Static analysis of a beam with different end boundary conditions via Carrera Unified Formulation (CUF)

Abstract

In this study, lineer static analysis of a rectangular beam with compact cross-section for different end boundary conditions subjected to uniformly distributed load is analyzed within the framework of Carrera Unified Formulation (CUF), which is one of the unified beam theory. The unified formulation of cross-section displacement field is expressed by employing both Taylor and Lagrange type expansion functions defined over the cross-section. The Principle of Virtual Displacements (PVD) is used to obtain the governing differential equations and the Finite Element formulation. First, by using separately both Taylor and Lagrange types of expansion functions for a rectangular beam with compact cross-section with different end boundary conditions study of convergence and comparison with results obtained from the analytical solutions in the literature is performed in order to examine the reliability of the results obtained. Then, using the appropriate expansion function, lineer static analysis of sample problems is made within the framework of CUF and numerical results are presented with the help of tables and graphics. The computer algorithm used in the present paper is developed by MUL2 group and tested by many studies, available in the relevant literature.

Keywords

• Refined beam theory
• Carrera unified formulation (CUF)
• Finite element method

Farklı uç sınır koşullarına sahip kirişin Carrera Birleşik Formulasyon (CUF) çerçevesinde statik analizi

Öz

Bu çalışma kapsamında düzgün yayılı yük etkisinde farklı uç sınır koşullarına sahip dikdörtgen kesitli bir kirişin, birleşik kiriş teorilerinden biri olan Carrera Birleşik Formulasyon (CUF) çerçevesinde lineer statik analizi incelenmiştir. Kesit yer değiştirme alanının birleşik formulasyonu, kesit düzlemi üzerinde tanımlanmış eşdeğer Taylor ve Lagrange tipi açılım fonksiyonları ile ayrı ayrı ifade edilmiştir. Yönetici denklemler ve sonlu elemanlar formulasyonunun elde edilmesinde virtüel iş prensibi kullanılmıştır. İlk olarak, hem Taylor tipi hem de Lagrange tipi açılım fonksiyonlarının ayrı ayrı kullanılması ile farklı uç sınır koşullarına ait dikdörtgen kesitli kiriş için bir yakınsama çalışması ve elde edilen sayısal sonuçların güvenilirliğini test etmek amacı ile literatürden alınan analitik çözümler ile bir karşılaştırma çalışması yapılmıştır. Daha sonra, uygun olan açılım fonksiyonu kullanılarak CUF çerçevesinde, örnek problemlerin lineer statik analizi yapılmış, sayısal sonuçlar tablo ve grafikler ile sunulmuştur. Bu çalışmada kullanılan bilgisayar algoritması MUL2 grubu tarafından geliştirilmiş olup, literatürde mevcut olan pek çok çalışma ile test edilmiştir.

Anahtar Kelimeler

• Geliştirilmiş kiriş teorisi,
• Carrera Birleşik Formulasyon (CUF),
• sonlu elemanlar yöntemi.

Kaynakça

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