Numerical Study of Secondary Buckling and Mode-Coupling of Spherical Caps

Abstract

The aim ef this paper is to i 皿 vestigate the seeondary buckling behaviDuT and medecoupling of spllerical caps u 皿 der u 皿 ifermly distributed pressure by using a rotational fillite shell element 、 The past −buckli 皿 g behaviours after bifurcation pei 皿 t are analyzed exa £ tly by co 皿sideri 皿 g multi −mode coupli 皿 g ( with several higer order harmonic wave numbers ) 1 and on the way of post − buckhng path the positive definite皿 ess of incremelltal stifflless matriX of u 皿 coupled mQdes is examined step by step ． The seco 皿 dary buckli 皿 g pohlt that has zelo eigen −value of 血 cremelltal stifhe8s matlix a皿 d s ondary mode ale obtailled ， mereover ， tlle secolldary pos レ buckling path is traced ． Beside ， with the ebtailed displaceme 皿 t fields ， the tota1 potential energy ， strain eneTgy including 皿 embrane a 皿 d bendillg energy compQnents and Astatic buckhn 呂 10ads are alSo calculated ， From the above energy compone 皿 tsl the complicated posVbuckh 皿 g behaviours are ex ined， Keywords ： 3pherical c α P， secondaf y buckting ， mode − eoupting post − buckting ， Astatic buckting toad ， potentiat enerpy