Buckling analysis of filament wound composite cylindrical shell for considering the filament undulation and crossover

The buckling equations of filament wound composite cylindrical shell are established. The coefficients $K_{ij}$ and $L_{ij}$ of the buckling equations are determined by solving the equations. The geometric analysis and the effective stiffness calculation for the fiber crossover and undulation region are respectively accomplished. Using the effective stiffness of the undulation region, the specific formulas of the coefficients ${K^{\prime}}_{ij}$ and ${L^{\prime}}_{ij}$ of the buckling equations are determined. Numerical examples of the buckling critical loads have been performed for the different winding angles and stacking sequences cylindrical shell designs. It can be concluded that the fiber undulation results in the less effect on the buckling critical loads $P_{cr}$. $P_{cr}$ increases with the thickness-radius ratio. The effect on $P_{cr}$ due to the fiber undulation is more obvious with the thickness-radius ratio. $P_{cr}$ decreases with the length-radius ratio. The effect on $P_{cr}$ due to the fiber undulation can be neglected when the ratio is large.