Dynamic Stability Behavior Prediction of Initially Cracked Doubly Curved Laminated Composite Shell Structures-A Higher-Order FE Approach

The current investigation explores the presence of cracks and their influence on the dynamic instability behavior of laminated composite curved (single/doubly) shell structures when subjected to in-plane loading. The numerical model is developed in a higher-order strain–displacement relation utilizing a nine-noded iso-parametric element possessing nine degrees of freedom per node. The mathematical model incorporates the crack type of damage to investigate the parametric excitation response. The final form of the equation of motion for a damaged layered structure is derived using Lagrangian equations under the parametric excitation. The instability zone and the eigenfrequencies are obtained by solving the Mathieu-type ordinary differential equations with a first-order approximation obtained through a Fourier series expansion. First, the mesh independence behavior of the predicted numerical solution is verified and extended to check the model accuracy by comparing the results with published data. The frequency responses obtained using the derived computational are close to the reference data and the deviations are close to a value within the accepted range ([Formula: see text]10.31%). Additionally, a few examples are solved to evaluate the influence of varieties of input design parameters on the final responses while the structure is under parametric excitation.