Nonlinear buckling optimization technique to predict critical imperfection wavelength of combined liquid-filled steel conical tanks

Abstract

The shape of the imperfection induced by welding has an influence on the buckling resistance of thin shell structures, and many previous studies have come up with various models to estimate the critical imperfection shape. The aim of the current study is to assess the adequacy of three different approaches available in the literature, which consider that the imperfection wavelength matching the first buckling mode of a perfect tank to be the critical one. The first approach is based on buckling formulae calculated using a linear eigenvalue analysis performed on extensive experimental results of buckling of conical shells. The second approach assumes the critical wavelength, in view of the buckling mode profile detected from finite element analysis, as the distance between the inflection points of the elastic curve of the first buckling mode of a perfect tank. The third approach estimates the critical wavelength as double the distance between maximum and minimum points of the elastic curve. To determine the optimum wavelength that would lead to the minimum buckling capacity of the tank, the current study is conducted numerically by coupling a nonlinear finite element model, developed in house, and a direct search optimization technique. The results obtained from this numerical tool show good agreement with the first and the second approaches, which proves the adequacy of these two approaches in estimating the critical wavelength of the governing buckling mode, while the third approach yields a wavelength that overestimates the buckling capacity of the tank.