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 formulated adopting model. powerful variational iteration method implemented find approximate analytical buckling modes loads based on response intact column. A novel generalized Lagrange multiplier derived. incorporates effects width into consideration when deriving modes. allows addressing influences multiple damages applied both concentrated distributed cracks. famous Rayleigh–Ritz utilized verify computed loads. application with VIM efficient accurate for handling problems cracked columns