Semi-analytical solutions for buckling and free vibration of composite anisogrid lattice cylindrical panels

In this study, highly accurate approximate closed-form solution is presented for buckling and free vibration of clamped composite anisogrid lattice cylindrical panels. Using theory of orthotropic cylindrical shallow shells based on the continuous model of lattice structures, the system of governing partial differential equations (PDEs) of motion is derived. The resulted PDEs are converted to a couple of systems of ordinary differential equations (ODEs) by employing of the Extended Kantorovich Method (EKM). Semi-analytical solutions are presented for both buckling and free vibration of anisogrid lattice panels via iterative application of infinite power series solution for the sets of ODEs. Efficiency of the presented method in terms of accuracy, stability, fast convergence and low computational cost for prediction of the critical buckling loads and natural frequencies are examined. Accuracy of the predictions for various cases are studied by comparing with available numerical and analytical results. Moreover, it is shown that the method can be used to obtain accurate solutions for buckling and free vibration of composite lattice rectangular plates by assuming large values for the radius together with small values for the angle of the panel. This implies stability of the method for large or small values while providing accurate predictions.