Nonlinear Behavior of Initially Imperfect Beams Subjected to Sinusoidal Load

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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