Nonlinear Behavior of Beams Having Initially Small Imperfection Subjected to Sinusoidal Load
Abstract
In the present study, the buckling and postbuckling behaviors of beams having initially 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. It is seen that as the value of the small initial imperfection is increased, the
buckling force is increased and buckling deflection is decreased. Unlike previous studies on the subject, the
diagrams of the deformed shapes of the beam having initially small imperfection as well as the diagrams of the
internal forces at various stages of the deformation including the prebuckling, buckling and postbuckling states
are presented for various values of the initial imperfection.
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