Vibration and buckling of laminated beams by a multi-layer finite element model

This paper presents a multi-layer finite element for buckling and free vibration analyses of laminated beams based on a higher-order layer-wise theory. An N-layer beam element with (9<i>N</i> + 7) degrees-of-freedom is proposed for analyses. Delamination and slip between the layers are not allowed. Element matrices for the single- and multi-layer beam elements are derived by Lagrange&#39;s equations. Buckling loads and natural frequencies are calculated for different end conditions and lamina stacking. Comparisons are made to show the accuracy of proposed element.