Asymptotic Numerical Method for dynamic buckling of shell structures with follower pressure

Abstract

Asymptotic Numerical Method (ANM) is applied to non-linear dynamics of thin-shells subjected to conservative and non-conservative loads such as follower pressure. ANM is decomposed into several stages: the finite element discretization of the non-linear equations of motion of the shell dynamics, a homotopy transformation of the semi-discrete non-linear equations, a perturbation technique to expand the quantities into Taylor series according to the homotopy parameter and the time integration scheme to solve the series of linear problems resulting from the perturbation technique. ANM is applied here with the 7-parameter shell elements thanks to the Enhanced Assumed Strain (EAS) concept and implicit Newmark integration. In the case of non-conservative force, follower pressure also requires to be decomposed in either Taylor series or rational Padé approximants. The academic case of the cylindrical roof with dynamic snap-through phenomenon is investigated for the purpose of comparing ANM strategies and the classical Newton–Raphson (NR) method. Two engineering cases including an I-shaped thin-walled beam and a closed thin-shell cylinder under dynamic external follower pressure are also investigated. ANM turns out to be accurate, robust and efficient in terms of computation time, providing an alternative method to the well-established Newton–Raphson method.