Bifurcation buckling of unsymmetrically laminated plates

Abstract

It is well known that the presence of bending-extension coupling in unsymmetrically laminated plates gives rise to bending curvatures under the action of pure in-plane loading. In view of this behaviour, it is generally believed that bifurcation buckling could normally not take place. In this investigation, the possibility of bifurcation instability in unsymmetrically laminated plates subjected to in-plane loading is examined. Based on the variationally consistent governing equations and edge conditions, conditions are derived which, if satisfied, ensure that the plate remains flat during the pre-buckling regime and thus guarantee bifurcation buckling. It is shown that these conditions are not essential for the bifurcation instability phenomenon to occur. A few plate configurations for which bending curvatures do occur during the pre-buckling stage but nevertheless still exhibit bifurcation instability are reported. The prescribed in-plane edge conditions assumed in the literature for the study of buckling phenomena are also examined with regard to their applicability. The existence of this phenomenon in the case of rectangular composite plates is demonstrated by modelling the plate with a four-node finite element having 10 degrees of freedom per node. a number of representative problems are examined, which reveal a number of interesting features.