Nonlinear Behavior of Initially Imperfect Beams Subjected to Sinusoidal Load

Year 2020, Volume: 9 Issue: 1, 466 - 477, 13.03.2020

Ayfer Tekin Atacan , Receb Faruk Yükseler

https://doi.org/10.17798/bitlisfen.592938

Cited By: 5

Abstract

In
the present study, the buckling and post-buckling behaviors of beams having
small sinusoidal imperfection with pinned ends subjected to sinusoidal loading
are examined by using Euler-Bernoulli beam theory. The governing differential
equations of the geometrically nonlinear problem consisting of the equilibrium
equations, kinematical equations and the constitutive equations are converted
into algebraic equations via the finite differences and solved numerically by
using the Newton-Raphson method. The values of buckling loads and buckling
deflections are determined by drawing load-deflection curves. The effect of the
initial imperfection on the buckling values is investigated. Unlike previous
studies on the subject, the diagrams of the deformed shapes of the initially
sinusoidal curved beams as well as the diagrams of the internal forces at
various stages of the deformation including the prebuckling, buckling and
postbuckling states are presented. 

Keywords

Snap-through instability, initially imperfect beam, nonlinear equation, finite differences method, buckling

Nonlinear Behavior of Beams Having Initially Small Imperfection Subjected to Sinusoidal Load

Abstract

Bu
çalışmada, sinüzoidal yüke maruz, uçları sabit mesnetli sinüzoidal sığ
kemerlerin burkulma ve burkulma sonrası davranışları Euler-Bernoulli kiriş
teorisi kullanılarak incelenmiştir. Denge denklemleri, kinematik denklemler ve
bünye denklemlerini içeren, geometrik olarak doğrusal olmayan problemin
yönetici diferansiyel denklemleri, sonlu farklar yöntemi ile cebirsel
denklemlere dönüştürülmüş ve Newton-Raphson yöntemi kullanılarak sayısal olarak
çözülmüştür. Burkulma yüklerin ve burkulma çökmelerin değerleri, yük-çökme
eğrileri çizilerek belirlenmiştir. İlkel kusurun burkulma değerleri üzerindeki
etkisi incelenmiştir. Konuyla ilgili daha önceki çalışmalardan farklı olarak;
başlangıçta sinüzoidal kavisli olan kirişlerin, şekil değiştirmenin çeşitli
aşamalarındaki elastik eğri diyagramlarının yanı sıra; burkulma öncesindeki,
burkulma sırasındaki ve burkulma sonrasındaki durumlarına karşı gelen kesit
tesirlerinin diyagramları sunulmuştur.

Keywords

Vurgu tipi stabilite, ilkel kusurlu kiriş, doğrusal olmayan denklem, sonlu farklar yöntemi, burkulma

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