Bubble Complex Finite Strip Method in the Stability and Vibration Analysis of Orthotropic Laminated Composite Plates

Abstract

In this study, a bubble complex finite strip method (BCFSM) with the higher-order zigzag theory is formulated for mechanical buckling and free vibration analysis of laminated composite plates, including cross-ply and angle-ply laminates. Few studies have been done to obtain the analytical solutions for clamped and free boundary conditions in the longitudinal and transverse edges. Therefore, this study, for the first time, investigates the effects of various boundary conditions on the stability and vibration results of laminated composite plates subjected to axial or pure shear forces with the use of higher-order zigzag theory and BCFSM. Following this, both the interlaminar continuity conditions of transverse shear stresses and the shear-free surface conditions are satisfied by applying a cubic displacement and a zigzag linear varying displacement with the same number of unknowns as the first-order shear deformation theories. Moreover, the effects of width-to-thickness ratio, fiber orientation, number of modes, different dimensional ratios of the plate, and finally, the number of layers are investigated through numerical examples. The bubble shape functions are exploited in the transverse direction to improve the convergence of the method. Finally, the shearing and axial interaction diagrams of composite laminated plates are presented for various types of boundary conditions.