FONKSİYONEL DERECELENDİRİLMİŞ GÖZENEKLİ KİRİŞLERİN SONLU ELEMANLAR YÖNTEMİYLE STATİK ANALİZİ

Öz

Bu çalışmada, trigonometrik kayma deformasyonlu kiriş teorisine göre fonksiyonel derecelendirilmiş gözenekli kirişlerin (FDGB) sonlu elemanlar yöntemiyle statik analizi incelenmiştir. Sonlu eleman yöntemi için üç düğüm noktalı 12 serbestlik dereceli yüksek mertebe sonlu kiriş elemanı önerilmiştir. Denge denklemleri Lagrange prensibi kullanılarak elde edilmiştir. Kiriş bileşenlerinin hacim içerisindeki değişimleri, bir kuvvet fonksiyonu ile tanımlanmıştır. Kirişin çeşitli mesnet şartlarına, hacimsel değişim üsteline (k), gözeneklilik katsayısına (e) ve narinlik oranlarına (L/h) göre boyutsuz yer değiştirme değerleri, boyutsuz normal ve kayma gerilme değerleri elde edilmiştir. Önerilen yüksek mertebe sonlu kiriş elemanının doğruluğu araştırılmıştır. Sayısal sonuçlar literatürdeki mevcut çalışmaların sonuçları ile karşılaştırılmış ve son derece uyumlu oldukları görülmüştür.

Anahtar Kelimeler

• Fonksiyonel Derecelendirilmiş Gözenekli Kiriş
• Sonlu Eleman Yöntemi
• Statik Analiz.

STATIC ANALYSIS OF FUNCTIONALLY GRADED POROUS BEAMS WITH FINITE ELEMENT METHOD

Öz

In this study, the static analysis of functionally graded porous beams (FDGB) using the finite element method according to the trigonometric shear deformation beam theory was investigated. A high-order finite beam element with three nodes and 12 degrees of freedom is proposed for the finite element method. The governing equations are obtained using Lagrange's principle. The variation of the beam components in the volume is defined by a power-law rule. Dimensionless deflection values and dimensionless normal and shear stress values were obtained according to various boundary conditions, power-law exponent (k), porosity coefficient (e), and slenderness ratio (L/h) of the beam. The accuracy of the proposed higher-order beam element has been investigated. Numerical results are compared with the available literature, and a good agreement has been shown between the results.

Anahtar Kelimeler

• Functionally graded porous beam
• Finite element method
• Static analysis.

Kaynakça

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