Approximate analytical solution of buckling of multi-damaged column-like structures using a continuous diffused crack model by variational iteration method

Abstract

Compressive structural members can be locally damaged by overloading, corrosion, car crash and fire. In this work, a continuous diffused crack model is proposed to study the static stability of Euler–Bernoulli rectangular column-like structures under different boundary conditions. The governing differential equation is formulated by adopting a diffused crack model. The powerful variational iteration method is implemented to find the approximate analytical buckling modes and buckling loads based on the buckling response of the intact column. A novel generalized Lagrange multiplier is derived. The proposed method incorporates the effects of the crack width into consideration when deriving the buckling modes. The stability equation allows addressing the influences of multiple damages and can be applied to both concentrated and distributed cracks. The famous Rayleigh–Ritz method is utilized to verify the computed buckling loads. The proposed diffused crack model and the application with VIM is efficient and accurate for handling buckling problems of cracked columns under different boundary conditions.