi için uyarlanmıştır. Çalımada önce nano kirişin stabilite denklemi yerel olmayan Euler kiriş teorisi yardımıyla oluşturulmuştur. Diferansiyel denklemin çözümü ile önce elemanın sonlu elamanlar matrisi yazılmış daha sonra yapılan dönüşümle Ricatti taşıma matrisi elde edilmiştir. Çalışmanın sonunda sunulan yöntemin uygunluğunu literatürden alınan bir örnek üzerinde gösterilmiştir. Sunulan yöntemde matris boyutları klasik sonlu elemanlar yöntemine göre kayda değer bir şekilde azalmakta ve dolayısıyla çözüm süreside kısalmaktadır. Sunulan yöntem özellikle çok açıklıklı ve değişken kesitli nano kirişlerin çözümünde kullanılabilir.

Anahtar Kelimeler

• Nano kiriş
• Sonlu eleman
• Taşıma matrisi
• Euler kirişi

Stability Analysis of Nanobeams by Modified Finıie Element Transfer Matrix Method

Öz

In this study, the modified finite element-transfer matrix method has been adapted for the stability analysis of nanobeams. In the study, the stability equation of the nanobeam was first established with the help of the nonlocal Euler beam theory. With the solution of the differential equation, first, the finite element matrix of the element was written and then the Ricatti transfer matrix was obtained by the transformation. The suitability of the presented method is shown on an example taken from the literature. In the presented method, matrix dimensions are significantly reduced compared to the classical finite element method and therefore the solution time is shortened. The presented method can be used especially for the solution of multi-span and variable cross-section nanobeams.

Anahtar Kelimeler

• Nanobeam
• Finite element
• Transfer matrix
• Euler beam

Kaynakça

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