On Approximate Solution of the Euler-Bernoulli Beam Equation via Galerkin Method

Abstract

In this paper, numerical solution of a boundary value problem for a fourth-order ordinary differential equation, known as the Euler-Bernoulli beam equation, is presented. The related equation is used extensively in engineering areas such as huge buildings, long bridges across big rivers, planes and cars. The approximate solution of the problem considered is obtained by using the Galerkin method with basis functions that satisfy the boundary conditions given. The accuracy of the proposed method is given through two numerical examples with the help of Maple^®program.

Keywords

• Euler-Bernoulli beam equation,Galerkin method,Ordinary differential equations

On Approximate Solution of the Euler-Bernoulli Beam Equation via Galerkin Method

Abstract

Bu çalışmada Euler-Bernoulli kiriş denklemi olarak bilinen dördüncü mertebeden bir adi diferansiyel denklem için sınır değer probleminin sayısal çözümü sunulmuştur. İlgili denklem büyük binalar, büyük nehirler arasındaki uzun köprüler, uçaklar ve arabalar gibi mühendislik alanlarında yaygın olarak kullanılmaktadır. Ele alınan problemin yaklaşık çözümü, sınır koşullarını sağlayan temel fonksiyonlar ile Galerkin metodu kullanılarak elde edilmektedir. Önerilen yöntemin doğruluğu Maple^® programı yardımıyla iki nümerik örnek üzerinden gösterilmektedir.

Keywords

• Euler-Bernoulli kiriş denklemi,Galerkin metodu,Adi diferansiyel denklemler

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