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

Year 2018, Volume: 11 Issue: 2, 341 - 346, 31.08.2018

Yeşim Saraç

https://doi.org/10.18185/erzifbed.396146

Cited By: 1

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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